Cusum Charts for Monitoring an Autocorrelated Process

Abstract

Control charts for process monitoring have traditionally been designed and evaluated under the assumption that observations on the process output at different times are independent. However, autocorrelation may be present in many processes, and may have a strong impact on the properties of control charts. This paper investigates CUSUM control charts for monitoring the process mean for the situation in which observations from the process can be modeled as an AR(1) process plus an additional random error. CUSUM charts based on plotting the residuals from model forecasts, or on plotting the original observations, are considered. CUSUM charts based on the original observations perform as well as CUSUM charts of residuals, except in the case in which the level of autocorrelation is high and the shift in the process mean is large. A method for designing the CUSUM chart of the observations in the presence of autocorrelation is given. The CUSUM charts are compared to Shewhart and EWMA charts based on the residuals or on the original observations. The CUSUM and EWMA charts perform similarly in terms of the ability to detect shifts in the process mean.

• Autocorrelated Observations
• Autoregressive Moving Average Model
• Average Run Length
• Cumulative Sum Control Charts
• Exponentially Weighted Moving Average Control Charts
• First Order Moving Average Model
• Shewhart Control Charts
• Statistical Process Control

Additional information

Notes on contributors

Chao-Wen Lu

Dr. Lu is an Associate Professor in the Department of Finance. He is a Member of ASQ. His email address is [email protected].

Marion R. Reynolds

Dr. Reynolds is a Professor in the Departments of Statistics and Forestry. He is a Member of ASQ. His email address is [email protected].