Economic Design of Cumulative Sum Control Chart for Non-Normally Correlated Data

Abstract

Traditionally, one usually assumes that the measurements within a sample are independently and normally distributed when designing the control charts. However, this assumption may not be tenable in practice. In this study, the economic design of cumulative sum (CUSUM) control chart for non-normally correlated data is developed. The optimal design parameters are determined such that the cost function is minimized, in which the Burr distribution is used to represent various types of non-normal distribution. The numerical results show that skewness coefficient, kurtosis coefficient and correlation coefficient affect the economic design of the CUSUM chart. Keywords: Economic design; cumulative sum chart; non-normality; correlation; genetic algorithm 2010 Mathematics Subject Classification 62K05, 62P30.