Mar 5 2024
The statistical quality profession has a love/hate relationship with the Gaussian distribution. In SPC, it treats it like an embarrassing spouse. It uses the Gaussian distribution as the basis for all its control limits while claiming it doesn’t matter. In 2024, what role, if any, should this distribution play in the setting of action limits for quality characteristics?
Nov 4 2019
“The ability to react to process changes is more important than protecting yourself from occasional false alarms. […] So do not worry so much about straining out the gnats of false alarms that you end up swallowing the camels of undetected process changes.”
Sourced through Quality Digest
Michel Baudin‘s comments:
The people of the Honda plant in Anna, OH, claim to make the best engines in the world. On the floor, there is neither a single control chart nor any engineer trained in SPC.
Of course, we should fact-check their claim. Rankings of engine quality are not readily googleable. The closest I could find is a ranking of engine reliability from 2014 in a UK blog called The Car Expert, based on data from Warranty Direct, a UK provider of extended warranties. According to them, Honda indeed made the most reliable engines:
“Only one in every 344 Honda owners have had engine trouble, with second-placed rival Toyota notching up just 1 in 171.”
According to Anna engineers, their machine tools can hold tolerance ten times tighter than necessary. The few quality problems they do have are due to operators picking the wrong parts in assembly. Control charts in the machine shop would produce nothing but false alarms. With the charts crying wolf, the alarms would lose credibility and nobody would react when a real one hit.
In this kind of situation, Wheeler’s statement can be reversed. The ability to protect yourself against false alarms that send your engineers on wild goose chases is more important than detecting changes that hardly ever happen. You do want to detect changes in the process but control charts are too crude a tool for this purpose.
Mar 12 2019
In statistics on time series with “moving” in their name, each value is correlated with past and future neighbors — that is, the series is autocorrelated. It affects the way you can use these statistics to detect anomalies and issue alarms.
The moving range in the XmR chart is a case in point. Its autocorrelation in the moving range chart is self-inflicted. It is autocorrelated by construction, regardless of whether the raw data themselves are.
Some raw data are autocorrelated. For example, when you issue a replenishment order for a part by pulling a Kanban from a bin, you are assuming that the demand for a coming period to match that of the period that just elapsed, with minor fluctuations. Implicitly, you are leveraging the autocorrelation of the part consumption across periods.
On the other hand, if a physical characteristic of a manufactured part is the sum of a constant and noise, then the noises are independent, and therefore uncorrelated. Taking moving ranges introduces an autocorrelation between consecutive values that is absent in the raw data.
Nov 7 2025
The Lowdown on the Range Chart
To use in-process measurements for quality control 100 years ago, Walter Shewhart proposed the \bar{X}-\sigma charts. It entailed arranging workpieces in rational subgroups, summarizing measurements by subgroup into means and standard deviations, charting both, and checking new values against control limits.
When Harold Dodge tried to implement the \bar{X}-\sigma charts at Western Electric, the engineers balked at calculating sample standard deviations with paper, pencils, and slide rules. To gain acceptance, Dodge let them use sample ranges and plot them in R charts instead. While easier to understand and to use daily, sample ranges are mathematically more complex and more sensitive to extreme values than standard deviations.
The SPC literature glosses over the motivation for the R chart and its math. It provides recipes for using these charts, but no explanation. We shouldn’t ask manufacturing professionals to use a tool without explaining its purpose and its theory. This is what this post is trying to remedy.
Like all control charts, the R chart uses limits calculated for the Gaussian distribution. As no simple formula is available for the R chart, setting control limits for it requires numerical approximations that must have consumed months for human computers in 1924. Today, you can replicate them instantaneously with software. These calculations reveal that the \pm 3\sigma limits in the books for the range chart do not actually encompass the 99.73% of the distribution that they do in \bar{X} charts.
The R chart was an ingenious workaround to technical and human constraints of the 1920s that no longer exist. Today, rather than blindly applying these tools, we must draw inspiration from their inventors and develop solutions to meet the process capability challenges we are actually facing.
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By Michel Baudin • Quality 0 • Tags: Control Charts, Quality, Range Chart, SPC, Xbar-R chart