Variable parameter and double sampling X¯ charts in the presence of correlation: The Markov chain approach

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.