Bayesian Single Sampling Plans for a Gamma Prior

Suresh, K. K.; Latha, M.

doi:10.1515/eqc.2001.93

Cited by 11 publications

(5 citation statements)

References 5 publications

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“…For a single sampling plan using a prior Gamma distribution, Suresh and Latha (2001) obtained an average probability of acceptance. The inflection point formula and the tangent at the inflection point were also derived.…”

Section: Literature Reviewmentioning

confidence: 99%

Bayesian two-sided group chain sampling plan for beta binomial distribution under quality regions

Hafeez

Aziz

2021

IJQRM

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PurposeThis paper introduces a Bayesian two-sided group chain sampling plan (BT-SGChSP) by using binomial distribution to estimate the average proportion of defectives. In this Bayesian approach, beta distribution is used as a suitable prior of binomial distribution. The proposed plan considers both consumer's and producer's risks. Currently, group chain sampling plans only consider the consumer's risk and do not account for the producer's risk. All existing plans are used to estimate only a single point, but this plan gives a quality region for the pre-specified values of different design parameters. In other words, instead of point wise description for the designing of sampling plan based on a range of quality by involving a novel approach called quality region.Design/methodology/approachThe methodology is based on five phases, which are (1) operating procedure, (2) derivation of the probability of lot acceptance, (3) constructing plans for given acceptable quality level (AQL) and limiting quality level (LQL), (4) construction of quality intervals for BT-SGChSP and (5) selection of the sampling plans.FindingsThe findings show that the operating characteristic (OC) curve of BT-SGChSP is more ideal than the existing Bayesian group chain sampling plan because the quality regions for BT-SGChSP give less proportion of defectives for same consumer's and producer's risks.Research limitations/implicationsThere are four limitations in this study: first is the use of binomial distribution when deriving the probability of lot acceptance. Alternatively, it can be derived by using distributions such as Poisson, weighted Poisson and weighted binomial. The second is that beta distribution is used as prior distribution. Otherwise, different prior distributions can be used like: Rayleigh, exponential and generalized exponential. The third is that we adopt mean as a quality parameter, whereas median and other quintiles can be used. Forth, this paper considers probabilistic quality region (PQR) and indifference quality region (IQR).Practical implicationsThe proposed plan is an alternative of traditional group chain sampling plans that are based on only current lot information. This plan considers current lot information with preceding and succeeding lot and also considers prior information of the product.Originality/valueThis paper first time uses a tight (three acceptance criteria) and introduces a BT-SGChSP to find quality regions for both producer's and consumer's risk.

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Section: Literature Reviewmentioning

confidence: 99%

Bayesian two-sided group chain sampling plan for beta binomial distribution under quality regions

Hafeez

Aziz

2021

IJQRM

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“…Suresh and Saminathan (2010) have studied the selection of Repetitive Deferred Sampling Plan through acceptable and limiting quality levels. Suresh and Latha (2001) have studied Bayesian Single Sampling Plan through Average Probability of Acceptance involving Gamma-Poisson model.…”

Section: Bayesian Acceptance Samplingmentioning

confidence: 99%

Bayesian Repetitive Deferred Sampling Plan Indexed Through Relative Slopes

Suresh

Umamaheswari

Veerakumari

2013

MJIS

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This paper deals with designing of Bayesian Repetitive Deferred Sampling Plan (BRDS) indexed through incoming and outgoing quality levels with their relative slopes on the OC curve. The Repetitive Deferred Sampling (RDS) Plan has been developed by Shankar and Mohapatra (1991) and this plan is an extension of the Multiple Deferred Sampling Plan MDS-(c 1 , c 2) , which was proposed by Rambert Vaerst (1981).

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“…5 Later SSP was extended to minimize average cost for attributes by Hald. 6 Suresh and Latha 7 proposed a Bayesian SSP for Poisson distribution with gamma prior. They derived the inflection point and tangent at the inflection point and provide tables for the selection of plan parameters.…”

Section: Introductionmentioning

confidence: 99%

Designing Bayesian new two‐sided group chain sampling plan for quality regions based on beta prior

Hafeez

Aziz

2023

Quality & Reliability Eng

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Acceptance sampling is used to determine whether to accept or reject the lot that is being inspected. The Bayesian strategy is the ideal method to use when historical data about the product is available in order to make decision. To estimate quality regions, we suggest a Bayesian new two‐sided group chain sampling plan in this study. The operating characteristic function is developed using the binomial distribution, and average probability of acceptance is estimated using beta distribution as prior. Four quality regions are estimated for certain predetermined values of producer's and consumer's risks. Producer's risk and consumer's risk are correlated with acceptable quality level and limiting quality level of quality regions, respectively. For the proposed plan, inflection point values are estimated based on various combinations of design parameters. Operating characteristic curves are use up to compare the current Bayesian group chain sampling plan (BGChSP) with the effects of changing the values of specified parameter values. The suggested plan is a well replacement for current industry plans, according to the operating characteristic curve's findings.

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Bayesian Single Sampling Plans for a Gamma Prior

Abstract: The average probability of acceptance (AP A) is obtained for a single sampling plan assuming a Gamma prior distribution. Formula for inflection point and tangent at the inflection point are also derived. Tables are provided for selection of plan parameters.

Cited by 11 publications

References 5 publications

Bayesian two-sided group chain sampling plan for beta binomial distribution under quality regions

Bayesian two-sided group chain sampling plan for beta binomial distribution under quality regions

Bayesian Repetitive Deferred Sampling Plan Indexed Through Relative Slopes

Designing Bayesian new two‐sided group chain sampling plan for quality regions based on beta prior

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