Economic design of variable parameters [Xmacr ] control charts for processes with fuzzy mean shifts

• Published in: The Journal of the Operational Research Society Vol. 59; no. 8; p. 1128
• Main Authors: Chen, Y-k, Chang, H-h
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Ltd 01.08.2008
• Subjects: Control charts; Design optimization; Hypothesis testing; Mathematical programming; Sample size
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/palgrave.jors.2602461

Modern studies have shown that the [Xmacr ] control charts with variable parameters (VPs) detect process shifts faster than the traditional [Xmacr ] control charts. This article developed the economic design of the VP [Xmacr ] control chart to determine the values of the design parameters of the chart. However, this study, different from previous studies, was focused on the process that is subject to a disturbing cause, and the occurrence of the cause can result in a fuzzy mean shift (ie the magnitude of the mean shift could not be recognized exactly). The issue of economically selecting the design parameters for the chart was firstly formulated as a mathematical programming model with a fuzzy objective function that could cope with fuzzy number type of mean shift. A fuzzy-simulation-based genetic algorithm was then employed to search for the optimal values of the design parameters from the model. An industrial example was provided to illustrate the solution procedure, and was used for comparison between the VP and the traditional [Xmacr ] chart. Effects of model parameters on the solution of the economic design were also discussed. [PUBLICATION ABSTRACT]