A mathematical model for the joint determination of optimal process and sampling plan parameters

Abstract

Purpose

The purpose of this paper is to integrate the decisions regarding optimal process mean and the parameters of a sampling plan.

Design/methodology/approach

A model is developed to determine these parameters. The model maximizes producer expected profit, while protecting the consumer through a constraint on the probability of accepting lots with low incoming quality. The model is presented for two cases. The first one is for non‐destructive testing and the other for destructive testing. An example is presented to demonstrate that the utility of the model and sensitivity analysis on key parameters of the model has been conducted.

Findings

The findings indicated that the optimal parameters for the process and the sampling plan are significantly different from when determined separately. The sensitivity analysis showed that the process parameters are very sensitive to changes in the process variance, moderately sensitive to the limit on incoming quality, and insensitive to the consumer risk and inspection cost.

Practical implications

The models developed offer an alternative approach for quality managers to address setting process targets, taking into consideration a sampling plan.

Originality/value

The originality of the paper is in the integration of two elements of quality that are usually treated separately in the literature.

Citation

Darwish, M.A. and Duffuaa, S.O. (2010), "A mathematical model for the joint determination of optimal process and sampling plan parameters", Journal of Quality in Maintenance Engineering, Vol. 16 No. 2, pp. 181-189. https://doi.org/10.1108/13552511011048913