  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.
