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.

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 Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
S. Balamurali ◽  
M. Usha
Keyword(s):  
Operating Characteristic ◽  
Characteristic Curve ◽  
Sampling Plan ◽  
Quality Level ◽  
Sample Number ◽  
Acceptable Quality ◽  
Acceptable Quality Level ◽  
Limiting Quality Level ◽  
Optimal Designing ◽  
Average Sample

We investigate the optimal designing of chain sampling plan for the application of normally distributed quality characteristics. The chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be useful when testing is costly and destructive. The advantages of this proposed variables plan over variables single sampling plan and variables double sampling plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables chain sampling plan for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level, along with the producer’s and consumer’s risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

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.

Equal-Risk Acceptance Sampling Plan

2013 ◽  
Vol 401-403 ◽  
pp. 2234-2237 ◽  
Author(s):  
Ren Yan Jiang
Keyword(s):  
Characteristic Curve ◽  
Sampling Plan ◽  
Quality Level ◽  
Acceptance Sampling ◽  
New Approach ◽  
Acceptance Sampling Plan ◽  
Acceptable Quality ◽  
Acceptable Quality Level ◽  
The Common ◽  
Mean Risk

The common acceptance sampling plan needs to specify two points in the operating characteristic curve, which represent the producers and customers risks, respectively. The points are determined in a subjective way and hence may result in unfairness. This paper presents a new approach, which determines the acceptance sampling plan based on the condition that the risks of producer and customer at acceptable quality level are the same. Another condition is introduced to control the mean risk of producer. The approach can considerably simplify the design of acceptance sampling plan, and is illustrated by an example.

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.

A new economical scheme of acceptance sampling plan in a two-stage approach based on the maxima nomination sampling technique

2016 ◽  
Vol 39 (7) ◽  
pp. 1097-1103 ◽  
Author(s):  
MS Fallahnezhad ◽  
E Qazvini
Keyword(s):  
Sampling Technique ◽  
Sampling Plan ◽  
Quality Level ◽  
Acceptance Sampling ◽  
Two Stage ◽  
Sampling Inspection ◽  
Assurance System ◽  
Economical Design ◽  
Acceptance Sampling Plan ◽  
Proposed Model

An acceptance sampling plan plays a very important role in any quality assurance system. In this new economical design of acceptance sampling plan, three types of costs are included in the objective function by considering average outgoing quality limit (AOQL), average quality level (AQL) and lot tolerance percent defective (LTPD) constraints based on the maxima nomination sampling (MNS) method in a two-stage approach. The design of this sampling inspection plan involves the minimum average total inspection (ATI). The model is designed to minimize the summation of costs and the proposed MNS economical sampling plan is compared with the classical one. Practitioners can use the proposed model to decrease the total cost of inspection.

scholarly journals Mejoramiento de la calidad en la recepción de materias primas, mediante la implementación de un plan de muestreo por variables

2020 ◽  
pp. 19-31
Author(s):  
Fernando Hernández-Benito ◽  
Martín González-Sóbal ◽  
Montserrat Gómez-Márquez ◽  
Miguel Ángel Solís-Jiménez
Keyword(s):  
Sampling Plan ◽  
Raw Material ◽  
Quality Level ◽  
Current State ◽  
Acceptable Quality ◽  
Inspection Process ◽  
Acceptable Quality Level ◽  
Action Strategies ◽  
Process Methodology

Objective: To guarantee the adequate inspection of raw material and packaging material by the inspection-receipt area by implementing an effective sampling plan that allows reducing the percentage of defective raw material and its impact on the production process. Methodology: It is based on the continuous improvement cycle (PHVA) within which a diagnosis is made to determine the current state of the inspection process, which will allow defining new action strategies aimed at standardizing the inspection process, through the implementation of a sampling plan by variables based on the MIL-STD 414 standard, once implemented, this process is documented, at the same time the integration of suppliers is carried out, through periodic evaluations in order to know the dynamics of the new inspection process and work only with those suppliers committed to the quality of their inputs. Contribution: Reduction of the percentage of defective raw material, from 21% to 13%, which means an acceptable quality level of the materials of 87%.

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