Effect of measurement error on phase II monitoring of simple linear profiles

In this paper, we study the effect of classical additive measurement error model on the most commonly used control charts for monitoring simple linear profiles with random explanatory variable. We showed that the in-control and out-of-control performances of these methods are significantly affected when measurement error is present in the explanatory variable. The average run length criterion is applied to represent the performance of the methods. For instance, we can clearly see that even a small amount of measurement error introduced in the explanatory variable of a profile can increase the false alarm rate about 55 %. With the same negligible amount of error, the out-of-control average run length of the exponentially weighted moving average chart (EWMA)-3 method in detecting a moderate-size shift in the slope parameter increases 15 %. Two different strategies on the basis of control limit modification have been proposed to compensate for the undesired effect of measurement error. Results indicate that the proposed strategies substantially offset the poor performances of the control charts resulted from the presence of measurement error.