Re‐evaluation of the VSI‐ chart performance with estimated parameters

Abstract

AbstractThe performance of the variable sampling interval‐ (VSI‐ ) chart with estimated parameters has been investigated on the basis of the average time to signal (ATS) and standard deviation of time to signal (SDTS) in past research studies. Since the values of ATS and SDTS vary from practitioner to practitioner, the use of these 2 measures is not reliable. The use of different historical data sets in phase I results in varying parameter estimates, control limits, warning limits, ATS, and SDTS values. In this study, we use the standard deviation of average time to signal (SDATS) to evaluate and compare the performance of the VSI‐ chart with known parameters and estimated parameters. This study shows that variation reduction in ATS values requires a larger than previously recommended phase I data. Also, detection of up to moderate shifts in the process mean with the desired ATS value would be achievable with the number of samples recommended in the past, but the in‐control performance of the chart would not be reliable. Furthermore, we evaluate the effect of using large and small desired values of ATS0 on the performance of in‐control and out‐of‐control VSI‐ chart. We also study the effects of estimating the mean and standard deviation on the ATS values using numerical simulation. Finally, we present a method based on warning and control limits coefficients for the estimated parameters case to reduce the number of samples required in phase I.