Change Point Estimation of a Process Variance with a Linear Trend Disturbance

Abstract

When a change occurs in a process, one expects to receive a signal from a control chart as quickly as possible. Upon the receipt of signal from the control chart a search for identifying the source of disturbance begins. However, searching for assignable cause around the signal time, due to the fact that the disturbance may have manifested itself into the rocess sometimes back, may not always lead to successful identification of assignable cause(s). If process engineers could identify the change point, i.e. the time when the disturbance first manifested itself into the process, then corrective actions could be directed towards effective elimination of the source of disturbance. In this paper we develop a maximum likelihood estimator (MLE) for process change point designed to detect changes in process variance of a normal quality characteristic when the change follows a linear trend. We describe how this estimator can be used to identify the change point when a Shewhart S-control chart signals a change in the process variance. Numerical results reveal that the proposed estimator outperforms the MLE designed for step change when a linear trend disturbance is present.

Keywords

• Assignable cause
• Change point estimation
• Maximum Likelihood Estimator
• Newton method
• Shewhart S-control chart
• Statistical process control