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

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Waqar Hafeez ◽  
Nazrina Aziz
Keyword(s):  
Beta Distribution ◽  
Binomial Distribution ◽  
Single Point ◽  
Sampling Plan ◽  
Design Parameters ◽  
Quality Level ◽  
Consumer’S Risk ◽  
Traditional Group ◽  
Sampling Plans ◽  
Content Type

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.

scholarly journals Bayesian Two-sided Complete Group Chain Sampling Plan for Binomial Distribution using Beta Prior through Quality Regions

2021 ◽  
Vol 21 (No.1) ◽  
pp. 51-69
Author(s):  
Waqar Hafeez ◽  
Nazrina Aziz
Keyword(s):  
Binomial Distribution ◽  
Sampling Plan ◽  
Design Parameters ◽  
Quality Level ◽  
Acceptance Sampling ◽  
Consumer’S Risk ◽  
Complete Group ◽  
Acceptable Quality Level ◽  
Limiting Quality Level ◽  
Estimate Quality

Acceptance sampling is a technique for statistical quality assurance based on the inspection of a random sample to decide the lot disposition: accept or reject. Producer’s risk and consumer’s risk are inevitable in acceptance sampling. Most conventional plans only focus on minimizing the consumer’s risk. This study focused on minimizing both producer’s and consumer’s risks through the quality region. Experts from available historical knowledge concurred that Bayesian is the best approach to make the correct decision. In this study, a Bayesian two-sided complete group chain sampling plan (BTSCGChSP) was proposed for the average probability of acceptance. The binomial distribution was used to derive the probability of lot acceptance, and the beta distribution was used as the prior distribution. For selected design parameters in BTSCGChSP, the acceptable quality level and limiting quality level were considered to estimate quality regions that were directly associated with producer’s and consumer’s risks, respectively. Four quality regions: (i) quality decision region , (ii) probabilistic quality region (PQR), (iii) limiting quality region, and (iv) indifference quality region, were evaluated. To compare with the existing Bayesian group chain sampling plan (BGChSP), operating characteristic curves were used for the same parameter values and probability of lot acceptance. The findings explained that BTSCGChSP provided a smaller proportion of defectives than BGChSP for the same probability of acceptance. If quality regions were found for the same values of consumer and producer risks, then the BTSCGChSP region would contain fewer defectives than in the BGChSP region. Therefore, for industrial practitioners, the proposed plan is a better substitute for existing BGChSP and other conventional plans.

Group acceptance sampling plan for resubmitted lots based on life tests for odds exponential log logistic distribution

2017 ◽  
Vol 34 (8) ◽  
pp. 1343-1351 ◽  
Author(s):  
Rosaiah K. ◽  
Srinivasa Rao Gadde ◽  
Kalyani K. ◽  
Sivakumar D.C.U.
Keyword(s):  
Group Size ◽  
Sampling Plan ◽  
Logistic Distribution ◽  
Acceptance Sampling ◽  
Consumer’S Risk ◽  
Content Type ◽  
Acceptance Sampling Plan ◽  
Minimum Group ◽  
Termination Time ◽  
Group Acceptance

Purpose The purpose of this paper is to develop a group acceptance sampling plan (GASP) for a resubmitted lot when the lifetime of a product follows odds exponential log logistic distribution introduced by Rao and Rao (2014). The parameters of the proposed plan such as minimum group size and acceptance number are determined for a pre-specified consumer’s risk, number of testers and the test termination time. The authors compare the proposed plan with the ordinary GASP, and the results are illustrated with live data example. Design/methodology/approach The parameters of the proposed plan such as minimum group size and acceptance number are determined for a pre-specified consumer’s risk, number of testers and the test termination time. Findings The authors determined the group size and acceptance number. Research limitations/implications No specific limitations. Practical implications This methodology can be applicable in industry to study quality control. Social implications This methodology can be applicable in health study. Originality/value The parameters of the proposed plan such as minimum group size and acceptance number are determined for a pre-specified consumer’s risk, number of testers and the test termination time.

scholarly journals Sampling Hazelnuts for Aflatoxin: Effect of Sample Size and Accept/Reject Limit on Reducing the Risk of Misclassifying Lots

2007 ◽  
Vol 90 (4) ◽  
pp. 1028-1035 ◽  
Author(s):  
Guner Ozay ◽  
Ferda Seyhan ◽  
Aysun Yilmaz ◽  
Thomas B Whitaker ◽  
Andrew B Slate ◽  
...  
Keyword(s):  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Food Additives ◽  
Sampling Plan ◽  
Test Results ◽  
Sampling Plans ◽  
Wide Range ◽  
Sample Test

Abstract About 100 countries have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely among regulating countries, the Codex Committee on Food Additives and Contaminants began work in 2004 to harmonize aflatoxin limits and sampling plans for aflatoxin in almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among replicated sample aflatoxin test results taken from aflatoxin-contaminated treenut lots. The uncertainty and distribution information is used to develop a model that can evaluate the performance (risk of misclassifying lots) of aflatoxin sampling plan designs for treenuts. Once the performance of aflatoxin sampling plans can be predicted, they can be designed to reduce the risks of misclassifying lots traded in either the domestic or export markets. A method was developed to evaluate the performance of sampling plans designed to detect aflatoxin in hazelnuts lots. Twenty hazelnut lots with varying levels of contamination were sampled according to an experimental protocol where 16 test samples were taken from each lot. The observed aflatoxin distribution among the 16 aflatoxin sample test results was compared to lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed distributions among sample test results taken from a wide range of lot concentrations. Using the negative binomial distribution, computer models were developed to calculate operating characteristic curves for specific aflatoxin sampling plan designs. The effect of sample size and accept/reject limits on the chances of rejecting good lots (sellers' risk) and accepting bad lots (buyers' risk) was demonstrated for various sampling plan designs.

