The Effect of Autocorrelation on the Shewhart-RZ Control Chart

In many industrial manufacturing processes, the quality of products depends on the relation between two main ingredients or characteristics. Often, this calls for monitoring the ratio of two normal random variables with statistical process control (SPC) techniques. A large number of studies related to designing control charts monitoring this ratio have been published. However, these studies are based purely on the assumption of independent observations. In practice, autocorrelation between observations can exist and should be modeled to protect against the false alarm rate inflation when implementing a control chart. In this paper, we tackle this problem by investigating the performance of the Shewhart control chart monitoring the ratio of two normal variables, (denoted as Shewhart-RZ), in the presence of autocorrelation between successive observations. The autocorrelation is modeled through the bivariate autoregressive model VAR(1). We also provide an example to illustrates the use of the Shewhart-RZ control chart on a quality control problem.