People can make mistakes when they test a hypothesis with statistical analysis. Specifically, they can make either Type I or Type II errors.

As you analyze your own data and test hypotheses, understanding the difference between Type I and Type II errors is extremely important, because there's a risk of making each type of error in every analysis, and the amount of risk is in your control.   

So if you're testing a hypothesis about a safety or quality issue that could affect people's lives, or a project that might save your business millions of dollars, which type of error has more serious or costly consequences? Is there one type of error that's more important to control than another? 

Before we attempt to answer that question, let's review what these errors are. 

These errors relate to the statistical concepts of risk, significance, and power.

Statisticians call the risk, or probability, of making a Type I error "alpha," aka "significance level." In other words, it's your willingness to risk rejecting the null when it's true. Alpha is commonly set at 0.05, which is a 5 percent chance of rejecting the null when it is true. The lower the alpha, the less your risk of rejecting the null incorrectly. In life-or-death situations, for example, an alpha of 0.01 reduces the chance of a Type I error to just 1 percent.
 
A Type 2 error relates to the concept of "power," and the probability of making this error is referred to as "beta." We can reduce our risk of making a Type II error by making sure our test has enough power—which depends on whether the sample size is sufficiently large to detect a difference when it exists.  

Let's return to the question of which error, Type 1 or Type 2, is worse. The go-to example to help people think about this is a defendant accused of a crime that demands an extremely harsh sentence.

The null hypothesis is that the defendant is innocent. Of course you wouldn't want to let a guilty person off the hook, but most people would say that sentencing an innocent person to such punishment is a worse consequence.

Hence, many textbooks and instructors will say that the Type 1 (false positive) is worse than a Type 2 (false negative) error. The rationale boils down to the idea that if you stick to the status quo or default assumption, at least you're not making things worse.   

And in many cases, that's true. But like so much in statistics, in application it's not really so black or white. The analogy of the defendant is great for teaching the concept, but when we try to make it a rule of thumb for which type of error is worse in practice, it falls apart.

I'm sorry to disappoint you, but as with so many things in life and statistics, the honest answer to this question has to be, "It depends."

In one instance, the Type I error may have consequences that are less acceptable than those from a Type II error. In another, the Type II error could be less costly than a Type I error. And sometimes, as Dan Smith pointed out in Significancea few years back with respect to Six Sigma and quality improvement, "neither" is the only answer to which error is worse: 

Most Six Sigma students are going to use the skills they learn in the context of business. In business, whether we cost a company $3 million by suggesting an alternative process when there is nothing wrong with the current process or we fail to realize $3 million in gains when we should switch to a new process but fail to do so, the end result is the same. The company failed to capture $3 million in additional revenue. 

Since there's not a clear rule of thumb about whether Type 1 or Type 2 errors are worse, our best option when using data to test a hypothesis is to look very carefully at the fallout that might follow both kinds of errors. Several experts suggest using a table like the one below to detail the consequences for a Type 1 and a Type 2 error in your particular analysis. 

Whatever your analysis involves, understanding the difference between Type 1 and Type 2 errors, and considering and mitigating their respective risks as appropriate, is always wise. For each type of error, make sure you've answered this question: "What's the worst that could happen?"  

To explore this topic further, check out this article on using power and sample size calculations to balance your risk of a type 2 error and testing costs, or this blog post about considering the appropriate alpha for your particular test. 

Isn't it great when you get a set of data and it's perfectly organized and ready for you to analyze? I love it when the people who collect the data take special care to make sure to format it consistently, arrange it correctly, and eliminate the junk, clutter, and useless information I don't need.  

You've never received a data set in such perfect condition, you say?

Yeah, me neither. But I can dream, right? 

The truth is, when other people give me data, it's typically not ready to analyze. It's frequently messy, disorganized, and inconsistent. I get big headaches if I try to analyze it without doing a little clean-up work first. 

I've talked with many people who've shared similar experiences, so I'm writing a series of posts on how to get your data in usable condition. In this first post, I'll talk about some basic methods you can use to make your data easier to work with. 

I'm not complaining about the people who give me data. In most cases, they aren't statisticians and they have many higher priorities than giving me data in exactly the form I want.  

The end result is that getting data is a little bit like getting food: it's not always going to be ready to eat when you pick it up. You don't eat raw chicken, and usually you can't analyze raw data, either.  In both cases, you need to prepare it first or the results aren't going to be pretty.

Here are a couple of very basic things to look for when you get a messy data set, and how to handle them.  

Frequently I get a data set that includes a lot of information that I don't need for my analysis. I also get data sets that combine or group information in ways that make analyzing it more difficult. 

For example, let's say I needed to analyze data about different types of events that take place at a local theater. Here's my raw data sheet:  

With each type of event jammed into a single worksheet, it's a challenge to analyze just one event category. What would work better?  A separate worksheet for each type of occasion. In Minitab Statistical Software, I can go to Data > Split Worksheet... and choose the Event column: 

And Minitab will create new worksheets that include only the data for each type of event. 

Minitab also lets you merge worksheets to combine items provided in separate data files. 

Let's say the data set you've been given contains a lot of columns that you don't need: irrelevant factors, redundant information, and the like. Those items just clutter up your data set, and getting rid of them will make it easier to identify and access the columns of data you actually need. You can delete rows and columns you don't need, or use the Data > Erase Variables tool to make your worksheet more manageable. 

What if you don't want to actually delete any data, but you only want to see the columns you intend to use? For instance, in the data below, I don't need the Date, Manager, or Duration columns now, but I may have use for them in the future: 

I can select and right-click those columns, then use Column > Hide Selected Columns to make them disappear. 

Voila! They're gone from my sight. Note how the displayed columns jump from C1 to C5, indicating that some columns are hidden:  

It's just as easy to bring those columns back in the limelight. When I want them to reappear, I select the C1 and C5 columns, right-click, and choose "Unhide Selected Columns." 

Data may arrive in a disorganized and messy state, but you don't need to keep it that way. Getting rid of extraneous information and choosing the elements that are visible can make your work much easier. But that's just the tip of the iceberg. In my next post, I'll cover some more ways to make unruly data behave.  

In my last post, I wrote about making a cluttered data set easier to work with by removing unneeded columns entirely, and by displaying just those columns you want to work with now. But too much unneeded data isn't always the problem.

What can you do when someone gives you data that isn't organized the way you need it to be?  

That happens for a variety of reasons, but most often it's because the simplest way for people to collect data is with a format that might make it difficult to assess in a worksheet. Most statistical software will accept a wide range of data layouts, but just because a layout is readable doesn't mean it will be easy to analyze.

You may not be in control of how your data were collected, but you can use tools like sorting, stacking, and ordering to put your data into a format that makes sense and is easy for you to use. 

Depending on how its arranged, the same data can be easier to work with, simpler to understand, and can even yield deeper and more sophisticated insights. I can't tell you the best way to organize your specific data set, because that will depend on the types of analysis you want to perform, and the nature of the data you're working with. However, I can show you some easy ways to rearrange your data into the form that you select. 

The data below show concession sales for different types of events held at a local theater. 

If we wanted to perform an analysis that requires each type of event to be in its own column, we can choose Data > Unstack Columns... and complete the dialog box as shown:

Minitab creates a new worksheet that contains a separate column of Concessions sales data for each type of event:

A similar tool will help you put data from separate columns into a single column for the type of analysis required. The data below show sales figures for four employees: 

Select Data > Stack > Columns... and select the columns you wish to combine. Checking the "Use variable names in subscript column" will create a second column that identifies the person who made each sale. 

When you press OK, the sales data are stacked into a single column of measurements and ready for analysis, with Employee available as a grouping variable: 

The following data appear in the worksheet in the order in which individual stores in a chain sent them into the central accounting system.

When the data appear in this uncontrolled order, finding an observation for any particular item, or from any specific store, would entail reviewing the entire list. We can fix that problem by selecting Data > Sort... and reordering the data by either store or item. 

What if you need to analyze information about the same items, but that were recorded on separate worksheets?  For instance, if one group was gathering historic data about all of a corporation's manufacturing operations, while another was working on strategic planning, and your analysis required data from each? 