The Implementation of Sampling Plan for Optimal Inspection Allocation in Multi-Station Systems with Consideration of Rework

2010 ◽  
Vol 450 ◽  
pp. 393-396
Author(s):  
Hsin Rau ◽  
Yi Hsiang Wang ◽  
Kuo Hua Cho
Keyword(s):  
Production System ◽  
Cost Model ◽  
Sampling Plan ◽  
Quality Level ◽  
Sampling Plans ◽  
Serial Production ◽  
Total Cost ◽  
Proper Sampling

This study explores sampling plans for optimal inspection allocation in multi-station systems with consideration of rework. After components have processed from each workstation in a serial production system, we can apply different sampling plans for inspection in order to maintain the outgoing quality level. The defective components that are detected at each sampling plan will return to the specific workstation to rework. This study proposes a minimum total cost model with a proper sampling plan after each workstation, which can help people to manager production better.

scholarly journals Group Acceptance Sampling Plan Using Marshall–Olkin Kumaraswamy Exponential (MOKw-E) Distribution

Processes ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 1066
Author(s):  
Abdullah M. Almarashi ◽  
Khushnoor Khan ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Probability Distributions ◽  
Sampling Plan ◽  
Design Parameters ◽  
Future Research ◽  
Quality Level ◽  
Acceptance Sampling ◽  
Average Life ◽  
Real World Data ◽  
Acceptance Sampling Plan ◽  
Group Acceptance

The current research concerns the group acceptance sampling plan in the case where (i) the lifetime of the items follows the Marshall–Olkin Kumaraswamy exponential distribution (MOKw-E) and (ii) a large number of items, considered as a group, can be tested at the same time. When the consumer’s risk and the test terminsation period are defined, the key design parameters are extracted. The values of the operating characteristic function are determined for different quality levels. At the specified producer’s risk, the minimum ratios of the true average life to the specified average life are also calculated. The results of the present study will set the platform for future research on various nano quality level topics when the items follow different probability distributions under the Marshall–Olkin Kumaraswamy scheme. Real-world data are used to explain the technique.

A new mixed repetitive group sampling plan based on the process capability index for product acceptance

2018 ◽  
Vol 35 (2) ◽  
pp. 463-480 ◽  
Author(s):  
Balamurali Saminathan ◽  
Usha Mahalingam
Keyword(s):  
Process Capability ◽  
Process Capability Index ◽  
Sampling Plan ◽  
Optimal Parameters ◽  
Sampling Plans ◽  
Content Type ◽  
Practical Applications ◽  
Capability Index ◽  
Unknown Variance ◽  
Repetitive Group Sampling

Purpose The purpose of this paper is to propose a new mixed repetitive group sampling (RGS) plan based on the process capability index, Cpk, where the quality characteristics of interest follow the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications for both symmetric and asymmetric fraction non-conforming cases. The advantages of this proposed mixed sampling plan are also discussed. The proposed sampling plan is also compared with other existing sampling plans. Design/methodology/approach In order to determine the optimal parameters of the proposed mixed RGS plan based on Cpk, the authors constructed tables for various combinations of acceptable and limiting quality levels (LQLs). For constructing tables, the authors followed the approach of two points on the operating characteristic (OC) curve. The optimal problem is formulated as a non-linear programming where the objective function to be minimized is the average sample number (ASN) and the constraints are related to lot acceptance probabilities at acceptable quality level and LQL under the OC curve. Findings The proposed mixed RGS plan will be a new addition to the literature of acceptance sampling. It is shown that the proposed mixed plan involves minimum ASN with desired protection to both producers and consumers compared to other existing sampling plans. The practical application of the proposed mixed sampling plan is also explained with an illustrative real-time example. Originality/value In this paper, the authors propose a new mixed RGS plan based on the process capability index Cpk, where the quality characteristic of interest follows the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications. The proposed mixed sampling plan can be used in all production industries. This kind of mixed RGS plan is not available in the literature.

