Economic design of X‾$\bar{X}$ control charts with multiple assignable causes under Burr XII shock model

Aitin Saadatmelli, M. Bameni Moghadam, Asghar Seif and Alireza Faraz

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 3, 500-522

Abstract: The economic design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects, one of the proper alternatives may be the Burr XII (Burr) distribution which is quite flexible and its hazard rate can be fixed, increasing, decreasing, single mode or even U-shaped. Yet, in Burr distribution context, only one assignable cause model were considered where more realistic approach may be to consider multiple assignable causes. Thus, in this paper, an economic design of the X‾$\bar{X}$ control charts under the Burr shock model and multiple assignable causes were considered and compared with three types of prior distribution for the mean shift parameter. Also, a numerical example and a sensitivity analysis for more illustration and studying the effect of changing parameters of the shock model distribution on the optimum values of proposed design models were conducted, respectively. The results indicate that when the prior distribution is of negative exponential distribution, the multiple assignable cause models under Burr XII (Burr) distribution have minimum loss-cost.

Date: 2019
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DOI: 10.1080/03610926.2017.1414262

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