Design of a Self-Starting Combined Shewhart-CUSUM Chart for Short Run Scenarios

Statistical Process Control/Monitoring (SPC/M) in short run scenarios, here understood as processes that generate low volumes of data and require monitoring from process start-up along with online estimates of the process parameters, is a challenging endeavor. Self-starting control charts were introduced to meet this challenge and, in this paper, the design and performance of a self-starting extension to the Combined Shewhart-CUSUM (CSC) chart is discussed. The CSC chart is a mixed method SPC/M-scheme that combines the Shewhart chart's capability to effectively detect large transient shifts with the cumulative sum chart's capability to detect small to medium sized persistent shifts in a process parameter's underlying distribution. Albeit its usefulness in monitoring processes that are prone to persistent and transient shifts, research into the design of a CSC chart for monitoring individual and continuous observations in short run processes is nonexistent. This paper introduces a self-starting extension of the CSC chart and gives some consideration to its optimal design. In contrast to previous research on Q-statistics, it is argued in favor of a CUSUM reference value close to CUSUM-optimality. The paper is considered of interest to industrial and systems researchers, as well as engineers with an interest in SPC/M.