Construction of Quality Regions Based on Consumer’s and Producer’s Risks for Two Sided Group Chain Sampling Plan with Binomial Distribution

Waqar  Hafeez; Nazrina  Aziz; Javid  Shabbir; Said  Farooq Shah; Akbar Ali Khan Ali Khan

Authors

Waqar Hafeez School of Quantitative Sciences, University Utara Malaysia, Kedah Darul Aman, Malaysia
Nazrina Aziz School of Quantitative Sciences, University Utara Malaysia, Kedah Darul Aman, Malaysia
Javid Shabbir Department of Statistics, University of Wah, Punjab, Pakistan
Said Farooq Shah Department of Statistics, University of Peshawar, Peshawar, Pakistan
Akbar Ali Khan Ali Khan Department of Statistics, Govt Postgraduate College Kohat, Karak Khyber Pakhtunkhwa, Pakistan

Keywords:

Acceptance sampling, quality region, consumer’s risk, producer’s risk, two sided group chain

Abstract

Acceptance sampling is a technique that is used to make decision about the lot under inspection. Based on representative sample the decision is made about the whole lot that is under inspection. Mostly existing plans consider consumer’s risk and they do not care about producer loss. This study will consider consumer’s risk as well as producer’s risk and provide a criterion to satisfy both parties at the same time. A two sided group chain sampling plan (TSGChSP) is used in this paper. Based on both risks probability of lot acceptance, L(p) is determined. Four different quality regions are estimated for specified values of producer’s and consumer’s risks. By satisfying the specified design parameters, it is assessed that as the value of design parameters increases, the proportion of defectives decreases such as g, r, i, j, $\beta$ and $\alpha$ . In comparison TSGChSP is compared with existing Bayesian two sided group chain sampling plan (BTSGChSP). If both plans are applied under similar environments, then the results explain that the TSGChSP produces a lower proportion of defectives than the BTSGChSP. Hence, we suggest that TSGChSP is better substitute for lot inspection in the manufacturing industry, particularly for those working with destructive testing of high-quality products.

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