Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance

In statistical process control (SPC), when dealing with a quality characteristic x that is a variable, it is usually necessary to monitor both the mean value and variability. This article proposes an optimization algorithm (called the holistic algorithm) to design the CUSUM charts for this purpose....

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Bibliographic Details
Published in:European journal of operational research 2010-08, Vol.205 (1), p.136-150
Main Authors: Wu, Zhang, Yang, Mei, Khoo, Michael B.C., Yu, Fong-Jung
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Computer science
control theory
systems
Control charts
Control theory. Systems
Exact sciences and technology
Inventory control, production control. Distribution
Loss function
Markov processes
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Process control. Computer integrated manufacturing
Process controls
Quality control
Quality control chart
Quality control Loss function Markov processes Quality control chart Statistical process control
Statistical process control
Studies
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Summary:In statistical process control (SPC), when dealing with a quality characteristic x that is a variable, it is usually necessary to monitor both the mean value and variability. This article proposes an optimization algorithm (called the holistic algorithm) to design the CUSUM charts for this purpose. It facilitates the determination of the charting parameters of the CUSUM charts and considerably or significantly increases their overall detection effectiveness. A single CUSUM chart (called the ABS CUSUM chart) has been developed by the holistic algorithm and fully investigated. This chart is able to detect two-sided mean shifts and increasing variance shifts by inspecting the absolute value of sample mean shift. The results of performance studies show that the overall performance of the ABS CUSUM chart is nearly as good as an optimal 3-CUSUM scheme (a scheme incorporating three individual CUSUM charts). However, since the ABS CUSUM chart is easier for implementation and design, it may be more suitable for many SPC applications in which both mean and variance of a variable have to be monitored.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2009.12.005