Department seminar by William Woodall, Virginia TechExport this event to calendar

Friday, May 15, 2015 — 10:30 AM EDT

The Difficulty in Designing Process Monitoring Methods with Estimated In-Control Parameters

The performance of monitoring methods, such as the Shewhart  control chart, with estimated in-control parameters has been widely discussed in the literature. Previous studies showed, for example, that at least 400/(n-1) Phase I samples, where n > 1 is the sample size, are required so that the - chart performs on average as if the in-control process parameter values were known. This recommendation was based on the in-control expected average run length (ARL) performance. The reliance on the expected ARL metric, however, neglects the practitioner-to-practitioner variability. This variability occurs due to the different historical data sets practitioners use, which results in varying parameter estimates, control limits, and in-control ARL values.

In this presentation, it is shown that taking this additional type of variability into consideration leads to much larger Phase I samples, far beyond what many previous researchers have recommended, in order to have low levels of variation of in-control performance among practitioners. The standard deviation of the ARL (SDARL) metric is used to evaluate performance for various amounts of Phase I data. Surprisingly, we show that for a variety of methods no realistic Phase I sample size is sufficient to have confidence that the attained in-control performance is close to that desired. These results have significant implications on the relationship between process monitoring theory and practice. An alternative approach is presented for designing and evaluating process monitoring methods.

Location 
M3 - Mathematics 3
3127
200 University Avenue West

Waterloo, ON N2L 3G1
Canada
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