Effects of the two-component measurement error model on X control charts

The statistical properties of Shewhart control charts are known to be highly sensitive to measurement errors. The statistical model relating the measured value to the true, albeit not observable, value of a product characteristic, is usually Gaussian and additive. In this paper we propose to extend the said model to a more general formulation by introducing the two-component error model structure. We study the effects of the proposed error-model on the performance of the mean control charts, since gauge imprecision may seriously alter the statistical properties of the control charts. In order to take measurement errors into account in the design of the control charts we explore the use of different methods based on a weighted variance concept, a skewness correction method and an empirical reference distribution approach respectively. The different approaches are discussed and compared by Monte Carlo simulation. Results indicate that the last two methods produce the best results.