Optimal monitoring of Poisson data with known and unknown shifts. (April 2021)

• Record Type: Journal Article
• Authors: Wang, Junjie; Chong, Zhi Lin; Qiu, Peihua
• Is Part Of: Computers & industrial engineering. Volume 154(2021)
• Publication Date: 2021-04
• Subjects: Count data -- Expected average run length -- Fibonacci search algorithm -- Poisson EWMA chart -- Statistical process control; Engineering -- Data processing -- Periodicals; Industrial engineering -- Periodicals; 620.00285
• DOI: 10.1016/j.cie.2021.107100
• Languages: English
• ISSNs: 0360-8352

Abstract

Highlights: Known and unknown shift information are integrated respectively into the optimal design of Poisson EWMA charting scheme. The existence of a unique solution to the optimization problem is proved based on numerous simulation results. The Fibonacci search algorithm is proposed to find out the optimal parameter in a short time. Simulation results and two real applications show the satisfactory performance of proposed methods. Abstract: The number of event occurrences, called counts are prevalent in many fields such as manufacturing industry and public health. Control charts have been widely employed to monitor such count data for quality improvement of products or medical service by assuming the data follows the Poisson distribution. However, the shift information of Poisson mean has not been well considered in current design of the exponentially weighted moving average (EWMA) control chart. This article studies the optimal design of the Poisson EWMA chart with known and unknown shift sizes integrated respectively in order to bridge the research gap. We simplify these two optimization problems to searching for a unique smoothing parameter in minimizing the out-of-control (OC) average run length (ARL) and OC expected ARL (EARL) over random shifts respectively. Due to the intractability of obtaining a closed-form solution, the Fibonacci search algorithm is proposed to find out the optimal smoothing parameter in a short time. The satisfactory performance of proposed optimal design method is demonstrated by numerous simulation results and two real datasets from manufacturing industry and public health.