Performance Analysis of Cumulative Sum Control Charts Based on Parameter Estimation

Abstract

Abstract As an important means of quality monitoring, Cumulative Sum (CUSUM) control charts can quickly detect whether the production process is out of control. However, in the actual production process, the parameters required for the control chart-the overall mean and standard deviation are usually unknown, so it needs to be accurately estimated. This paper uses multiple estimators to estimate the mean and variance of the population by using samples in phase I. When the testing process in phase II is out of control, this paper analyzes the influence of each estimator combination on the cumulative sum control chart based on running length distribution of control charts. This paper comprehensively analyzes the average, standard deviation and percentile of the control chart running length in four different environments in order to find the parameter combination that optimizes the control chart performance. The research results show that the CUSUM control chart based on X ¯ ¯ − σ ^ p o o l e d and W H ¯ − σ ^ H o z o estimators performs best in a non-polluted environment, while the control chart based on X ¯ ¯ − σ ^ I Q R and W H ¯ − σ ^ I Q R estimators performs best in a polluted environment.