Designing of Double Acceptance Sampling Plan for Zero-inflated and Over-dispersed Data Using Multi-objective Optimization
The double acceptance sampling plan (DSP) is wildly used tools for the decision of production quality control. In actually, most production processes have excellent quality control and well inspected, the number of defective items for many samples will be zero. For this reason, the traditional probability distribution is not appropriate for the DSP. This research proposed the DSP for the manufacturing that was affected by zero-inflated and over-dispersed count data. The number of defects for a sample inspection is considered under the zero-inflated Negative Binomial (ZINB) distribution. The required sample sizes (n1, n2) are designed to achieve the optimal plan parameter of (n1, n2, c1, c2)* the DSP under the ZINB distribution (DSPZINB). The Genetic Algorithm with multi-objective optimization is used to estimate the optimal plan parameters which are maximizing the probability of accepting a lot (Pa) and minimizing the total cost of inspection (TC) and the average number of samples (ASN) simultaneously. The sensitivity analysis of the required sample size is used to analyze the performance of the proposed DSPZINB which is presented through three numerical examples. The results showed that a smaller of required sample sizes and n1 < n2 are provide the optimal plan parameters to achieve the minimum and maximum value of the multi-objective function. Moreover, the proposed DSPZINB give a good performance when a shape parameter of ZINB distribution (k) is small and approaches zeros while a zero-inflation parameter (ϕ) is a large value.
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