A dynamic economic model for an x-control chart design.: An article from: IIE Transactions
Book Details
Author(s)Hiroshi Ohta, M.A. Rahim
ISBN / ASINB00097PYIC
ISBN-13978B00097PYI8
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This digital document is an article from IIE Transactions, published by Institute of Industrial Engineers, Inc. (IIE) on June 1, 1997. The length of the article is 3822 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.
From the author: Parkhideh and Case (IIE Transactions, 21, 313-323 (1989)) developed an economic model for a dynamic x-control chart. In developing the model they considered six decision variables in their design methodology. It therefore became very complicated to obtain the optimal combination that resulted in the minimum loss-cost. This note proposes an alternative and simplified design methodology that reduces the number of design variables from six to three. The optimal values are obtained by imposing the following constraints. The optimal sampling interval [h.sub.i] (i = 1, 2, . . .) is chosen such that the integrated hazard rate over each sampling interval is constant. The optimal sample size [n.sub.i] (i = 1, 2, . . .) is chosen such that the relative sample size per unit time during each sampling interval is constant. Analogously, the optimal control limit coefficient [k.sub.i] (i = 1, 2, . . .) is chosen so that the power of the control charts remains constant over each sampling interval. The process failure mechanism is assumed to follow a Weibull shock model and the product quality characteristic is considered to be normal. Computational experience indicates that the proposed dynamic nonuniform control chart design is much simpler and provides a lower cost than that of Parkhideh and Case's dynamic model.
Citation Details
Title: A dynamic economic model for an x-control chart design.
Author: Hiroshi Ohta
Publication:IIE Transactions (Refereed)
Date: June 1, 1997
Publisher: Institute of Industrial Engineers, Inc. (IIE)
Volume: v29 Issue: n6 Page: p481(6)
Distributed by Thomson Gale
From the author: Parkhideh and Case (IIE Transactions, 21, 313-323 (1989)) developed an economic model for a dynamic x-control chart. In developing the model they considered six decision variables in their design methodology. It therefore became very complicated to obtain the optimal combination that resulted in the minimum loss-cost. This note proposes an alternative and simplified design methodology that reduces the number of design variables from six to three. The optimal values are obtained by imposing the following constraints. The optimal sampling interval [h.sub.i] (i = 1, 2, . . .) is chosen such that the integrated hazard rate over each sampling interval is constant. The optimal sample size [n.sub.i] (i = 1, 2, . . .) is chosen such that the relative sample size per unit time during each sampling interval is constant. Analogously, the optimal control limit coefficient [k.sub.i] (i = 1, 2, . . .) is chosen so that the power of the control charts remains constant over each sampling interval. The process failure mechanism is assumed to follow a Weibull shock model and the product quality characteristic is considered to be normal. Computational experience indicates that the proposed dynamic nonuniform control chart design is much simpler and provides a lower cost than that of Parkhideh and Case's dynamic model.
Citation Details
Title: A dynamic economic model for an x-control chart design.
Author: Hiroshi Ohta
Publication:IIE Transactions (Refereed)
Date: June 1, 1997
Publisher: Institute of Industrial Engineers, Inc. (IIE)
Volume: v29 Issue: n6 Page: p481(6)
Distributed by Thomson Gale