You can use Data > Merge Worksheets to bring the data together into a single worksheet, using the Division column to match the observations:

You can also choose whether or not multiple, missing, or unmatched observations will be included in the merged worksheet.  

Making changes to the layout of your worksheet does entail a small investment of time, but it can bring big returns in making analyses quicker and easier to perform. The next time you're confronted with raw data that isn't ready to play nice, try some of these approaches to get it under control. 

In my next post, I'll share some tips and tricks that can help you get more information out of your data.

You've collected a bunch of data. It wasn't easy, but you did it. Yep, there it is, right there...just look at all those numbers, right there in neat columns and rows. Congratulations.

I hate to ask...but what are you going to do with your data?

If you're not sure precisely what to do with the data you've got, graphing it is a great way to get some valuable insight and direction. And a good graph to start with is an individual value plot, which you can create in Minitab Statistical Software by going to Graph > Individual Value Plot. 

There are other graphs you could start with, so what makes the individual value plot such a strong contender? That fact it lets you view important data features, find miscoded values, and identify unusual cases. 

In other words, taking a look at an individual value plot can help you to choose the appropriate direction for your analysis and to avoid wasted time and frustration.

IDENTIFY INDIVIDUAL VALUES

Many people like to look at their data in boxplots, and you can learn many valuable things from those graphs. Unlike boxplots, individual value plots display all data values and may be more informative than boxplots for small amounts of data.

The boxplots for the two variables look identical.

The individual value plot of the same data shows that there are many more values for Batch 1 than for Batch 2.

You can use individual value plots to identify possible outliers and other values of interest. Hover the cursor over any point to see its exact value and position in the worksheet.

Individual value plots can also clearly illustrate characteristics of the data distribution. In this graph, most values are in a cluster between 4 and 10. Minitab can jitter (randomly nudge) the points horizontally, so that one value doesn’t obscure another. You can edit the plot to turn on or turn off jitter.

MAKE GROUP COMPARISONS

Because individual value plots display all values for all groups at the same time, they are especially helpful when you compare variables, groups, and even subgroups.

This plot shows the diameter of pipes from two lines over four shifts. You can see that the diameters of pipes produced by Line 1 seem to increase in variability across shifts, while the diameters of pipes from Line 2 appear more stable.

SUPPORT OTHER ANALYSES

An individual value plot is one of the built-in graphs that are available with many Minitab statistical analyses. You can easily display an individual value plot while you perform these analyses. In the analysis dialog box, simply clickGraphs and check Individual Value Plot.

Some built-in individual value plots include specific analysis information. For example, the plot that accompanies a 1-sample t-test displays the 95% confidence interval for the mean and the reference value for the null hypothesis mean. These plots give you a graphical representation of the analysis results.

This plot accompanies a 1-sample t-test. All of the data values are between 4.5 and 5.75. The reference mean lies outside of the confidence interval, which suggests that the population mean differs from the hypothesized value.

Suppose that salad dressing is bottled by four different machines and that you want to make sure that the bottles are filled correctly to 16 ounces. You weigh 30 samples from each machine. You plan to run an ANOVA to see if the means of the samples from each machine are equal. But, first, you display an individual value plot of the samples to get a better understanding of the data.

Choose Graph > Individual Value Plot.
Under One Y, choose With Groups.
Click OK.
In Graph variables, enter Weight.
In Categorical variables for grouping, enter Machine.
Click Data View.
Under Data Display, check Interval bar and Mean symbol.
Click OK in each dialog box.

The mean fill weight is about 16 ounces for Fill2, Fill3, and Fill4, with no suspicious data points. For Fill1, however, the mean appears higher, with a possible outlier at the lower end.

Before you continue with the analysis, you may want to investigate problems with the Fill1 machine.

Use Minitab’s individual value plot to get a quick overview of your data before you begin your analysis—especially if you have a small data set or if you want to compare groups. The insight that you gain can help you to decide what to do next and may save you time exploring other paths.

For more information on individual value plots and other Minitab graphs, see Minitab Help.

Everyone who analyzes data regularly has the experience of getting a worksheet that just isn't ready to use. Previously I wrote about tools you can use to clean up and eliminate clutter in your data and reorganize your data. 

In this post, I'm going to highlight tools that help you get the most out of messy data by altering its characteristics.

Many problems with data don't become obvious until you begin to analyze it. A shortcut or abbreviation that seemed to make sense while the data was being collected, for instance, might turn out to be a time-waster in the end. What if abbreviated values in the data set only make sense to the person who collected it? Or a column of numeric data accidentally gets coded as text?  You can solve those problems quickly with statistical software packages.

Here's an instance where a data entry error resulted in a column of numbers being incorrectly classified as text data. This will severely limit the types of analysis that can be performed using the data.

To fix this, select Data > Change Data Type and use the dialog box to choose the column you want to change.

One click later, and the errant text data has been converted to the desired numeric format:

When this company collected data on the performance of its different functions across all its locations, it used numbers to represent both locations and units. 

That may have been a convenient way to record the data, but unless you've memorized what each set of numbers stands for, interpreting the results of your analysis will be a confusing chore. You can make the results easy to understand and communicating by coding the data. 

In this case, we select Data > Code > Numeric to Text...

And we complete the dialog box as follows, telling the software to replace the numbers with more meaningful information, like the town each facility is located in.  

Now you have data columns that can be understood by anyone. When you create graphs and figures, they will be clearly labeled.  

Dates and times can be very important in looking at performance data and other indicators that might have a cyclical or time-sensitive effect.  But the way the date is recorded in your data sheet might not be exactly what you need. 

For example, if you wanted to see if the day of the week had an influence on the activities in certain divisions of your company, a list of dates in the MM/DD/YYYY format won't be very helpful.   

You can use Data > Date/Time > Extract to Text... to identify the day of the week for each date.

Now you have a column that lists the day of the week, and you can easily use it in your analysis. 

These tools are commonly seen as a way to correct data-entry errors, but as we've seen, you can use them to make your data sets more meaningful and easier to work with.

There are many other tools available in Minitab's Data menu, including an array of options for arranging, combining, dividing, fine-tuning, rounding, and otherwise massaging your data to make it easier to use. Next time you've got a column of data that isn't quite what you need, try using the Data menu to get it into shape.

Earlier, I wrote about the different types of data statisticians typically encounter. In this post, we're going to look at why, when given a choice in the matter, we prefer to analyze continuous data rather than categorical/attribute or discrete data. 

As a reminder, when we assign something to a group or give it a name, we have created attribute or categorical data.  If we count something, like defects, we have gathered discrete data. And if we can measure something to a (theoretically) infinite degree, we have continuous data.

Or, to put in bullet points: 

• Categorical = naming or grouping data
• Discrete = count data
• Continuous = measurement data

A statistical software package like Minitab is extremely powerful and can tell us many valuable things—as long as we're able to feed it good numbers. Without numbers, we have no analyses nor graphs. Even categorical or attribute data needs to be converted into numeric form by counting before we can analyze it. 

At this point, you may be thinking, "Wait a minute—we can't really measure anything infinitely,so isn't measurement data actually discrete, too?" That's a fair question. 

If you're a strict literalist, the answer is "yes"—when we measure a property that's continuous, like height or distance, we are de facto making a discrete assessment. When we collect a lot of those discrete measurements, it's the amount of detail they contain that will dictate whether we can treat the collection as discrete or continuous.

I like to think of it as a question of scale. Say I want to measure the weight of 16-ounce cereal boxes coming off a production line, and I want to be sure that the weight of each box is at least 16 ounces, but no more than 1/2 ounce over that.

With a scale calibrated to whole pounds, all I can do is put every box into one of three categories: less than a pound, 1 pound, or more than a pound. 

With a scale that can distinguish ounces, I will be able to measure with a bit more accuracy just how close to a pound the individual boxes are. I'm getting nearer to continuous data, but there are still only 16 degrees between each pound. 

