Bayesian Two-sided Complete Group Chain Sampling Plan for Binomial Distribution using Beta Prior through Quality Regions

Acceptance sampling is a technique for statistical quality assurance based on the inspection of a random sample to decide the lot disposition: accept or reject. Producer’s risk and consumer’s risk are inevitable in acceptance sampling. Most conventional plans only focus on minimizing the consumer’s risk. This study focused on minimizing both producer’s and consumer’s risks through the quality region. Experts from available historical knowledge concurred that Bayesian is the best approach to make the correct decision. In this study, a Bayesian two-sided complete group chain sampling plan (BTSCGChSP) was proposed for the average probability of acceptance. The binomial distribution was used to derive the probability of lot acceptance, and the beta distribution was used as the prior distribution. For selected design parameters in BTSCGChSP, the acceptable quality level and limiting quality level were considered to estimate quality regions that were directly associated with producer’s and consumer’s risks, respectively. Four quality regions: (i) quality decision region , (ii) probabilistic quality region (PQR), (iii) limiting quality region, and (iv) indifference quality region, were evaluated. To compare with the existing Bayesian group chain sampling plan (BGChSP), operating characteristic curves were used for the same parameter values and probability of lot acceptance. The findings explained that BTSCGChSP provided a smaller proportion of defectives than BGChSP for the same probability of acceptance. If quality regions were found for the same values of consumer and producer risks, then the BTSCGChSP region would contain fewer defectives than in the BGChSP region. Therefore, for industrial practitioners, the proposed plan is a better substitute for existing BGChSP and other conventional plans.

Designing a Repetitive Group Sampling Plan for Weibull Distributed Processes

Acceptance sampling plans are useful tools to determine whether the submitted lots should be accepted or rejected. An efficient and economic sampling plan is very desirable for the high quality levels required by the production processes. The process capability indexCLis an important quality parameter to measure the product quality. Utilizing the relationship between theCLindex and the nonconforming rate, a repetitive group sampling (RGS) plan based onCLindex is developed in this paper when the quality characteristic follows the Weibull distribution. The optimal plan parameters of the proposed RGS plan are determined by satisfying the commonly used producer’s risk and consumer’s risk at the same time by minimizing the average sample number (ASN) and then tabulated for different combinations of acceptance quality level (AQL) and limiting quality level (LQL). The results show that the proposed plan has better performance than the single sampling plan in terms of ASN. Finally, the proposed RGS plan is illustrated with an industrial example.

Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

We investigate the optimal designing of chain sampling plan for the application of normally distributed quality characteristics. The chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be useful when testing is costly and destructive. The advantages of this proposed variables plan over variables single sampling plan and variables double sampling plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables chain sampling plan for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level, along with the producer’s and consumer’s risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

VARIABLES QUICK SWITCHING SYSTEM WITH DOUBLE SPECIFICATION LIMITS

This paper investigates a variables quick switching sampling system when a measurable quality characteristic has double specification limits beyond which an item is considered to be a nonconforming. The quality characteristic of interest is assumed to follow a normal distribution. The optimal parameters of the variables quick switching system are determined for both known and unknown standard deviations which satisfy the producer's and consumer's risks at the corresponding specified quality levels. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. The problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to a lot of acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.