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.
Mathematics Subject Classification: