Wimonmas Bamrungsetthapong and Sirinapa Aryuyuen

DOI: 10.14456/sjst-psu.2022.140

pp. 1075 - 1085

Abstract

A sampling plan can help to determine the quality of products, monitor the goodness of materials, and validate whether
the yields are free from defects. When the manufacturing process is precisely aligned, defects are minimized during sampling
inspection. This study proposed a multiple dependent state (MDS) sampling plan under a zero-inflated Poisson quasi-Lindley
(ZIPQL) distribution, denoted by MDS_ZIPQL to count zero-inflated data. A genetic algorithm with multi-objective optimization
was used to estimate the optimal plan parameters to maximize the probability of accepting a lot (P_a) and minimize the total cost
of inspection (TC) and the average sample number (ASN) simultaneously. A sensitivity analysis of the required sample size
assessed the performance of the proposed MDS_ZIPQL as numerical examples compared to the MDS plan under a zero-inflated
Poisson (MDS_ZIP) distribution. Simulation study results found that the required sample sizes and ASN of the MDS_ZIPQL plan were
less than the MDS_ZIP plan, indicating that the MDS_ZIPQL plan performed better than the MDS_ZIP plan regarding the required
sample size and ASN. Two real data sets were illustrated under the proposed MDS_ZIPQL plan and compared to the MDS_ZIP plan.
Results showed that the MDS_ZIPQL plan had a smaller number of required sample sizes, ASN value and TC value than the
MDS_ZIP plan (or maximum value of P_a). Therefore, the proposed MDS_ZIPQL plan was more efficient than the existing MDS_ZIP plan.

Keywords

• multiple dependent state sampling plan
• multi-objective optimization
• zero-inflated distribution
• zero-inflated
   Poisson quasi-Lindley distribution
• over-dispersion