Adaptive control charts: A Markovian approach for processes subject to independent disturbances

Recent studies have shown that adaptive X¯ control charts are quicker than traditional X¯ charts in detecting small to moderate shifts in a process. In this article, we propose a joint statistical design of adaptive X¯ and R charts having all design parameters varying adaptively. The process is subjected to two independent assignable causes. One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. It is assumed that the quality characteristic is normally distributed and the time that the process remains in control has exponential distribution. Performance measures of these adaptive control charts are obtained through a Markov chain approach.