But if I measure with a scale capable of distinguishing 1/1000th of an ounce, I will have quite a wide scale—a continuum—of potential values between pounds. The individual boxes could have any value between 0.000 and 1.999 pounds. The scale of these measurements is fine enough to be analyzed with powerful statistical tools made for continuous data.   

Not all data points are equally valuable, and you can glean a lot more insight from 100 points of continuous data than you can from 100 points of attribute or count data. How does this finer degree of detail affect what we can learn from a set of data? It's easy to see. 

Let's start with the simplest kind of data, attribute data that rates a the weight of a cereal box as good or bad. For 100 boxes of cereal, any that are under 1 pound are classified as bad, so each box can have one of only two values.

We can create a bar chart or a pie chart to visualize this data, and that's about it:

If we bump up the precision of our scale to differentiate between boxes that are over and under 1 pound, we can put each box of cereal into one of three categories. Here's what that looks like in a pie chart:

This gives us a little bit more insight—we now see that we are overfilling more boxes than we are underfilling—but there is still a very limited amount of information we can extract from the data.  

If we measure each box to the nearest ounce, we open the door to using methods for continuous data, and get a still better picture of what's going on. We can see that, on average, the boxes weigh 1 pound. But there's high variability, with a standard deviation of 0.9. There's also a wide range in our data, with observed values from 12 to 20 ounces: 

If I measure the boxes with a scale capable of differentiating thousandths of an ounce, more options for analysis open up. For example, now that the data are fine enough to distinguish half-ounces (and then some), I can perform a capability analysis to see if my process is even capable of consistently delivering boxes that fall between 16 and 16.5 ounces. I'll use the Assistant in Minitab to do it, selecting Assistant > Capability Analysis: 

The analysis has revealed that my process isn't capable of meeting specifications. Looks like I have some work to do...but the Assistant also gives me an I-MR control chart, which reveals where and when my process is going out of spec, so I can start looking for root causes.

If I were only looking at attribute data, I might think my process was just fine. Continuous data has allowed me to see that I can make the process better, and given me a rough idea where to start. By making changes and collecting additional continuous data, I'll be able to conduct hypothesis tests, analyze sources of variances, and more.  

Does this mean discrete data is no good at all?  Of course not—we are concerned with many things that can't be measured effectively except through discrete data, such as opinions and demographics. But when you can get it, continuous data is the better option. The table below lays out the reasons why. 

Continuous Data

Discrete Data

I hope this very basic overview has effectively illustrated why you should opt for continuous data over discrete data whenever you can get it. 

Do your executives see how your quality initiatives affect the bottom line? Perhaps they would more often if they had accessible insights on the performance, and ultimately the overall impact, of improvement projects. 

For example, 60% of the organizations surveyed by the American Society for Quality in their 2016 Global State of Quality study say they don’t know or don’t measure the financial impact of quality.

Evidence shows company leaders just don't have good access to the kind of information they need about their quality improvement initiatives.

The 2013 ASQ Global State of Quality study indicated that more than half of the executives are getting updates about quality only once a quarter, or even less. You can bet they make decisions that impact quality much more frequently than that.

Even for organizations that are working hard to assess the impact of quality, communicating that impact effectively to C-level executives is a huge challenge. The 2013 report revealed that the higher people rise in an organization's leadership, the less often they receive reports about quality metrics. Only 2% of senior executives get daily quality reports, compared to 33% of front-line staff members.  

A quarter of the senior executives reported getting quality metrics only on an annual basis. That's a huge problem, and it resonates across all industries. The Juran Institute, which specializes in training, certification, and consulting on quality management globally, also concluded that a lack of management support is the No. 1 reason quality improvement initiatives fail.

Quality practitioners are a dedicated, hard-working lot, and their task is challenging and frequently thankless. Their successes should be understood and recognized. But their efforts don't appear to be reaching C-level executive offices as often as they deserve. 

Why do so many leaders get so few reports about their quality programs?

In fairness to everyone involved, from the practitioner to the executive, piecing together the full picture of quality in a company is daunting. Practitioners tell us that even in organizations with robust, mature quality programs, assessing the cumulative impact of an initiative can be difficult, and sometimes impossible. The reasons include:

Individual teams are very good at capturing and reporting their results, but a large company may have thousands of simultaneous quality projects. Just gathering the critical information from all of those projects and putting it into a form leaders can use is a monumental task. 

Teams typically use an array of different applications to create charters, process maps, value stream maps, and other documents. So the project record becomes a mix of files from many different applications. Adding to the confusion, the latest versions of some documents may reside on several different computers, project leaders often need to track multiple versions of a document to keep the official project record current. 

Results and metrics aren’t always measured the same way from one team's project to another. If one team measures apples and the next team measures oranges, their results can't be evaluated or aggregated as if they were equivalent. 

Many organizations have tried quality tracking methods ranging from homegrown project databases to full-featured project portfolio management (PPM) systems. But homegrown systems often become a burden to maintain, while off-the-shelf solutions created for IT or other business functions don’t effectively support projects involving continuous quality improvement methods like Lean and Six Sigma. 

Reporting on projects can be a burden. There are only so many hours in the day, and busy team members need to prioritize. Copying and pasting information from project documents into an external system seems like non-value-added time, so it's easy to see why putting the latest information into the system gets low priority—if it happens at all.

Given the complexity of the task, and the systemic and human factors involved in improving quality, it's not hard to see why many organizations struggle with knowing how well their initiatives are doing. 

But for quality professionals and leaders, the challenge is to make sure that reporting on results becomes a critical step in every individual project, and that all projects are using consistent metrics. Teams that can do that will find their results getting more attention and more credit for how they affect the bottom line. 

This finding in the ASQ report caught dramatically underscores problems we at Minitab have been focusing on recently—in fact, our Companion by Minitab software tackles many of these factors head-on. 

Companion takes a desktop app that provides a complete set of integrated tools for completing projects, and combines it with a cloud-based project storage system and web-based dashboard. For teams, the desktop app makes it easier to complete projects—and since project data is centrally stored and rolls up to the dashboard automatically, reporting on projects is literally effortless.

For executives, managers, and stakeholders, Companion delivers unprecedented and unparalleled insight into the progress, performance, and bottom-line impact of the organization’s entire quality initiative, or any individual piece of it. 

Regardless of the tools they use, this issue—how to ensure the results of quality improvement initiatives are understood throughout an organization—is one that every practitioner is likely to grapple with in their career.  

How will you make sure the results of your work reach your organization's decision-makers?   

If you have a process that isn’t meeting specifications, using the Monte Carlo simulation and optimization tool in Companion by Minitab can help. Here’s how you, as a chemical technician for a paper products company, could use Companion to optimize a chemical process and ensure it consistently delivers a paper product that meets brightness standards.

The brightness of Perfect Papyrus Company’s new copier paper needs to be at least 84 on the TAPPI brightness scale. The important process inputs are the bleach concentration of the solution used to treat the pulp, and the processing temperature. The relationship is explained by this equation:

Brightness = 70.37 + 44.4 Bleach + 0.04767 Temp – 64.3 Bleach*Bleach

Bleach concentration follows a normal distribution with a mean of 0.25 and a standard deviation of 0.0095 percent. Temperature also follows a normal distribution, with a mean of 145 and a standard deviation of 15.3 degrees C.

To assess the process capability, you can enter the parameter information, transfer function, and specification limit into Companion's straightforward interface, and instantly run 50,000 simulations.

The process performance measurement (Cpk) is 0.162, far short of the minimum standard of 1.33. Companion also indicates that under current conditions, you can expect the paper’s brightness to fall below standards about 31.5% of the time.

Quality Companion's smart workflow guides you to the next step for improving your process: optimizing your inputs.

You set the goal—in this case, maximizing the brightness of the paper—and enter the high and low values for your inputs.

After finding the optimal input settings in the ranges you specified, Companion presents the simulated results for the recommended process changes.

The results indicate that if the bleach amount was set to approximately 0.3 percent and the temperature to 160 degrees, the % outside of specification would be reduced to about 2% with a Cpk of 0.687. Much better, but not good enough.

