Design of Optimal Exponential CUSUM Control Charts

Abstract

Control charts are needed in many manufacturing processes for monitoring the rate of occurrences of events such as nonconforming items. This rate can usually be modeled by the interarrival times for a homogeneous Poisson process, which are independent and identically distributed exponential random variables. The monitoring of the exponential mean provides an alternative method for monitoring the rate of occurrences of events. An extensive numerical study indicates that the reference value k obtained from the sequential probability ratio test is the optimal chart parameter k for the exponential CUSUM chart. Graphs of chart parameters are given and these graphs can be used to easily obtain the chart parameters of an optimal exponential CUSUM chart. The relative performance of exponential CUSUM and Poisson CUSUM charts for monitoring the rate of occurrences of events is also assessed.

• Average Run Length
• Cumulative Sum Control Charts
• Exponential Distribution
• Poisson Process

Additional information

Notes on contributors

F. F. Gan

Dr. Gan is a Statistical Consultant and Senior Lecturer in the Department of Mathematics. He is a Member of ASQC.