ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Optimal Design of Xbar Control Charts under Bathtub-shaped Shock Models with Application of Total Time on Test Plot

13 September 2017, 10:10 – 10:30

Abstract

Submitted by
Shabnam Fani
Authors
Shabnam Fani (Allameh Tabataba'i University), Mojtaba A. Pasha (Allameh Tabataba'i University), Mohammad B. Moghadam (Allameh Tabataba'i University)
Abstract
Some recent research in statistical quality control has paid attention to the economic and economic statistical design of X bar-control charts for monitoring the mean variation of a production process. The majority of these studies assumed that the process failure mechanism or the shock model obeys a lifetime distribution with monotone hazard rate such as exponential, Weibull, and Gamma. However, virtually sparse research efforts have been investigated non-monotone failure mechanism such as bathtub or U-shaped. In order to choose a more precise lifetime distribution, we propose to apply the total time on test plot as a great tool for identification of the shape of failure data set. Based on the result of this plot, an appropriate distribution will be picked out whose unknown parameters can be estimated by the maximum likelihood method. Finally, the optimal parameters of both the economic and economic statistical design of Xbar-control charts for systems with bathtub-shaped shock models can be determined by adapting the non-uniform generalized cost model of Rahim and Banerjee (1993). A numerical study is presented to illustrate the proposed approach for a exact failure time data set.

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