A Self-Starting CUSUM Chart Combined with a Maximum Likelihood Estimator for the Time of a Detected Shift in the Process Mean

作者：Tercero Gomez Victor G^*; Cordero Franco Alvaro; Perez Blanco Angel; Hernandez Luna Alberto

来源：Quality and Reliability Engineering International, 2014, 30(4): 591-599.

DOI：10.1002/qre.1511

• change-point estimation
• SPC
• control chart
• unknown parameters
• normal distribution

Detection of a special cause of variation and the identification of the time it occurs are two important activities in any quality improvement strategy. Detection of changes in a process can be done using control charts. One of these charts, the self-starting CUSUM chart, was created to detect small sustained changes and be implemented without a Phase I or a priori knowledge of the parameters of the process. To estimate the time of a detected change, a CUSUM-based change-point estimator can be used, but experiments show that the corresponding MLE has smaller bias and standard error. This paper proposes the sequential use of the self-starting CUSUM chart and the MLE of a change point in series of independent normal observations. Performance is studied with Monte Carlo simulations showing that the use of the MLE reduces the bias of the change-point estimation. It is also shown how extra observations after a change is detected can be used to improve estimation of the change-point time.

• 出版日期2014-6