The development and evaluation of CUSUM-based control charts for an AR(1) process

An important component of the quality program of many manufacturing operations is the use of control chart for variables. Inherent in the construction of these control charts is the assumption that the sampled process is a normal distribution whose observations are independent and identically distributed (iid). Many processes such as those found in chemical manufacturing, refinery operations, smelting operations, wood product manufacturing, waste-water processing and the operation of nuclear reactors have been shown to have autocorrelated observations. Autocorrelation, which violates the independence assumption of standard control charts, is known to have an adverse effect on the average run length (ARL) performance of control charts. This paper will consider a statistical testing procedure for the change-point problem for monitoring the level parameter of the AR(1) process. This test is shown to result in a CUSUM-based control chart. Two different solutions of the change-point problem are given which result in slightly different control charts. The average run length of each of these CUSUM control charts is found via the Markov chain approach. A methodology for designing the CUSUM-based control chart is presented and the performance of these control charts is compared to other approaches in the literature.