Adeyeye, Sunday I. and Adewara, Ademola J. and Gadde, Rao S. and Adekeye, Samuel K. and Adedotun, Adedayo F. and Aako, Lawrence O. (2023) DESIGN OF MULTIPLE DEPENDENT STATE SAMPLING PLAN USING ZECH DISTRIBUTION WITH APPLICATION TO REAL LIFE DATA. RT&A, 74 (3). pp. 471-481.
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Abstract
In this work, a multiple dependent state sampling plan, which is an inspection procedure that determines whether an attribute is conforming or non-conforming to a specific requirement, in which the decision criterion for each lot dictates whether to accept the lot; reject the lot; or conditionally accept or reject the lot based on the disposition of future related lots, is introduced. This plan has some advantages over other acceptance sampling plans, like increased efficiency, improved ability to discriminate between acceptable and non – acceptable lots or batches, flexibility in designing the sampling process, and improved cost-effectiveness. To reject a lot, the plan made use of the properties of the sampled current and preceding lots. The study aims to reduce the average sampling number by using a non-linear optimization problem that is subjected to some constraints. With regards to a life test that is truncated in time, the product’s median life was used for the proposed sampling plan assuming that the lifetime of the product follows Zech distribution. The usage of median life was necessitated because Zech distribution is an asymmetric distribution with longer tail to the right. Two points on the operating characteristic curve were used for the proposed sampling plan and the following parameters were found; number of preceding lots which is required for deciding if the current lot should be accepted or rejected, the size of the sample, rejection number, and acceptance number. For different shape parameters, we constructed tables for various combinations of consumers’ and producers’ risks. A real example was provided which showed that a multiple dependent state sampling plan is a good sampling plan for fitting the datasets. Comparing the proposed plan with a single sampling plan, the results reveal that the proposed plan is more effective at securing the consumer and the producer with less inspection. The approach introduced in this study provides an ample opportunity for the manufacturers to reduce the cost and time of inspection by having the sample size reduced without compromising the decision-making accuracy. By implementing the findings of this study, the consumers are confident that their hard-earned money is not used to purchase sub-standard goods.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Acceptance Sampling, Zech Distribution, MDSSP, Single Sampling Plan, Operating Characteristic Curve, Average Sampling Number. |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |
| Depositing User: | nwokealisi |
| Date Deposited: | 10 Nov 2023 11:38 |
| Last Modified: | 10 Nov 2023 11:38 |
| URI: | http://eprints.covenantuniversity.edu.ng/id/eprint/17557 |
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