Title: Minimum loss design of asymmetric X and S control charts under two independent Weibull shocks

Authors: Su-Fen Yang, M.A. Rahim

Addresses: Department of Statistics, National Chengchi University, Taipei, 116, Taiwan, ROC. ' Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Abstract: This paper proposes a minimum loss cost model for the joint economic design of an x-bar chart and an s-control chart for monitoring both the process mean and process variance simultaneously. The process is subject to the occurrences of two independent Weibull shocks each having increasing failure rates. One shock shifts the process mean and the other shock changes the process variance. When the failure mechanism obeys a Weibull shock model, the length of the sampling interval should vary with the age of the system. This approach is more appropriate than the traditional uniform sampling approach to keep the length of sampling intervals constant. The loss cost model, including an asymmetric quadratic loss function, emphasises the importance of continuously reducing performance variation and overcomes the difficulty in estimating various quality costs. Application of the proposed model is demonstrated through numerical examples.

Keywords: Weibull shock model; x-bar charts; s-control charts; renewal reward processes; control charts; SPC; statistical process control; minimum loss cost models.

DOI: 10.1504/IJPQM.2009.023697

International Journal of Productivity and Quality Management, 2009 Vol.4 No.3, pp.247 - 282

Available online: 08 Mar 2009 *

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