Rethinking Statistics for Quality Control

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Notes

¹The distinguished scientist Sir Arthur Eddington (1935) said, “The second law of thermodynamics holds, I think, the supreme position among the laws of nature. …If your theory is found to be against the second law of thermodynamics I can give you no hope.”

²The sun is, of course, the unique source of continuous replenishment for lost entropy. Without it we could not exist.

³However, the process might be stable if the “data” were the controlled output from, say, a correctly operating automatic feedback system.

⁴By a responsive system it is meant that an adjustment at the input is fully effective at the output in one time period.

⁵Examples of permanent common causes might be a slight but unappreciated difference in a raw material or in an operating procedure.

⁶The autocorrelation function measures the correlation of observations at successive lags.

⁷When using “data” from previous publications for illustration, it is important to find out whether these are genuine observations from a manufacturing process or have been generated according to some assumed model, for which, not surprisingly, the assumptions hold true. Also remember that even when the data are genuine, there may be reason to suspect unrecorded adjustments.

⁸Other sets of data treated this way may be seen in Box et al. (2007) and Box et al. (2009).

⁹They showed that for an IMA disturbance, assuming a quadratic loss function for deviations from target and a fixed loss for each adjustment, the scheme giving the minimum overall cost was obtained by plotting an appropriate EWMA between parallel lines at T ± L and making an adjustment as soon as either line was crossed. It was later shown that the same schemes produced the smallest variation of the output for a given average adjustment interval.