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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.

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.

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.

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.

The proposed model can provide industry/business application for promoting the product/service quality assurance for the customer.

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.

The present paper aims to present the results of a simulation study on the behavior of the four 95 percent bootstrap confidence intervals for estimating C_pk when collected data are from a multiple streams process.

A computer simulation study is developed to present the behavior of four 95 percent bootstrap confidence intervals, i.e. standard bootstrap (SB), percentile bootstrap (PB), biased‐corrected percentile bootstrap (BCPB), and biased‐corrected and accelerated (BCa) bootstrap for estimating the capability index C_pk of a multiple streams process. An analysis of variance using two factorial and three‐stage nested designs is applied for experimental planning and data analysis.

For multiple process streams, the relationship between the true value of C_pk and the required sample size for effective experiment is presented. Based on the simulation study, the two‐stream process always gives a higher coverage percentage of bootstrap confidence interval than the four‐stream process. Meanwhile, BCPB and BCa intervals lead to better coverage percentage than SB and PB intervals.

Since a large number of process streams decreases the coverage percentage of the bootstrap confidence interval, it may be inappropriate to use the bootstrap method for constructing the confidence interval of a process capability index as the number of process streams is large.

The present paper is the first work to explore the behavior of bootstrap confidence intervals for estimating the capability index C_pk of a multiple streams process. It is concluded that the number of process streams definitively affects the performance of bootstrap methods.