To further improve the paper brightness, Companion’s smart workflow suggests that you next perform a sensitivity analysis.

Companion’s unique graphic presentation of the sensitivity analysis gives you more insight into how the variation of your inputs influences the percentage of your output that doesn’t meet specifications.

The blue line representing temperature indicates that variation in this factor has a greater impact on your process than variation in bleach concentration, so you run another simulation to visualize the brightness using the 50% variation reduction in temperature.

The simulation shows that reducing the variability will result in 0.000 percent of the paper falling out of spec, with a Cpk of 1.34. Thanks to you, the outlook for the Perfect Papyrus Company’s new copier paper is looking very bright.

Figuring out how to improve a process is easier when you have the right tool to do it. With Monte Carlo simulation to assess process capability, Parameter Optimization to identify optimal settings, and Sensitivity Analysis to pinpoint exactly where to reduce variation, Companion can help you get there.

To try the Monte Carlo simulation tool, as well as Companion's more than 100 other tools for executing and reporting quality projects, learn more and get the free 30-day trial version for you and your team at companionbyminitab,com.

"Data! Data! Data! I can't make bricks without clay."
 — Sherlock Holmes, in Arthur Conan Doyle's The Adventure of the Copper Beeches

Whether you're the world's greatest detective trying to crack a case or a person trying to solve a problem at work, you're going to need information. Facts. Data, as Sherlock Holmes says. 

But not all data is created equal, especially if you plan to analyze as part of a quality improvement project.

If you're using Minitab Statistical Software, you can access the Assistant to guide you through your analysis step-by-step, and help identify the type of data you have.

But it's still important to have at least a basic understanding of the different types of data, and the kinds of questions you can use them to answer. 

In this post, I'll provide a basic overview of the types of data you're likely to encounter, and we'll use a box of my favorite candy—Jujubes—to illustrate how we can gather these different kinds of data, and what types of analysis we might use it for. 

At the highest level, two kinds of data exist: quantitative and qualitative.

Quantitativedata deals with numbers and things you can measure objectively: dimensions such as height, width, and length. Temperature and humidity. Prices. Area and volume.

Qualitative data deals with characteristics and descriptors that can't be easily measured, but can be observed subjectively—such as smells, tastes, textures, attractiveness, and color. 

Broadly speaking, when you measure something and give it a number value, you create quantitative data. When you classify or judge something, you create qualitative data. So far, so good. But this is just the highest level of data: there are also different types of quantitative and qualitative data.

There are two types of quantitative data, which is also referred to as numeric data: continuous and discrete. As a general rule, counts are discrete and measurements are continuous.

Discrete data is a count that can't be made more precise. Typically it involves integers. For instance, the number of children (or adults, or pets) in your family is discrete data, because you are counting whole, indivisible entities: you can't have 2.5 kids, or 1.3 pets.

Continuousdata, on the other hand, could be divided and reduced to finer and finer levels. For example, you can measure the height of your kids at progressively more precise scales—meters, centimeters, millimeters, and beyond—so height is continuous data.

If I tally the number of individual Jujubes in a box, that number is a piece of discrete data.

If I use a scale to measure the weight of each Jujube, or the weight of the entire box, that's continuous data. 

Continuous data can be used in many different kinds of hypothesis tests. For example, to assess the accuracy of the weight printed on the Jujubes box, we could measure 30 boxes and perform a 1-sample t-test. 

Some analyses use continuous and discrete quantitative data at the same time. For instance, we could perform a regression analysis to see if the weight of Jujube boxes (continuous data) is correlated with the number of Jujubes inside (discrete data). 

When you classify or categorize something, you create Qualitative or attribute data. There are three main kinds of qualitative data.

Binary data place things in one of two mutually exclusive categories: right/wrong, true/false, or accept/reject. 

Occasionally, I'll get a box of Jujubes that contains a couple of individual pieces that are either too hard or too dry. If I went through the box and classified each piece as "Good" or "Bad," that would be binary data. I could use this kind of data to develop a statistical model to predict how frequently I can expect to get a bad Jujube.

When collecting unordered or nominal data, we assign individual items to named categories that do not have an implicit or natural value or rank. If I went through a box of Jujubes and recorded the color of each in my worksheet, that would be nominal data. 

This kind of data can be used in many different ways—for instance, I could use chi-square analysis to see if there are statistically significant differences in the amounts of each color in a box. 

We also can have ordered or ordinal data, in which items are assigned to categories that do have some kind of implicit or natural order, such as "Short, Medium, or Tall."  Another example is a survey question that asks us to rate an item on a 1 to 10 scale, with 10 being the best. This implies that 10 is better than 9, which is better than 8, and so on. 

The uses for ordered data is a matter of some debate among statisticians. Everyone agrees its appropriate for creating bar charts, but beyond that the answer to the question "What should I do with my ordinal data?" is "It depends."  Here's a post from another blog that offers an excellent summary of the considerations involved. 

For more fun statistics you can do with candy, check out this article (PDF format): Statistical Concepts: What M&M's Can Teach Us. 

For a deeper exploration of the probability distributions that apply to different types of data, check out my colleague Jim Frost's posts about understanding and using discrete distributions and how to identify the distribution of your data.

One highlight of writing for and editing the Minitab Blog is the opportunity to read your responses and answer your questions. Sometimes, to my chagrin, you point out that we've made a mistake. However, I'm particularly grateful for those comments, because it permits us to correct inadvertent errors. 

I feared I had an opportunity to fix just such an error when I saw this comment appear on one of our older blog posts:

You said a p-value greater than 0.05 gives a good fit. However, in another post, you say the p-value should be below 0.05 if the result is significant. Please, check it out!

You ever get a chill down your back when you realize you goofed? That's what I felt when I read that comment. Oh no, I thought. If the p-value is greater than 0.05, the results of a test certainly wouldn't be significant. Did I overlook an error that basic?  

Before beating myself up about it, I decided to check out the posts in question. After reviewing them, I realized I wouldn't need to put on the hairshirt after all. But the question reminded me about the importance of a fundamental idea. 

If you took an introductory statistics course at some point, you probably recall the instructor telling the class how important it is to formulate your hypotheses clearly. Excellent advice.

However, many commonly used statistical tools formulate their hypotheses in ways that don't quite match. That's what this sharp-eyed commenter noticed and pointed out.

The writer of the first post detailed how to use Minitab to identify the distribution of your data, and in her example pointed out that a p-value greater than 0.05 meant that the data were a good fit for a given distribution. The writer of second post—yours truly—commented on the alarming tendency to use deceptive language to describe a high p-value as if it indicated statistical significance. 

To put it in plain language, my colleague's post cited the high p-value as an indicator of a positive result. And my post chided people who cite a high p-value as an indicator of a positive result. 

Now, what's so confusing about that? 

You can see where this looks like a contradiction, but to my relief, the posts were consistent. The appearance of contradiction stemmed from the hypotheses discussed in the two posts. Let's take a look. 

My colleague presented this graph, output from the Individual Distribution Identification:

The individual distribution identification is a kind of hypothesis test, and so the p-value helps you determine whether or not to reject the null hypothesis.

Here, the null hypothesis is "The data follow a normal distribution," and the alternative hypothesis would be "The data DO NOT follow a normal distribution." If the p-value is over 0.05, we will fail to reject the null hypothesis and conclude that the data follow the normal distribution.

Just have a look at that p-value:

That's a high p-value. And for this test, that means we can conclude the normal distribution fits the data. So if we're checking these data for the assumption of normality, this high p-value is good. 

But more often we're looking for a low p-value. In a t-test, the null hypothesis might be "The sample means ARE NOT different," and the alternative hypothesis, "The sample means ARE different." Seen this way, the value or arrangement of the hypotheses is the opposite of that in the distribution identification. 

Hence, the apparent contradiction. But in both cases a p-value greater than 0.05 means we fail to reject the null hypothesis. We're interpreting the p-value in each test the same way.

However, because the connotations of "good" and "bad" are different in the two examples, how we talk about these respective p-values appears contradictory—until we consider exactly what the null and alternative hypotheses are saying. 

