Variable parameter and double sampling [formula omitted] charts in the presence of correlation: The Markov chain approach

Abstract

The general assumption under which the X ¯ chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the X ¯ chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the X ¯ chart. The performance of the X ¯ chat with variable parameters and the X ¯ with double sampling are compared.