Data science

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Nov 13 2023

Process Capability Indices

Within the quality profession, a capable process is one with a high C_{p_k}. In the field, it is not quite so simple. My colleague Joerg Muenzing recently shared concerns about the process capability indices:

“Many manufacturers that I know struggle with incapable processes. Intellectually, people understand the concept of capability, but are unable to effectively apply it to an entire process. A single-figure measure for the entire chain would be ideal to better understand and manage it. The challenge is that the chain consists of processes with measurable characteristics, like thickness, substitute characteristics, like leak current to infer dryness, and also visual inspection results like blemishes or scratches.

They know that C_{p_k} < 1 is bad, and scrap shrinks the bottom line, but not much more. At the same time, customers like large Automotive OEMs demand from their suppliers a C_{p_k} > 1.33 for manual and “uncritical” characteristics, and C_{p_k} >1.66 or even >2.00 for critical characteristics.

What would be useful without being ‘too wrong’?”

Let’s take a closer look.

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Sep 23 2023

Orbit Charts, Revisited

Data visualization is not just the art of presenting data to an audience. Upstream from this, you use visualizations in data cleaning to identify defective points, and in exploratory analysis, to identify patterns of interest. Then, you validate these patterns with a more formal analysis. Once confident that you have findings of value to communicate, you worry about making a compelling presentation.

Nick Desbarats and I had a long exchange on LinkedIn prompted by his article Connected Scatterplots Make Me Feel Dumb in Nightingale, the Data Visualization Society journal, on 8/29/2023. What he called Connected Scatterplot is what I call orbit charts, and I have found them helpful, particularly in analysis.

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May 13 2023

Effect of COVID-19 Vaccines on Excess Deaths

Even on LinkedIn, you still see posts and comments asserting that the COVID-19 vaccines aren’t “real” and alleging that they do more harm than good. This is usually based on articles of questionable value and the author’s brother-in-law catching COVID-19 while vaccinated. Public health, however, warrants serious research and is not a matter of anecdotes.

The real question is whether the administration of these vaccines to large populations was effective in curbing the pandemic and saving lives. Today, we can answer yes to some of these questions with simple methods applied to data from the US government. Specifically, we can analyze US CDC and census data on state-by-state Excess Deaths and fractions of the population vaccinated for 2021 and 2022. The results are obvious but, sometimes, the obvious needs belaboring. 

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Nov 7 2022

Analyzing Variation with Histograms, KDE, and the Bootstrap

Assume you have a dataset that is a clean sample of a measured variable. It could be a critical dimension of a product, delivery lead times from a supplier, or environmental characteristics like temperature and humidity. How do you make it talk about the variable’s distribution? This post explores this challenge in the simple case of 1-dimensional data. I have used methods from histograms to KDE and the Bootstrap, varying in vintage from the 1890s to the 1980s:

Timeline of tools used in this post

Other methods were surely invented for the same purpose between 1895 and 1960 or since 1979, that I don’t know about or haven’t used. Readers are welcome to point them out.

The ones discussed here are not black boxes, automatically producing answers from a stream of data. All require a human to tune the settings of the tools. And this human needs to know the back story of the data.

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Jul 18 2022

The Most Basic Problem in Quality

Two groups of parts are supposed to be identical in quality: they have the same item number and are made to the same specs, at different times in the same production lines, at the same time in different lines, or by different suppliers.

One group may be larger than the other, and both may contain defectives. Is the difference in fraction defectives between the two groups a fluctuation or does it have a cause you need to investigate? It’s as basic a question as it gets, but it’s a real problem, with solutions that aren’t quite as obvious as one might expect. We review several methods that have evolved over the years with information technology.

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Jun 12 2022

Perspectives On Probability In Operations

The spirited discussions on LinkedIn about whether probabilities are relative frequencies or quantifications of beliefs are guaranteed to baffle practitioners. They come up in threads about manufacturing quality, supply-chain management, and public health, and do not generate much light. Their participants trade barbs without much civility, and without actually exchanging on substance.

The latest one, by Alexander von Felbert, is among the more thoughtful, and therefore unlikely to inspire rants. I do, however, fault it with using words like “aleatory” or “epistemic” that I don’t think are helpful. I am trying to discuss it here in everyday language, and to apply the concepts to numerically specific cases, with an eye to operations.

While there are genuinely great and not-so-great ideas, the root of the most violent disagreements is elsewhere, with individuals generalizing from different experience bases. You may map probability to reality differently depending on whether you are developing drugs in the pharmaceutical industry, enhancing yield in a semiconductor process, or driving down dppms in auto parts. The math doesn’t care as long as you follow its rules, and it doesn’t invalidate other interpretations.

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