And that's a point I was happy to be reminded of. 

One of the most memorable presentations at the inaugural Minitab Insights conference reminded me that data analysis and quality improvement methods aren't only useful in our work and businesses: they can make our home life better, too. 

The presenter, a continuous improvement training program manager at an aviation company in the midwestern United States, told attendees how he used Minitab Statistical Software, and some simple quality improvement tools, to reduce his phone bill.

He took the audience back to 2003, when his family first obtained their cell phones. For a few months, everything was fine. Then the April bill arrived, and it was more than they expected. The family had used too many minutes. 

The same thing happened again in May. In June, the family went over the number of minutes allocated in their phone plan again, for the third month in row. Something had to change!

His wife summed up the problem this way: "There is a problem with our cell phone plan, because the current minutes are not enough for the family members over the past three months." 

He wasn't sure that "too few minutes" was the real problem. But instead of arguing, he applied his quality improvement training to find common ground. He and wife agreed that the previous three months' bills were too much, and they were able to agree that the family went over the plan minutes—for an unknown reason. Based on their areas of agreement, they revised the initial problem statement: 

There is a problem with our cell phone usage, and this is known because the minutes are over the plan for the past 3 months, leading to a strain on the family budget.

They further agreed that before taking further action—like switching to a costlier plan with more minutes—they needed to identify the root cause of the overage. 

By some estimates, up to 70 percent of quality initiatives fail. Why do so many improvement programs, which are championed and staffed by smart, dedicated people, ultimately end up on the chopping block?

According to the Juran Institute, which specializes in training, certification, and consulting on quality management, the No. 1 reason quality improvement initiatives fail is a lack of management support.

At first blush, doesn't that seem like a paradox? After all, it's company leaders who start quality improvement efforts in the first place. So what happens between the time a deployment kicks off—with the C-level's enthusiastic support and participation—and the day a disillusioned C-level executive pulls the plug on a program that never seemed to deliver on its potential?

Even projects which result in big improvements often fail to make an impression on decision-makers. Why?  

The answer may be that those C-level leaders never find out about that impact. The 2013 ASQ Global State of Quality study revealed that the higher people rise in an organization's leadership, the less often they receive reports about quality metrics. Only 2% of senior executives get daily quality reports, compared to 33% of front-line staff members.

Think that's bad? A full 25% of the senior executives reported getting quality metrics only on an annual basis. 

In light of findings like that, the apparent paradox of leaders losing their initial enthusiasm for quality initiatives begins to make sense. The success of the program often remains invisible to those at the top. 

That's not necessarily for a lack of trying, either. Even in organizations with robust, mature quality programs, understanding the full impact of an initiative on the bottom line can be difficult, and sometimes impossible.

For more than 45 years, Minitab has been helping companies in every industry, in virtually every country around the world, improve quality. Along the way, we've seen and identified five main challenges that can keep even the most successful deployments in the shadows.

Individual project teams usually do a great job capturing and reporting their results. But challenges quickly arise when projects accumulate. A large company may have thousands of simultaneous quality projects active now, and countless more completed. Gathering the critical information from all of those projects, then putting it into a format that leaders can easily access and use, is an extremely daunting task—which means that many organizations simply fail to do it, and the overall impact of their quality program remains a mystery.  

As they work through their projects, team members need to create project charters, do SIPOCs and FMEAs, evaluate potential solutions, facilitate brainstorming, and much more. In most organizations, teams have to use an assortment of separate applications for documents, process maps, value stream maps, and other essential project tools. That means the project record becomes a compilation of distinct, frequently incompatible files from many different software programs. Team members are forced to waste time entering the identical information into first one program, then another. Adding to the confusion, the latest versions of documents may reside on several different computers, so project leaders often need to track multiple versions of a document to keep the official project record current. 

Even projects in the same department often don't treat essential metrics consistently, or don't track the same data in the same way. Multiply that across the hundreds of projects under way at any given time in an organization with many different departments and divisions, and it's not hard to see why compiling a reliable report about the impact of all these projects never happens. Even if the theoretical KPIs are consistent across an organization, when one division tracks them in apples, and the next tracks them in oranges, their results can't be evaluated or aggregated as if they were equivalent. 

Many organizations attempt to monitor and assess the impact of quality initiatives using methods that range from homegrown project databases to full-blown, extremely expensive project portfolio management (PPM) systems. Sometimes these work—at least for a while. But many organizations find maintaining their homegrown systems turns into a major hassle and expense. And as others have discovered, the off-the-shelf solutions that were created to meet the needs of information technology, finance, customer service, or other business functions don’t adequately fit or support projects that are based on quality improvement methods such as Six Sigma or Lean. The result? Systems that slowly wither as resources are directed elsewhere, reporting mechanisms that go unused, and summaries that fail to convey a true assessment of an initiative's impact even if they are used. 

There are only so many hours in the day, and busy team members and leaders need to prioritize. Especially when operating under some of the conditions described already, team leaders find reporting on projects to be a burden that just never rises to the top of the priority list. It seems like non-value-added activity to copy-and-paste information from project documents, which had to be rounded up from a bunch of different computers and servers, and then place that information into yet another format. And if the boss isn't asking for those numbers—and it appears that many C-level executives don't—most project leaders have many other tasks to which they can devote their limited time. 

It's easy to understand why so many companies, faced with these constraints, don't have a good understanding of how their quality initiatives contribute to the overall financial picture. But recognizing the issues is the first step in fixing them. 

Organizations can establish standards and make sure that all project teams use consistent metrics. Quality professionals and their leaders can take steps to make sure that reporting on results becomes a critical step in every individual project. 

There also are solutions that tackle many of these challenges head-on. For example, Companion by Minitab takes a desktop app that provides a complete set of integrated tools for completing projects, and combines it with centralized, cloud-based storage for projects and a customizable web-based dashboard. Companion's desktop app makes it easier for practitioners to work through and finish projects—and since their project data automatically rolls up to the dashboard, reporting on projects is effortless. Literally.

For the executives, managers, and stakeholders who have never had a clear picture of their quality program, Companion opens the window on the performance, progress, and bottom-line effects of the entire quality initiative, or specific pieces of it. 

Ensuring that the results of your improvement efforts are clearly seen and understood is a challenge that every quality pro is likely to face. How do you ensure your stakeholders appreciate the value of your activities?  

It's a very exciting time at Minitab's offices around the world, because we've just announced the availability of Minitab® 18 Statistical Software.

Data is everywhere today, but to use it to make sound, strategic business decisions, you need to have tools that turn that data into knowledge and insights. We've designed Minitab 18 to do exactly that. 

We've incorporated a lot of new features, made some great enhancements and put a lot of energy into developing a tool that will make getting insight from your data faster and easier than ever before, and we're excited to get feedback from you about the new release. 

The advanced capabilities we've added to Minitab 18 include tools for measurement systems analysis, statistical modeling, and Design of Experiments (DOE). With Minitab 18, it’s much easier to test how a large number of factors influence process output, and to get more accurate results from models with both fixed and random factors.

We'll delve into more detail about these features in the coming weeks, but today I wanted to give you a quick overview of some of the most exciting additions and improvements. You can also check out one of our upcoming webinars to see the new features demonstrated. Then I hope you'll check them out for yourself—you can get Minitab 18 free for 30 days.

The first thing longtime Minitab users are likely to notice when they launch Minitab 18 is the enhancements we've made to the Session window, which contains the output of all your analyses. 

• Specify the number of significant digits (decimal places) in your output
• Go directly to graphs by clicking links in the output
• Expand and collapse analyses for easier navigation
• Zoom in and out 

We've also added the option to sort the worksheets in your project by title or in chronological order, so you can manage and work with your data in the Project Manager more easily.

Many businesses need to determine which inputs make the biggest impact on the output of a process. When you have a lot of inputs, as most processes do, this can be a huge challenge. Standard experimental methods can be costly and time-consuming, and may not be able to distinguish main effects from the two-way interactions that occur between inputs.

That challenge is answered in Minitab 18 with Definitive Screening Designs, a type of designed experiment that minimizes the number of experimental runs required, but still lets you identify important inputs without confounding main effects and two-way interactions.