Comment on “Exact Bayesian variable sampling plans for the exponential distribution based on type-I hybrid censored samples” and “its corrections”

2013 ◽  
Vol 44 (2) ◽  
pp. 113-122
Author(s):  
Tachen Liang
Keyword(s):  
Exponential Distribution ◽  
Sampling Plan ◽  
Design Parameters ◽  
Type I ◽  
Sampling Plans ◽  
Bayesian Sampling ◽  
Censored Samples ◽  
Variable Sampling

We compare the performances of two sampling plans, namely, the Lin-Liang-Huang (2002)'s Bayesian sampling plan $(n^*,\xi^*)$ and the Lin-Huang-Balakrishnan (2008a, 2010a)'s exact Bayesian sampling plan $(n_0,r_0,t_0,\xi_0)$. We also comment the accuracy of the values of the design parameters $(n_0,r_0,t_0,\xi_0)$ provided in Lin-Huang-Balakrishnan (2010a). We conclude that among the class of sampling plans $(n,r,t,\xi)$ of Lin et al.~(2008a, 2010a), the exact Bayesian sampling plan does not exist.

Design and Construction of Plan for Exponential Distribution Using Repetitive Sampling

2016 ◽  
Vol 13 (10) ◽  
pp. 6568-6575
Author(s):  
Muhammad Aslam ◽  
Ali Hamed S Algarni ◽  
Ramsha Saeed
Keyword(s):  
Exponential Distribution ◽  
Linear Optimization ◽  
Sampling Plan ◽  
Design Parameters ◽  
Sample Number ◽  
Sampling Plans ◽  
Industrial Data ◽  
Repetitive Group Sampling ◽  
Average Sample

In this paper, sampling plan using exact and approximated approaches is presented when the quality of interest follows the exponential distribution. The designing both presented using the repetitive group sampling plan. The design parameters of the proposed sampling plans are determined through non-linear optimization. The efficiency of proposed sampling plans is compared with the existing sampling plans in terms of average sample number. The application of the proposed plans is discussed by industrial data.

Group acceptance sampling plans based on time truncated life tests for compound Weibull-exponential distribution

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ayten Yiğiter ◽  
Canan Hamurkaroğlu ◽  
Nazan Danacıoğlu
Keyword(s):  
Acceptance Sampling ◽  
Type I ◽  
Consumer’S Risk ◽  
Producer’S Risk ◽  
Data Set ◽  
Sampling Plans ◽  
Content Type ◽  
Acceptance Sampling Plans ◽  
Life Tests ◽  
Group Acceptance

PurposeAcceptance sampling plans are a decision-making process on the basis of a randomly selected sampling from a party, where it is not possible to completely scan the products for reasons such as time and cost being limited or the formation of damaged products during the inspection. For some products, the life span (time from beginning to failure) may be an important quality characteristic. In this case, the quality control adequacy of the products can be checked with an acceptance sampling plan based on the truncated life test with a censored scheme for the lifetime of the products. In this study, group acceptance sampling plans (GASPs) based on life tests are studied under the Type-I censored scheme for the compound Weibull-exponential (CWE) distribution.Design/methodology/approachGASPs based on life tests under the Type-I censored scheme for the CWE distribution are developed by using both the producer's risk and the consumer's risk.FindingsIn this study, optimum sample size, optimum number of groups and acceptance number are obtained under the Type-I censored scheme for the CWE distribution. Real data set illustration is given to show GASPs how to be used for the industry applications.Originality/valueDifferent from acceptance sampling plans with just considering the producer's risk, GASPs are constructed by using two-point approach included both the producer's risk and the consumer's risk for CWE distribution.

Sampling dried figs for aflatoxin - Part II: effect of sampling plan design on reducing the risk of misclassifying lots

2017 ◽  
Vol 10 (2) ◽  
pp. 99-109 ◽  
Author(s):  
H. Ozer ◽  
H.I. Oktay Basegmez ◽  
T.B. Whitaker ◽  
A.B. Slate ◽  
F.G. Giesbrecht
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sampling Plan ◽  
Export Market ◽  
Test Results ◽  
Sampling Plans ◽  
Binomial Distributions ◽  
Sample Test ◽  
Codex Standard

Because aflatoxin limits vary widely among regulating countries, the Codex Committee on Contaminants in Foods (CCCF) began work in 2006 to harmonise maximum levels (MLs) and sampling plans for aflatoxin in dried figs. Studies were developed to measure the variability and distribution among replicated sample aflatoxin test results taken from the same aflatoxin contaminated lot of dried figs so that a model could be developed to evaluate the risk of misclassifying lots of dried figs by aflatoxin sampling plan designs. The model was then be used by the CCCF electronic working group (eWG) to recommend MLs and aflatoxin sampling plan designs to the full CCCF membership for lots traded in the export market. Sixteen 10 kg samples were taken from each of 20 dried fig lots with varying levels of contamination. The observed aflatoxin distribution among the 16-aflatoxin sample test results was compared to the normal, lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed aflatoxin distributions among sample test results taken from the same contaminated lot. Using the negative binomial distribution, a computer model was developed to show the effect of the number and size of samples and the accept/reject limits on the chances of rejecting good lots (seller's risk) and accepting bad lots (buyer's risk). The information was shared with the CCCF eWG and in March 2012, the 6th session of CCCF adopted at step 5/8 an aflatoxin sampling plan where three 10 kg samples must all test less than an ML of 10 µg/kg total aflatoxins to accept a dried fig lot. The 35th Session of the Codex Alimentarius Commission met in July 2012 and adopted the CCCF recommendations for the ML and the sampling plan as an official Codex standard.

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