Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution

Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam and Abdur Razzaque Mughal
Additional contact information
Muhammad Zahir Khan: Department of Mathematics and Statistics, Riphah International University Islamabad, Islamabad 45710, Pakistan
Muhammad Farid Khan: Department of Mathematics and Statistics, Riphah International University Islamabad, Islamabad 45710, Pakistan
Muhammad Aslam: Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia
Abdur Razzaque Mughal: Department of Mathematics and Statistics, Riphah International University Islamabad, Islamabad 45710, Pakistan

Mathematics, 2018, vol. 7, issue 1, 1-9

Abstract: Acceptance sampling is one of the essential areas of quality control. In a conventional environment, probability theory is used to study acceptance sampling plans. In some situations, it is not possible to apply conventional techniques due to vagueness in the values emerging from the complexities of processor measurement methods. There are two types of acceptance sampling plans: attribute and variable. One of the important elements in attribute acceptance sampling is the proportion of defective items. In some situations, this proportion is not a precise value, but vague. In this case, it is suitable to apply flexible techniques to study the fuzzy proportion. Fuzzy set theory is used to investigate such concepts. It is observed there is no research available to apply Birnbaum-Saunders distribution in fuzzy acceptance sampling. In this article, it is assumed that the proportion of defective items is fuzzy and follows the Birnbaum-Saunders distribution. A single acceptance sampling plan, based on binomial distribution, is used to design the fuzzy operating characteristic (FOC) curve. Results are illustrated with examples. One real-life example is also presented in the article. The results show the behavior of curves with different combinations of parameters of Birnbaum-Saunders distribution. The novelty of this study is to use the probability distribution function of Birnbaum-Saunders distribution as a proportion of defective items and find the acceptance probability in a fuzzy environment. This is an application of Birnbaum-Saunders distribution in fuzzy acceptance sampling.

Keywords: fuzzy operating characteristic curve; fuzzy OC band; Birnbaum-Sunders distribution; single acceptance sampling plan (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/1/9/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/1/9/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2018:i:1:p:9-:d:192491

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().