ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS

Mohammad Mirabi, Mohammad Saber Fallahnezhad

Abstract


ENGLISH ABSTRACT: In this research, a Markov analysis of acceptance sampling plans in a single stage and in two stages is proposed, based on the quality of the items inspected. In a stage of this policy, if the number of defective items in a sample of inspected items is more than the upper threshold, the batch is rejected. However, the batch is accepted if the number of defective items is less than the lower threshold. Nonetheless, when the number of defective items falls between the upper and lower thresholds, the decision-making process continues to inspect the items and collect further samples. The primary objective is to determine the optimal values of the upper and lower thresholds using a Markov process to minimise the total cost associated with a batch acceptance policy. A solution method is presented, along with a numerical demonstration of the application of the proposed methodology.

AFRIKAANSE OPSOMMING: In hierdie navorsing word n Markov-ontleding gedoen van aannamemonsternemingsplanne wat plaasvind in n enkele stap of in twee stappe na gelang van die kwaliteit van die items wat gespekteer word. Indien die eerste monster toon dat die aantal defektiewe items n boonste grens oorskry, word die lot afgekeur. Indien die eerste monster toon dat die aantal defektiewe items minder is as n onderste grens, word die lot aanvaar. Indien die eerste monster toon dat die aantal defektiewe items in die gebied tussen die boonste en onderste grense l word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die prime doel is om die optimale waardes van die booonste en onderste grense te bepaal deur gebruik te maak van n Markov-proses sodat die totale koste verbonde aan die proses geminimiseer kan word. n Oplossing word daarna voorgehou tesame met n numeriese voorbeeld van die toepassing van die voorgestelde oplossing.


Keywords


Markov analysis of acceptance sampling plans; defective items

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DOI: https://doi.org/10.7166/23-1-227

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Copyright (c) 2015 The South African Journal of Industrial Engineering


ISSN 2224-7890 (on-line) ; ISSN 1012-277X (print)


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