Another feature we've added to Minitab 18 is restricted maximum likelihood (REML) estimation. This is an advanced statistical method that improves inferences and predictions while minimizing bias for mixed models, which include both fixed and random factors.

With Minitab 18 we've made it easy to calculate statistical tolerance intervals for nonnormal data with a distributions including the Weibull, lognormal, exponential, and more.

In another enhancement to our Design of Experiments (DOE) functionality, we've added effects plots for general factorial and response surface designs, so you can visually identify significant X’s.

If you're doing the measurement system analysis method known as Gage R&R, Minitab 18 enables you to enter a user-specified process (historical) standard deviation in relevant calculations.

When you use the response optimizer for the general linear model (GLM), you can include both your factors and covariates to find optimal process settings.

The Session window output can be imported into Word and Excel in table format, which lets you easily customize the appearance of your results.

Many people use Minitab's command line to expand the software's functionality. With Minitab 18, we've made it easy to keep commands separate from the Session output with a docked command line pane. 

Finally, it's worth mentioning that the release of Minitab 18 is complemented by new version of Quality Trainer by Minitab®, our e-learning course. It teaches you how to solve real-world quality improvement challenges with statistics and Minitab, and lets you refresh that knowledge anytime. If you haven't tried it yet, you can check out a sample chapter now. 

We hope you'll try the latest Minitab release!  And when you do, please be sure to let us know what you think: we love to get your feedback and input about what we've done right, and what we can make better! Send your comments to feedback@minitab.com.  

Easy access to the right tools makes any task easier. That simple idea has made the Swiss Army knife essential for adventurers: just one item in your pocket gives you instant access to dozens of tools when you need them.  

If your current adventures include analyzing data, the multifaceted Editor menu in Minitab Statistical Software is just as essential.

Whether you’re organizing a data set, sifting through Session window output, or perfecting a graph, the Editor menu adapts so that you never have to search for the perfect tool.

The Editor menu only contains tools that apply to the task you're engaged in. When you’re working with a data set, the menu contains only items for use in the worksheet. When a graph is active, the menu contains only graph-related tools. You get the idea.

When a graph window is active, the Editor menu contains over a dozen graph tools. Here are a few of them.

ADD

Use Editor > Add to add reference lines, labels, subtitles, and much more to your graphs. The contents of the Add submenu will change depending on the type of graph you're editing.

MAKE SIMILAR GRAPH

The editing features in Minitab graphs make it easy to create a graph that looks just right. But it may not be easy to reproduce that look a few hours (or a few months) later.

With most graphs, you can use Editor > Make Similar Graph to produce another graph with the same edits, but with new variables.

When a worksheet is active, the Editor menu contains tools to manipulate both the layout and contents of your worksheet. You can add column descriptions; insert cells, columns or rows; and much more, including the items below.

VALUE ORDER

By default, Minitab displays text data alphabetically in output. But sometimes a different order is more appropriate (for example, “Before” then “After”, instead of alphabetical order). Use Editor > Column > Value Order to ensure that your graphs and other output appear the way that you intend.

ASSIGN FORMULA TO COLUMN

You can assign a formula to a worksheet column that updates when you add or change data.

As the repository for output, the Session window is already an important component of any Minitab project, but the Editor menu makes it even more powerful. 

SHOW COMMAND LINE

For example, most users rely on menus to run analyses, but you can extend the functionality of Minitab and save time on routine tasks with Minitab macros. If you select the "Show Command Line" option, you'll see the command language generated  with each analysis, which opens the door to macro writing.

In previous versions of Minitab, the Command Line appeared in the Session window. In Minitab 18, the Command Line appears in an another pane, which keeps the Session window output clean and displays all of the commands together. The new Command Line pane is highlighted in the screen shot below:

NEXT COMMAND / PREVIOUS COMMAND / EXPAND ALL / COLLAPSE ALL

After you run several analyses, you may have a great deal of output in your Session window. This group of items makes it easy to find the results that you want, regardless of project size.

Next Command and Previous Command will take you back or forward one step from the currently selected location in your output.

Expand All and Collapse All capitalize on a new feature in Minitab 18's redesigned Session window. Now you can select individual components of your output and choose whether to display all of the output (Expanded), or only the output title (Collapsed). Here's an example of an expanded output item:

And here's how the same output item appears when collapsed:

When you have a lot of output items in the session window, the "Collapse All" function can make it extremely fast to scroll through them and find exactly the piece of your analysis you need at any given moment. 

Graph exploration sometimes calls for graph brushing, which is a powerful way to learn more about the points on a graph that interest you. Here are two of the specialized tools in the Editor menu when you are in “brushing mode”.

SET ID VARIABLES

It’s easy to spot an outlier on a graph, but do you know why it’s an outlier? Setting ID variables allows you to see all of the information that your dataset contains for an individual observation, so that you can uncover the factors that are associated with its abnormality.

CREATE INDICATOR VARIABLE

As you brush points on a graph, an indicator variable “tags” the observations in the worksheet. This enables you to identify these points of interest when you return to the worksheet.

Working on a Minitab project can feel like many jobs rolled into one—data wrestler, graph creator, statistical output producer. Each task has its own challenges, but in every case you can reach for the Editor menu to locate the right tools.

Last week I was fielding questions on social media about Minitab 18, the latest version of our statistical software. Almost as soon as the new release was announced, we received a question that comes up often from people in pharmaceutical and medical device companies:

"Is Minitab 18 FDA-validated?"

That's a great question. To satisfy U.S. Food and Drug Administration (FDA) regulatory requirements, many firms—including those in the pharmaceutical and medical device industries—must validate their data analysis software. That can be a big hassle, so to make this process easier, Minitab offers a Validation Kit.

We conduct extremely rigorous and extensive internal testing of Minitab Statistical Software to assure the numerical accuracy and reliability of all statistical output. Details on our software testing procedures can be found in the validation kit. The kit also includes an automated macro script to generate various statistical and graphical analyses on your machine. You can then compare your results to the provided output file that we have validated internally to ensure that the results on your machine match the validated results.

FDA regulations state that the purchaser must validate software used in production or as part of a quality system for the “intended use” of the software. FDA’s Code of Federal Regulations Title 21 Part 820.70(i) lays it out:

“When computers or automated data processing systems are used as part of production or the quality system, the manufacturer shall validate computer software for its intended use according to an established protocol.”

FDA provides additional guidance for medical device makers in Section 6.3 of “Validation of Automated Process Equipment and Quality System Software” in the Principles of Software Validation; Final Guidance for Industry and FDA Staff, January 11, 2002.

“The device manufacturer is responsible for ensuring that the product development methodologies used by the off-the-shelf (OTS) software developer are appropriate and sufficient for the device manufacturer's intended use of that OTS software. For OTS software and equipment, the device manufacturer may or may not have access to the vendor's software validation documentation. If the vendor can provide information about their system requirements, software requirements, validation process, and the results of their validation, the medical device manufacturer can use that information as a beginning point for their required validation documentation.”

Validation for intended use consists of mapping the software requirements to test cases, where each requirement is traced to a test case. Test cases can contain:

• A test case description. For example, Validate capability analysis for Non-Normal Data.
• Steps for execution. For example, go to Stat > Quality Tools > Capability Analysis > Nonnormal and enter the column to be evaluated and select the appropriate distribution.
• Test results (with screen shots).
• Test pass/fail determination.
• Tester signature and date.

There is good reason for the “intended use” guidance when it comes to validation. Here is an example:

Company XYZ is using Minitab to estimate the probability of a defective part in a manufacturing process. If the size of Part X exceeds 10, the product is considered defective. They use Minitab to perform a capability analysis by selecting Stat > Quality Tools > Capability Analysis > Normal.

In the following graph, the Ppk (1.32) and PPM (37 defects per million) are satisfactory.

However, these good numbers would mislead the manufacturer into believing this is a good process. Minitab's calculations are correct, but this data is non-normal, so normal capability analysis was the wrong procedure to use.

