Mar 2 2019

## The Math Behind The Process Behavior Chart

Ever since asking Is SPC Obsolete? on this blog almost 6 years ago, multiple sources have told me that the XmR chart is a wonderful and currently useful process behavior chart, universally applicable, a data analysis panacea, requiring no assumption on the structure of the monitored variables. So I dug into it and this what I found.

Mar 12 2019

## More About the Math of the Process Behavior Chart

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.

Someraw 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 rangesintroduces an autocorrelation between consecutive values that is absent in the raw data.Continue reading…

By Michel Baudin • Data science • 6 • Tags: Autoregression, Control Charts, SPC, XmR