Optimum process mean, standard deviation and specification limits settings under the Burr distribution

Abstract

Purpose The quality level setting problem determines the optimal process mean, standard deviation and specification limits of product/process characteristic to minimize the expected total cost associated with products. Traditionally, it is assumed that the product/process characteristic is normally distributed. However, this may not be true. This paper aims to explore the quality level setting problem when the probability distribution of the process characteristic deviates from normality. Design/methodology/approach Burr developed a density function that can represent a wide range of normal and non-normal distributions. This can be applied to investigate the effect of non-normality on the studies of statistical quality control, for example, designs of control charts and sampling plans. The quality level setting problem is examined by introducing Burr’s density function as the underlying probability distribution of product/process characteristic such that the effect of non-normality to the determination of optimal process mean, standard deviation and specification limits of product/process characteristic can be studied. The expected total cost associated with products includes the quality loss of conforming products, the rework cost of non-conforming products and the scrap cost of non-conforming products. Findings Numerical results show that the expected total cost associated with products is significantly influenced by the parameter of Burr’s density function, the target value of product/process characteristic, quality loss coefficient, unit rework cost and unit scrap cost. Research limitations/implications The major assumption of the proposed model is that the lower specification limit must be positive for practical applications, which definitely affects the space of feasible solution for the different combinations of process mean and standard deviation. Social implications The proposed model can provide industry/business application for promoting the product/service quality assurance for the customer. Originality/value The authors adopt the Burr distribution to determine the optimum process mean, standard deviation and specification limits under non-normality. To the best of their knowledge, this is a new method for determining the optimum process and product policy, and it can be widely applied.