ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS

<p>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 th...

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Main Authors: Mohammad Mirabi, Mohammad Saber Fallahnezhad
Format: Article
Language:English
Published: Stellenbosch University 2012-01-01
Series:South African Journal of Industrial Engineering
Subjects:
Online Access:http://sajie.journals.ac.za/pub/article/view/227
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author Mohammad Mirabi
Mohammad Saber Fallahnezhad
author_facet Mohammad Mirabi
Mohammad Saber Fallahnezhad
author_sort Mohammad Mirabi
collection DOAJ
description <p>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.</p><p>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 geïnspekteer 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 lê, word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die primêre 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.</p>
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spelling doaj.art-b292b1e74b54409a9d4de1f8cf8b60092022-12-21T18:18:54ZengStellenbosch UniversitySouth African Journal of Industrial Engineering1012-277X2224-78902012-01-01231ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINSMohammad MirabiMohammad Saber Fallahnezhad<p>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.</p><p>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 geïnspekteer 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 lê, word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die primêre 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.</p>http://sajie.journals.ac.za/pub/article/view/227Markov analysis of acceptance sampling plansdefective items
spellingShingle Mohammad Mirabi
Mohammad Saber Fallahnezhad
ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
South African Journal of Industrial Engineering
Markov analysis of acceptance sampling plans
defective items
title ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
title_full ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
title_fullStr ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
title_full_unstemmed ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
title_short ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
title_sort analysing acceptance sampling plans by markov chains
topic Markov analysis of acceptance sampling plans
defective items
url http://sajie.journals.ac.za/pub/article/view/227
work_keys_str_mv AT mohammadmirabi analysingacceptancesamplingplansbymarkovchains
AT mohammadsaberfallahnezhad analysingacceptancesamplingplansbymarkovchains