On the Robustness of the Shewhart Control Chart to Different Types of Dependencies in Data

Abstract

Shewhart control charts were originally designed under the assumption of independence of consecutive observations. In the presence of dependence the authors usually assume dependencies in the form of autocorrelated and normally distributed data. However, there exist many other types of dependencies which are described by other mathematical models. The question arises then, how classical control charts are robust to different types of dependencies. This problem has been sufficiently well discussed for the case of autocorrelated and normal data. In the paper we use the concept of copulas to model dependencies of other types. We use Monte Carlo simulation experiments to investigate the impact of type and strength of dependence in data on the value of the ARL of Shewhart control charts.

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