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Publication date: 17 January 2023

Razieh Seirani, Mohsen Torabian, Mohammad Hassan Behzadi and Asghar Seif

The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian X…

93

Abstract

Purpose

The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian X control chart based on predictive distribution with two types of informative and noninformative prior distributions.

Design/methodology/approach

The design used in this study is based on determining the control chart of the predictive distribution and then its ESD. The new proposed cost model is presented by considering the conjugate and Jeffrey's prior distribution in calculating the expected total cycle time and expected cost per cycle, and finally, the optimal design parameters and related costs are compared with the fixed ratio sampling (FRS) mode.

Findings

Numerical results show decreases in costs in this Bayesian approach with both Jeffrey's and conjugate prior distribution compared to the FRS mode. This result shows that the Bayesian approach which is based on predictive density works better than the classical approach. Also, for the Bayesian approach, however, there is no significant difference between the results of using Jeffrey's and conjugate prior distributions. Using sensitivity analysis, the effect of cost parameters and shock model parameters and deviation from the mean on the optimal values of design parameters and related costs have been investigated and discussed.

Practical implications

This research adds to the body of knowledge related to quality control of process monitoring systems. This paper may be of particular interest to quality system practitioners for whom the effect of the prior distribution of parameters on the quality characteristic distribution is important.

Originality/value

economic statistical design (ESD) of Bayesian control charts based on predictive distribution is presented for the first time.

Details

International Journal of Quality & Reliability Management, vol. 40 no. 8
Type: Research Article
ISSN: 0265-671X

Keywords

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Article
Publication date: 17 January 2023

Salimeh Sadat Aghili, Mohsen Torabian, Mohammad Hassan Behzadi and Asghar Seif

The purpose of this paper is to develop a double-objective economic statistical design (ESD) of (X…

177

Abstract

Purpose

The purpose of this paper is to develop a double-objective economic statistical design (ESD) of (X) control chart under Weibull failure properties with the Linex asymmetric loss function. The authors have expressed the probability of type II error (β) as the statistical objective and the expected cost as the economic objective.

Design/methodology/approach

The design used in this study is based on a double-objective economic statistical design of (X) control chart with Weibull shock model via applying Banerjee and Rahim's model for non-uniform and uniform schemes with Linex asymmetric loss function. The results in the least average cost and β in uniform and non-uniform schemes by Linex loss function, compared with the same schemes without loss function.

Findings

Numerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the X control chart in practice. When the authors use non-uniform schemes instead of uniform schemes, the average cost per unit time decreases by an average and when the authors apply loss function, the average cost per unit time increases by an average. Also, this quantity for double-objective schemes with loss function compared to without loss function schemes in cases uniform and non-uniform increases. The reason for this result is that the model underestimated the costs before using the loss function.

Practical implications

This research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.

Originality/value

The cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.

Details

International Journal of Quality & Reliability Management, vol. 40 no. 8
Type: Research Article
ISSN: 0265-671X

Keywords

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