A Selection of Prior Binomial, Two Point Prior Binomial and Gamma Poisson based on Lot Size indexed by Average Lot Quality, Limiting Quality Level & Acceptance Quality Level

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A Selection of Prior Binomial, Two Point Prior Binomial and Gamma Poisson based on Lot Size indexed by Average Lot Quality, Limiting Quality Level & Acceptance Quality Level

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G Uma* & M Nirmala**

*& **Assistant Professor, PSG College of Arts & Science, Coimbatore, TN, India

Abstract:- The theory of prior distributions is connected with theory of process control. Bayesian methods try to incorporate prior process knowledge to account for the variation in the sampling scheme. Though most of the acceptance sampling literature is based on classical methodology, there have been a few attempts to make the Bayesian Paradigm to explain acceptance sampling techniques, most notably by Hald.A (1981). The basic idea behind the Bayesian approach for calculating the sample size is to use prior information about the parameter p. The Prior distribution is a key part of Bayesian Sampling plan to represent the information about an uncertain parameter. This chapter gives the study on Two Point Prior Binomial distribution and is used as a baseline distribution for designing the Single Sampling Plan to determine the average acceptance and rejection cost with AQL and LQL. Necessary Operating Characteristic curves are sketched by highlighting with illustrations.

Key Words:- Prior Binomial, Two Point Prior Binomial, Gamma Poisson, AQL, LQL, ALQ and OC

INTRODUCTION

The basic assumption underlying the theory of conventional sampling plans by attributes is that the lot or process fraction nonconforming is a constant, which intensively means that the production process is stable. However, in practice, the lots of products produced from a process may have quality variations due to random fluctuations. The variations in the lots can be separated into two namely within – lot and between lot variations. When the between lot variations more than the within lot variations, the proportion of nonconforming units in the lots will vary continuously. In such cases, the decision on the submitted lots should be made with the consideration of the between lot variations and hence the conventional sampling schemes cannot be employed.

A complete statistical model for basic sampling inspection contains three componentsThe CostPrior Binomial DistributionConditions of ApplicationDevelop and Design the Plan of Single Sampling Plan for Attributes Based on Prior Binomial Distribution for Average Acceptance CostOperating ProcedureTwo Point Prior Binomial DistributionProperties of Two Point Prior Binomial DistributionDeveloping and Designing the Plan of Single Sampling Plan for Attributes Based on Two Point Prior Binomial Distribution on Acceptance Cost K(N,n,c,p)Gamma Poisson Prior distributionConditions for the Gamma Poisson Prior distributionDevelop and Design the Plan of Single Sampling Plan for Attributes Based on Gamma – Poisson distribution for Average Acceptance CostComparison of prior binomial, two point prior and Gamma Poisson prior distribution based on AQL.Comparison of prior binomial, two point prior and gamma poisson prior distribution based on LQL.proportion defective pproportion defective p

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