# Lessons in Quality from Guadalajara and Mexico City

Last week, thanks to the collective effort from many people, we held very successful events in Guadalajara and Mexico City, which gave us a unique opportunity to meet with over 300 Spanish-speaking Minitab users. They represented many different industries, including automotive, textile, pharmaceutical, medical devices, oil and gas, electronics, and mining, as well as academic institutions and consultants.

As I listened to my peers Jose Padilla and Marilyn Wheatley deliver their presentations, it was interesting to see people's reactions as they learned more about our products and services. Several attendees were particularly pleased to learn more about Minitab's ease-of-use and step-by-step help with analysis offered by the Assistant menu. I saw others react to demonstrations of Minitab's comprehensive Help system, the use of executables for automation purposes, and several of the tips and tricks discussed throughout our presentations.

We also had multiple conversations on Minitab's flexible licensing options. Several attendees who spend a lot of time on the road were particularly glad to learn about our borrowing functionality, which lets you “check out” a license so you can use Minitab software without accessing your organization’s license server.

## Acceptance Sampling Plans

There were plenty of technical discussions as well. One interesting question came from a user who asked how Minitab's Acceptance Sampling Plans compare to the ANSI Z1.4 standard (a.k.a. MIL-STD 105E). The short answer is that the tables provided by the ANSI Z1.4 are for a specific AQL (Acceptable Quality Level), while implicitly assuming a certain RQL (Rejectable Quality Level) based solely on the lot size. The ANSI Z1.4 is an AQL-based system, while Minitab's acceptance sampling plans give you the flexibility to create a customized sampling scheme for a specific AQL, RQL, or lot size using both the binomial or hypergeometric distributions.

## Destructive Testing and Gage R&R

Other users had questions about Gage R&R and destructive testing. Practitioners commonly assess a destructive test using Nested Gage R&R; however, this is not always necessary. The main problem with destructive testing is that every part tested is destroyed and thus can only be measured by a single operator. Since the purpose of this type of analysis is to measure the repeatability and reproducibility of the measurement system, one must identify parts that are as homogeneous as possible. Typically, instead of 10 parts, practitioners may use multiple parts from each of 10 batches. If the within-batch variation is small enough then the parts from each batch can be considered to be "the same" and thus the readings measured by all the operators can be used to produce repeatability and reproducibility measures. The main trick is to have homogenous units or batches that can give you enough samples to be tested by all operators for all replicates. If this is the case, you can analyze a destructive test with crossed gage R&R.

## Control Charts and Subgroup Size

We also had an interesting discussion about the sensitivity of Shewhart control charts to the subgroup size. Specifically, one of the attendees asked our recommendation for subgroup size: 4, or 5?

The answer to this intriguing question requires an understanding of the reason why subgroups are recommended. Control charts have limits that are constructed so that if the process is stable, the probability of observing points out of these control limits is very small; this probability is typically referred to as the false alarm rate and it is usually set at 0.0027. This calculation assumes the process is normally distributed, so if we were plotting the individual data as in an Individuals chart, the control limits would be effective to determine an out-of-control situation only if the data came from a normal distribution. To reduce the dependence on normality, Shewhart suggested collecting the data in subgroups, because if we plot the means instead of the individual data the control limits would become less and less sensitive to normality as the subgroup size increases. This is a result of the Central Limit Theorem (CLT), which states that regardless of the underlying distribution of the data, that if we take independent samples and compute the average (or a sum) of all the observations in each sample then the distribution of these sample means will converge to a normal distribution.

So going back to the original question, what is the recommended subgroup size for building control charts? The answer depends on how skewed the underlying distribution may be. For various distributions a subgroup size of 5 is sufficient to have the CLT kick in making our control charts robust to normality; however for extremely skewed distributions like the exponential, the subgroup sizes may need to be much larger than 50. This topic was discussed in a paper Schilling and Nelson titled "The Effect of Non-normality on the Control Limits of Xbar Charts" published in JQT back in 1976.

## Analyzing Variability

We also had a great discussion about modeling variability in a process. One of the attendees, working for McDonald's, was looking for statistical methods for reducing the variation of the weight of apple slices. An apple is cut in 10 slices, and the goal was to minimize the variation in weight so that exactly four slices be placed in each bag without further rework. This gave me the opportunity to demonstrate how to use the Analyze Variability command in Minitab, which happens to be one of the topics we cover in our DOE in Practice course.

## We Love Your Questions

For me and my fellow trainers, there’s nothing better than talking with people who are using Minitab software to solve problems. Sometimes we’re able to provide a quick, helpful answer. Sometimes a question provokes a great discussion about some quality challenge we all have in common. And sometimes a question will lead to a great idea that we’re able to share with our developers and engineers to make our software better.

If you have a question about Minitab, statistics, or quality improvement, please feel free to comment here. And if you use Minitab software, you can always contact our customer support team for direct assistance from specialists in IT, statistics, and quality improvement.