Risk‐based metrics for performance evaluation of control charts

Abstract

AbstractControl charts are commonly evaluated in terms of their average run length (ARL). However, since run length distributions are typically strongly skewed, the ARL gives a very limited impression about the actual run length performance. In this study, it is proposed to evaluate a control chart's performance using risk metrics, specifically the value at risk and the tail conditional expectation. When a control chart is evaluated for an in‐control performance, the risk is an early occurrence of a false alarm, whereas in an out‐of‐control state, there is a risk of a delayed detection. For these situations, risk metric computations are derived and exemplified for diverse types of control charts. It is demonstrated that the use of such risk metrics leads to important new insights into a control chart's performance. In addition to the cases of known process parameters for control chart design, these risk metrics are further used to analyze the estimation uncertainty in evaluating a control chart's performance if the design parameters rely on a phase 1 analysis. Benefits of the risk‐based metrics are discussed thoroughly, and these are recommended as supplements to the traditional ARL metric.