An Integrated Approach for Designing a Phase I c-Control Chart Based on the Phase II Performance of Poisson Exponentially Weighted Moving Average Control Chart

Ugur Murat, Murat Caner Testik () and Christian H. Weiß ()
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Ugur Murat: Hacettepe University, Department of Industrial Engineering
Murat Caner Testik: Hacettepe University, Department of Industrial Engineering
Christian H. Weiß: Helmut Schmidt University Hamburg, Department of Mathematics and Statistics

A chapter in Advanced Statistical Methods in Process Monitoring, Finance, and Environmental Science, 2024, pp 173-194 from Springer

Abstract: Abstract A control chart implementation in practice generally consists of two stages: Phase I for control chart design and Phase II for process monitoring. It is well known that the choice and design of a control chart have significant effects on its performance. In this study, a Shewhart c-control chart is considered for the Phase-I study. The effects of parameter estimation in Phase I on the Phase-II performance of the Poisson exponentially weighted moving average (PEWMA) control chart are investigated. Chart designs are evaluated by taking a holistic approach for Phase I and Phase II. In this context, the out-of-control behavior of the process in Phase I is simulated for various shift and contamination scenarios, together with the c-chart implementation for parameter estimation. For each simulation replication, the Markov chain approach is used to calculate the average run length (ARL) performance in Phase II. Obtaining the ARL distributions for different design parameter and simulation variable combinations, the performances of different designs are evaluated. Using a scheme based on the average of ARL performances in Phase II, control limit widths are determined for Phase-I analysis. Practical suggestions are provided for real-world implementations.

Keywords: Process monitoring; PEWMA control chart; c-control chart; Phase-I and Phase-II analyses; Parameter estimation; Simulation; Markov chains (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-69111-9_8

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