Reliability Test Plan for the Gumbel-Uniform Distribution

Reliability sampling plans are used for determining the acceptability of any product. In this paper, reliability sampling plans for acceptance or rejection of a lot of products submitted for inspection are developed when the lifetimes follow the Gumbel-uniform distribution. The sampling plan proposed here can save the test time in practical situations. Some tables are also provided for the new sampling plans so that this method can be used conveniently by practitioners. Operating characteristic values and minimum ratios of the true value and the required value of the parameter with a given producers risk with respect to the newly developed sampling plans are also presented. The new test plan is applied to ordered failure times of software release to illustrate its use in industrial contexts.

Designing Bayesian Reliability Sampling Plans for Weibull Lifetime Models Using Progressively Censored Data

This paper presents Bayesian reliability sampling plans for the Weibull distribution based on progressively Type-II censored data with binomial removals. In constructing sampling plans, the decision theoretic approach is used. A dependent bivariate nonconjugate prior is employed. The total cost of the sampling plan consists of sampling, time-consuming, rejection, and acceptance costs. The decision rule is based on the Bayes estimator of the survival function. Lindley’s approximation is used to obtain Bayes estimates of the survival function under the quadratic and LINEX loss functions. However, the poor performance of Lindley’s approximation with small sample sizes can be observed. The Metropolis-within-Gibbs Markov Chain Monte Carlo (MCMC) algorithm show significantly improved performance compared to Lindley’s approximation. We use simulation studies to evaluate the Bayes risk and determine the optimal sampling plans for different sample sizes, observed number of failures, binomial removal probabilities and minimum acceptable reliability.

Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution

In this paper, an attempt is made to derive the most efficient economic reliability sampling plans for accepting a lot containing identical units having exponentially distributed lifetime with parameter θ. We consider two types of sampling plans, namely, (a) sequential sampling plan

Determination of Bayesian reliability sampling plans based on exponential-inverted gamma distribution

Purpose – The purpose of this paper is the determination of reliability sampling plans in the Bayesian approach assuming that the lifetime distribution is exponential. Design/methodology/approach – Sampling plans are used in manufacturing companies as a tool for carrying out sampling inspections, in order to make decisions about the disposition of many finished products. If the quality characteristic is considered as the lifetime of the products, the plan is known as a reliability sampling plan. In life testing, censoring schemes are adopted in order to save time and cost of life test. The inverted gamma distribution is employed as the natural conjugate prior to the average lifetime of the products. The sampling plans are developed assuming various probability distributions to the lifetime of the products. Findings – The optimum plans n and c are obtained for some sets of values of (p1, a, p2, ß). The selection of sampling plans is illustrated through numerical examples. Originality/value – Results obtained in this paper are original and the study has been done for the first time in this regard. Reliability sampling plans are essential for making decisions either to accept or reject based on the inspection of the sample.

Bayesian Reliability Sampling Plans under the Conditions of Rayleigh-Inverse-Rayleigh Distribution

Reliability sampling plans are used to take decisions on the disposition of lots based on life testing of products. Such plans are developed taking into the consideration of relevant probability distributions of the lifetimes of the products under testing. When the quality of products varies over lots, then a predictive distribution of the lifetime should be used to design sampling plans. In this paper, designing of reliability single sampling plan based on the predictive distribution of the lifetime is considered. It is assumed that sampling inspection is carried out through life testing of products with hybrid censoring. The predictive distribution is obtained assuming that the probability distribution of the lifetime of the product is Rayleigh and the process parameter has an inverse-Rayleigh prior. Plan parameters are determined using hypergeometric, binomial and Poisson probabilities, providing protection to both producer as well as consumer.