Fortunately, Minitab also offers non-normal capability analysis. As shown in the next graph, if we choose Stat > Quality Tools > Capability Analysis > Nonnormal and select an appropriate distribution (in this case, Weibull), we find that the Ppk (1.0) and PPM (1343 defects per million) are actually not acceptable:

Thoroughly identifying, documenting, and validating all intended uses of the software helps protect both businesses that make FDA-regulated products and the people who ultimately use them.

To download Minitab's software validation kit, visit http://www.minitab.com/support/software-validation/

In addition to details regarding our testing procedures and a macro script for comparing your results to our validated results, the kit also includes software lifecycle information.

Additional information about validating Minitab relative to the FDA guideline CFR Title 21 Part 11 is available at this link:

http://it.minitab.com/support/answers/answer.aspx?id=2588

If you have any questions about our software validation process, please contact us.

If you have a process that isn’t meeting specifications, using Monte Carlo simulation and optimization can help. Companion by Minitab offers a powerful, easy-to-use tool for Monte Carlo simulation and optimization, and in this blog we'll look at the case of product engineers involved in steel production for automobile parts, and how they could use Companion to improve a process.

The tensile strength of Superlative Auto Parts’ new steel parts needs to be at least 600 MPa. The important inputs for this manufacturing process are the melting temperature of the steel and the amount of carbon, manganese, cobalt, and phosphorus it contains. The following transfer equation models the steel’s tensile strength:

Strength = -1434 + 1.1101*MeltTemp + 1495*Carbon + 174.3*Manganese - 7585*Cobalt - 3023*Phosphorus

To assess the process capability, you can enter information about your current process inputs into Companion’s straightforward interface.

Suppose that while you know most of your inputs follow a normal distribution, you’re not sure about the distribution of melting temperature. As long as you have data about the process, you can just select the appropriate column in your data sheet and Companion will recommend the appropriate distribution for you.

In this case, Companion recommends the Weibull distribution as the best fit and then automatically enters the "MeltTemp" distribution information into the interface.

Once you have entered all of your input settings, your transfer equation, and the lower specification limit, Companion completes 50,000 simulations for the steel production.

The process performance measurement (Cpk) for your process is 0.417, far short of the minimum standard of 1.33. Companion also indicates that under current conditions, 14 percent of your parts won’t meet the minimum specification.

The Companion Monte Carlo tool’s smart workflow guides you to the next step for improving your process: optimizing your inputs.

You set the goal—maximizing the tensile strength—and enter the high and low values for your inputs. Companion does the rest.

After finding the optimal input settings in the ranges you specified, Companion presents the simulated results for the recommended process changes.

The simulation indicates that the optimal settings identified by Companion will virtually eliminate out-of-spec product from your process, with a Cpk of 1.56—a vast improvement that exceeds the 1.33 Cpk standard. Thanks to you, Superlative Auto Parts’ steel products won’t be hitting any bumps in the road.

Figuring out how to improve a process is easier when you have the right tool to do it. With Monte Carlo simulation to assess process capability and Parameter Optimization to identify optimal settings, Companion can help you get there. And with Sensitivity Analysis to pinpoint exactly where to reduce variation, you can further improve your process and get the product results you need.

To try the Monte Carlo simulation tool, as well as Companion's more than 100 other tools for executing and reporting quality projects, learn more and get the free 30-day trial version for you and your team at companionbyminitab,com.

If you have a process that isn’t meeting specifications, using the Monte Carlo simulation and optimization tools in Companion by Minitab can help. Here’s how you, as an engineer in the medical device industry, could use Companion to improve a packaging process and help ensure patient safety.

Your product line at AlphaGamma Medical Devices is shipped in heat-sealed packages with a minimum seal strength requirement of 13.5 Newtons per square millimeter (N/mm2). Meeting this specification is critical, because when a seal fails the product inside is no longer sterile and puts patients at risk.

Seal strength depends on the temperature of the sealing device and the sealing time. The relationship between the two factors is expressed by the model:

Seal Strength= 9.64 + 0.003*Temp + 4.0021*Time + 0.000145 Temp*Time

Currently, your packages are sealed at an average temperature of 120 degrees Celsius, with a standard deviation of 25.34. The mean sealing time is 1.5 seconds, with a standard deviation of 0.5. Both parameters follow a normal distribution.

To assess the process capability under the current conditions, you can enter the parameter, transfer function, and specification limits into Companion’s straightforward interface, verify that the model diagram matches your process, and then instantly simulate 50,000 package seals using your current input conditions.

The process performance measurement (Cpk) for your process is 0.42, far less than the minimum standard of 1.33. Under the current conditions, more than 10% of your seals will fail to meet specification.

Companion’s intuitive workflow guides you to the next step: optimizing your inputs.

You set the goal—in this case, minimizing the percent out of spec—and enter high and low values for your inputs. Companion does the rest.

After finding the optimal input settings in the ranges you specified, Companion presents the simulated results of the recommended process changes.

The simulation shows the new settings would reduce the amount of faulty seals to less than 1% with a Ppk of 0.78—an improvement, but still shy of the 1.33 Ppk standard.

To further improve the package sealing process, Companion then suggests that you perform a sensitivity analysis.

Companion’s unique graphic presentation of the sensitivity analysis provides you with insight into how the variation of your inputs influences seal strength.

The blue line representing time indicates that this input’s variability has more of an impact on percent of spec than temperature. The blue line also indicates how much of an impact you can expect to see: in this case, reducing the variability in time by 50% will reduce the percent out of spec to about 0 percent. Based on these results, you run another simulation to visualize the strength of your seals using the 50% variation reduction in time.

The simulation shows that reducing the variability will result in a Ppk of 1.55, with 0% of your seals out of spec, and you’ve just helped AlphaGamma Medical Devices bolster its reputation for excellent quality.

Figuring out how to improve a process is easier when you have the right tool to do it. With Monte Carlo simulation to assess process capability, Parameter Optimization to identify optimal settings, and Sensitivity Analysis to pinpoint exactly where to reduce variation,  Companion can help you get there.

To try the Monte Carlo simulation tool, as well as Companion's more than 100 other tools for executing and reporting quality projects, learn more and get the free 30-day trial version for you and your team at companionbyminitab,com.

All processes have variation, some of which is inherent in the process, and isn't a reason for concern. But when processes show unusual variation, it may indicate a change or a "special cause" that requires your attention. 

Control charts are the primary tool quality practitioners use to detect special cause variation and distinguish it from natural, inherent process variation. These charts graph process data against an upper and a lower control limit. To put it simply, when a data point goes beyond the limits on the control chart, investigation is probably warranted.

It seems so straightforward. But veteran control chart users can tell you about “false alarms,” instances where data points went outside the control limits, and those limits fell close to the mean—even though the process was in statistical control.

The attribute charts, the traditional P and U control charts we use monitor defectives and defects, are particularly prone to false alarms due to a phenomenon known as overdispersion. That problem had been known for decades, until quality engineer David Laney solved it by devising P' and U' charts. 

The P' and U' charts avoid false alarms so only important process deviations are detected. In contrast to the traditional charts, which assume a defective or defect rate remains constant, P' and U' charts assume that no process has a truly constant rate, and accounts for that when calculating control limits.

That's why the P' and U' charts deliver a more reliable indication of whether the process is really in control, or not.

Minitab's control chart capabilities include P' and U' charts, and the software also includes a diagnostic tool that identifies situations where you need to use them. When you choose the right chart, you can be confident any special-cause variation you're observing truly exists.

When you have too much variation, or “overdispersion,” in your process data, false alarms can result—especially with data collected in large subgroups. The larger the subgroups, the narrower the control limits on a traditional P or U chart. But those artificially tight control limits can make points on a traditional P chart appear out of control, even if they aren't.

However, too little variation, or “underdispersion,” in your process data also can lead to problems. Underdispersion can result in artificially wide control limits on a traditional P chart or U chart. Under that scenario, some points that appear to be in control could well be ones you should be concerned about.

If your data is affected by overdispersion or underdispersion, you need to use a P' or U' chart will to reliably distinguish common-cause from special-cause variation. 

