The Exact Run Length Distribution and Design of the Shewhart Chart with Estimated Parameters Based on Median Run Length. Issue 6 (2nd July 2016) - Teoh, W. L.; Khoo, Michael B. C.; Castagliola, Philippe; Lee, M. H.
Abstract : This paper investigates the Shewhart chart with estimated parameters. When parameters are unknown, we show that the average run length is a confusing performance measure and that the median run length, which is a better representation of the central tendency associated with different shapes of the run length distribution, is more intuitive. A new design model for the Shewhart chart with estimated parameters is developed. With this proposed design model, the Shewhart chart for both known and estimated parameters, even with a small number of Phase-I samples, will have an almost similar sensitivity for a specified shift.