RUN RULES $\bar{X}$ CHARTS WHEN PROCESS PARAMETERS ARE UNKNOWN

Abstract

Supplementary Run Rules are applied to increase the power of the standard Shewhart [Formula: see text] chart for detecting small shift. The performance of this chart is usually evaluated under the assumption of known parameters. However, in practice, the process parameters are rarely known and, usually estimated from an in-control Phase I data set. In this paper, we evaluate (using a Markov Chain model) the performances of the Run Rules [Formula: see text] chart when the process parameters are estimated, and compare them when the process parameters are assumed known. We draw the conclusion that these performances are quite different when the number of samples used during the phase I is small and we suggest new chart parameters in order to overcome this problem.