Part one of this article showed that it is possible, by means of a Visual Basic for Applications program in Microsoft Excel, to calculate the fraction of in-specification product that is rejected by a non-capable gage, as well as the fraction of nonconforming product that is accepted. This calculation requires only 1) the process performance metrics, including the parameters of the distribution of the critical to quality characteristic, which need not be normal; and 2) the gage variation as assessed by measurement systems analysis (MSA).

Part 2 of the series shows how to optimize the acceptance limits to either minimize the cost of wrong decisions, or assure the customer that it will receive no more than a specified fraction of nonconforming work.

IATF 16949:2016 clause 7.1.5.1.1 requires measurement systems analysis (MSA) to quantify gage and instrument variation. The deliverables of the generally accepted procedure are the repeatability or equipment variation, and the reproducibility or appraiser variation. The Automotive Industry Action Group¹ adds an analytic process with which to quantify the equipment variation (repeatability) of go/no-go gages if these come in specified dimensions, or can be adjusted to selected dimensions.

The anvils of a snap gage can, for example, be set accurately to specified dimensions with Johansson gage blocks. Pin gages (also known as plug gages), on the other hand, come in small but discrete increments. If the precision to tolerance (P/T) ratio is greater than the generally accepted target, the gage cannot distinguish reliably between good and nonconforming product near the specification limits. This means nonconforming work will reach internal or external customers, while good items will be rejected, as shown in figure 1 below.

Health-tracking devices and apps are becoming part of everyday life. More than 300,000 mobile phone applications claim to help with managing diverse personal health issues, from monitoring blood glucose levels to conceiving a child.

But so far the potential for health-tracking apps to improve healthcare has barely been tapped. Although they allow a user to collect and record personal health data, and sometimes even share it with friends and family, these apps typically don’t connect that information to a patient’s digital medical chart, or make it easier for healthcare providers to monitor or share feedback with their patients.

The first part of this series introduced measurement systems analysis for attribute data, or attribute agreement analysis. AIAG¹ provides a comprehensive overview, and Jd Marhevko² has done an outstanding job of extending it to judgment inspections as well as go/no-go gages. Part two will cover the analytical method, which allows more detailed quantification of the gage standard deviation and also bias, if any, with the aid of parts that can be measured in terms of real numbers.

Part one laid out the procedure for data collection as well as the signal detection approach, which identifies and quantifies the zone around the specification limits where inspectors and gages will not obtain consistent results. The signal detection approach can also deliver a rough estimate of the gage’s repeatability or equipment variation. Go/no-go gages that can be purchased in specific dimensions, or set to specific dimensions (e.g., with gage blocks) do indeed have gage standard deviations even though they return pass/fail results.

When we talk about measurement system analysis (MSA), people tend to focus on attribute agreement analysis because it is usually quicker and easier to do than a gauge repeatability and reproducibility (gauge R&R) study. This article is a review of the fundamentals for gauge R&R to remind us why it is so critical. We will review the basic definitions, go through a process for preparing a study, and then review the output in Minitab to make sure we understand what is going on in the analysis.

Why do we do a gauge R&R study in the first place? We do it for two reasons. One is to validate that the measurement process is acceptable. The second is to feel comfortable about the data. We want to avoid the potential for embarrassment by presenting data in a meeting and having it challenged. We want to be able to show what we did to validate it and to have confidence the data are good. Doing MSA also helps us to understand what is in the collection process and helps convince the people collecting the data why it’s important to do so. If the data collector understands why the study is being done, then he will be more likely to identify problems when they occur.

Measurement systems analysis (MSA) for attributes, or attribute agreement analysis, is a lot like eating broccoli or Brussels sprouts. We must often do things we don't like because they are necessary or good for us. While IATF 16949:2016, Clause 7.1.5.1.1—“Measurement systems analysis,” does not mention attribute agreement analysis explicitly, it does say that MSA shall be performed to assess “variation present in the results of each type of inspection, measurement, and test equipment system identified in the control plan.” It does not limit this requirement to the familiar real-number measurements with which we are comfortable.

Common sense says, meanwhile, that it is beneficial to understand the capabilities and limitations of inspections for attributes. The last thing we want to hear from a customer is, for example, “Your ANSI/ASQ Z1.4 sampling plan with an acceptable quality level of 0.1 percent just shipped us a lot with 2-percent nonconforming work.” Samuel Windsor describes how an attribute gage study saved a company $400,000 a year, which is a powerful incentive to learn about this and use it where applicable.¹ Jd Marhevko has done an outstanding job of extending attribute agreement analysis to judgment inspections as well as go/no-go gages.²

To date, this series focused on relatively simple data analyses, such as learning one summary statistic about our data at a time. In reality, we’re often interested in a slightly more sophisticated analysis, so we can learn multiple trends and takeaways at once and paint a richer picture of our data.

In this article, we will look at answering a collection of counting queries—which we call a workload—under differential privacy. This has been the subject of considerable research effort because it captures several interesting and important statistical tasks. By analyzing the specific workload queries carefully, we can design very effective mechanisms for this task that achieve low error.