If you aren't sure whether or not your process data has over- or underdispersion, the P Chart or U Chart Diagnostic in Minitab can test it and tell you if you need to use a Laney P' or U' chart.

Choose Stat > Control Charts > Attributes Charts > P Chart Diagnostic or Stat > Control Charts > Attributes Charts > U Chart Diagnostic. 

The following dialog appears:

Enter the worksheet column that contains the number of defectives under "Variables." If all of your samples were collected using the same subgroup size, enter that number in Subgroup sizes. Alternatively, identify the appropriate column if your subgroup sizes varied.

Let’s run this test on the DefectiveRecords.MTW from Minitab's sample data sets. This data set features very large subgroups, each having an average of about 2,500 observations.

The diagnostic for the P chart gives the following output:

Below the plot, check out the ratio of observed to expected variation. If the ratio is greater than the 95% upper limit that appears below it, your data are affected by overdispersion. Underdispersion is a concern if the ratio is less than 60%. Either way, a Laney P' chart will be a more reliable option than the traditional P chart.

To make a P' chart, go to Stat > Control Charts > Attributes Charts > Laney P'.  Minitab will generate the following chart for the Defectives.MTW data. 

This P' chart shows a stable process with no out-of-control points. But create a traditional P chart with this data, and several of the subgroups appear to be out of control, thanks to the artificially narrow limits caused by the overdispersion.  

So why do these data points appear to be out of control on the P but not the P' chart? It’s the way each defines and calculates process variation. The Laney P' chart control limits account for the overdispersion when calculating the variation and eliminate these false alarms.

The Laney P' chart calculations include within-subgroup variation as well as the variation between subgroups to adjust for overdispersion or underdispersion.

If over- or underdispersion is not a problem, the P' chart compares to a traditional P chart. But the P' chart expands the control limits where overdispersion exists, ensuring that only important deviations are identified as out of control. And in the case of underdispersion, the P' chart calculations result in narrower control limits.

To learn more about the statistical foundation underlying the Laney P' and U' charts, read On the Charts: A Conversation with David Laney.

Can you trust your data? 

That's the very first question we need to ask when we perform a statistical analysis. If the data's no good, it doesn't matter what statistical methods we employ, nor how much expertise we have in analyzing data. If we start with bad data, we'll end up with unreliable results. Garbage in, garbage out, as they say.

So, can you trust your data? Are you positive? Because, let's admit it, many of us forget to ask that question altogether, or respond too quickly and confidently.

You can’t just assume we have good data—you need to know you do. That may require a little bit more work up front, but the energy you spend getting good data will pay off in the form of better decisions and bigger improvements.

Here are 3 critical actions you can take to maximize your chance of getting data that will lead to correct conclusions. 

Failing to plan is a great way to get unreliable data. That’s because a solid plan is the key to successful data collection. Asking why you’re gathering data at the very start of a project will help you pinpoint the data you really need. A data collection plan should clarify:

• What data will be collected
• Who will collect it
• When it will be collected
• Where it will be collected
• How it will be collected

Answering these questions in advance will put you well on your way to getting meaningful data.

Many quality improvement projects require measurement data for factors like weight, diameter, or length and width. Not verifying the accuracy of your measurements practically guarantees that your data—and thus your results—are not reliable.

A branch of statistics called Measurement System Analysis lets you quickly assess and improve your measurement system so you can be sure you’re collecting data that is accurate and precise.

When gathering quantitative data, Gage Repeatability and Reproducibility (R&R) analysis confirms that instruments and operators are measuring parts consistently.

If you’re grading parts or identifying defects, an Attribute Agreement Analysis verifies that different
evaluators are making judgments consistent with each other and with established standards.

If you do not examine your measurement system, you’re much more likely to add variation and
inconsistency to your data that can wind up clouding your analysis.

As you collect data, be careful to avoid introducing unintended and unaccounted-for variables. These “lurking” variables can make even the most carefully collected data unreliable—and such hidden factors often are insidiously difficult to detect.

A well-known example involves World War II-era bombing runs. Analysis showed that accuracy increased when bombers encountered enemy fighters, confounding all expectations. But a key variable hadn’t been factored in: weather conditions. On cloudy days, accuracy was terrible
because the bombers couldn’t spot landmarks, and the enemy didn’t bother scrambling fighters.

Suppose that data for your company’s key product shows a much larger defect rate for items made by the second shift than items made by the first.

Given only this information, your boss might suggest a training program for the second shift, or perhaps even more drastic action.

But could something else be going on? Your raw materials come from three different suppliers.

What does the defect rate data look like if you include the supplier along with the shift?

Now you can see that defect rates for both shifts are higher when using supplier 2’s materials. Not
accounting for this confounding factor almost led to an expensive “solution” that probably would do little to reduce the overall defect rate.

Nobody sets out to waste time or sabotage their efforts by not collecting good data. But it’s all too easy to get problem data even when you’re being careful! When you collect data, be sure to spend
the little bit of time it takes to make sure your data is truly trustworthy. 

Six Sigma is a quality improvement method that businesses have used for decades—because it gets results. A Six Sigma project follows a clearly defined series of steps, and companies in every industry in every country around the world have used this method to resolve problems. Along the way, they've saved billions of dollars.

But Six Sigma relies heavily on statistics and data analysis, and many people new to quality improvement feel intimidated by the statistical aspects.

You needn't be intimidated. While it's true that data analysis is critical in improving quality, the majority of analyses in Six Sigma are not hard to understand, even if you’re not very knowledgeable about statistics.

Familiarizing yourself with these tools is a great place to start. This post briefly explains 5 statistical tools used in Six Sigma, what they do, and why they’re important.

The Pareto Chart stems from an idea called the Pareto Principle, which asserts that about 80% of outcomes result from 20% of the causes. It's easy to think of examples even in our personal lives. For instance, you may wear 20% of your clothes 80% of the time, or listen to 20% of the music in your library 80% of the time.

The Pareto chart helps you visualize how this principle applies to data you've collected. It is a specialized type of bar chart designed to distinguish the “critical few” causes from the “trivial many” enabling you to focus on the most important issues. For example, if you collect data about defect types each time one occurs, a Pareto chart reveals which types are most frequent, so you can focus energy on solving the most pressing problems. 

A histogram is a graphical snapshot of numeric, continuous data. Histo­grams enable you to quickly identify the center and spread of your data. It shows you where most of the data fall, as well as the minimum and maximum values. A histogram also reveals if your data are bell-shaped or not, and can help you find unusual data points and outliers that may need further investigation. 

Accurate measurements are critical. Would you want to weigh yourself with a scale you know is unre­liable? Would you keep using a thermometer that never shows the right temperature? If you can't measure a process accurately, you can't improve it, which is where Gage R&R comes in. This tool helps you determine if your continuous numeric measurements—such as weight, diameter, and pressure—are both repeatable and reproducible, both when the same person repeatedly measures the same part, and when different operators measure the same part.

Another tool for making sure you can trust your data is attribute agreement analysis. Where Gage R&R assesses the reliability and reproducibility of numeric measurements, attribute agree­ment analysis assess categorical assessments, such as Pass or Fail. This tool shows whether people rating these categories agree with a known standard, with other appraisers, and with themselves. 

Nearly every process has an acceptable lower and/or upper bound. For example, a supplier's parts can’t be too large or too small, wait times can’t extend beyond an acceptable threshold, fill weights need to exceed a specified minimum. Capability analysis shows you how well your process meets specifications and provides insight into how you can improve a poor process. Frequently cited capability metrics include Cpk, Ppk, defects per million opportunities (DPMO), and Sigma level. 

Six Sigma can bring significant benefits to any business, but reaping those benefits requires the collection and analysis of data so you can understand opportunities for improvement and make significant and sustainable changes.

The success of Six Sigma projects often depends on practitioners who are highly skilled experts in many fields, but not statistics. But with a basic understanding of the most commonly used Six Sigma statistics and easy-to-use statistical software, you can handle the statistical tasks associated with improving quality, and analyze your data with confidence.