A variables repetitive group sampling plan under failure-censored reliability tests for Weibull distribution

We propose a variables repetitive group sampling plan under type-II or failure-censored life testing when the lifetime of a part follows a Weibull distribution with a known shape parameter. The acceptance criteria do not involve unknown scale parameter differently from the existing plans. To determine the design parameters of the proposed plan, the usual approach of using two points on the operating characteristic curve is adopted and an optimization problem is formulated so as to minimize the average number of failures observed. Tables for design parameters are constructed when the quality of parts is represented by the unreliability or the ratio of the mean lifetime to the specified life. It is found that the proposed sampling plan can reduce the sample size significantly than do the single sampling plan.     

A two-stage group sampling plan based on truncated life tests for a general distribution

A two-stage group acceptance sampling plan based on a truncated life test is proposed, which can be used regardless of the underlying lifetime distribution when multi-item testers are employed. The decision upon lot acceptance can be made in the first or second stage according to the number of failures from each group. The design parameters of the proposed plan such as number of groups required and the acceptance number for each of two stages are determined independently of an underlying lifetime distribution so as to satisfy the consumer's risk at the specified unreliability. Single-stage group sampling plans are also considered as special cases of the proposed plan and compared with the proposed plan in terms of the average sample number and the operating characteristics. Some important distributions are considered to explain the procedure developed here.     

Economic design of acceptance sampling plans for truncated life test using Frechet distribution

In this article designing of acceptance sampling plans for the truncated life test is proposed using economic approach by assuming that the lifetime of a product follows Frechet distribution based on median. The optimal sampling plans to meet the consumer’s confidence level with minimum total cost are designed. Efficiency of the proposed plan is also analyzed.     

Economic design of quick switching sampling system for assuring Weibull distributed mean life

In this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.     

Accelerated life test sampling plans for the Weibull distribution under Type I progressive interval censoring with random removals

This paper considers the design of accelerated life test (ALT) sampling plans under Type I progressive interval censoring with random removals. We assume that the lifetime of products follows a Weibull distribution. Two levels of constant stress higher than the use condition are used. The sample size and the acceptability constant that satisfy given levels of producer's risk and consumer's risk are found. In particular, the optimal stress level and the allocation proportion are obtained by minimizing the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Furthermore, for validation purposes, a Monte Carlo simulation is conducted to assess the true probability of acceptance for the derived sampling plans.     

Acceptance sampling based on truncated life tests for generalized Rayleigh distribution

This paper considers the problem of an acceptance sampling plan for a truncated life test when the lifetime follows the generalized Rayleigh distribution. For different acceptance numbers, confidence levels, and values of the ratio of the fixed experiment time to the specified mean life, the minimum sample sizes necessary to ensure the specified mean life are found. The operating characteristic values of the sampling plans and producer's risk are discussed. Some tables are presented and the use of the tables is illustrated by a numerical example.     

Acceptance sampling based on life tests: log-logistic model

The problem of acceptance sampling when the life test is truncated at a preassigned time is considered. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified average life, the minimum sample size necessary to ensure the specified average life, are obtained under the assumption that the lifetime variate of the test items follows a distribution belonging to Burr's family XII of distributions - called the log-logistic model. The operating characteristic values of the sampling plans and producer's risk are presented. The results are illustrated by an example.     

Reliability acceptance sampling plans for the Weibull distribution under accelerated Type-I censoring

Type-I censored reliability acceptance sampling plans (RASPs) are developed for the Weibull lifetime distribution with unknown shape and scale parameters such that the producer and consumer risks are satisfied. It is assumed that the life test is conducted at an accelerated condition for which the acceleration factor (AF) is known, and each item is continuously monitored for failure. Sensitivity analyses are also conducted to assess the effect of the uncertainty in the assumed AF on the actual producer and consumer risks, and a method is developed for constructing RASPs that can accommodate the uncertainty in AF.     

Efficient Bayesian sampling plans for exponential distributions with type-I-censored samples

The aim of this paper is to introduce an efficient Bayesian sampling procedure for exponential distribution with type-I censoring. An online inspection method is suggested to reach a Bayes decision prior the termination time of life test. Bayesian sampling plans (BSPs) with quadratic loss function are established to illustrate the use of the proposed method. Some BSPs are tabulated, and the performance of the proposed BSPs is compared with two existing competitive methods. Numerical results indicate that a significant reduction in the experimental time over the conventional BSP can be achieved when the online inspection method is applied.     

Time truncated acceptance sampling plans for generalized exponential distribution

Acceptance sampling plans for generalized exponential distribution when the lifetime experiment is truncated at a pre-determined time are provided in this article. The tables are provided for the minimum sample size required to ensure a certain median life of the experimental unit when the shape parameter is two. The operating characteristic function values of the sampling plans and the associated producer's risks are also presented. It is shown that the tables presented here can be used if instead of median life, other percentile life is chosen as the criterion or if the shape parameter is not two. Examples are provided for illustrative purposes.     

Reliability sampling plans for the two-parameter exponential distribution under progressive censoring

This paper presents reliability sampling plans for the two-parameter exponential distribution under progressive censoring. These sampling plans are quite useful to practitioners, because they provide savings in resources and in total test time. Furthermore, they off er the flexibility to remove functioning test specimens from further testing at various stages of the experimentation. In the construction of these sampling plans, the operating characteristic curve is derived using the exact distributional properties of maximum likelihood estimators. An example is given to illustrate the application of the proposed sampling plans.     

Bayesian life test sampling plans for the two parameter exponential distribution

In this paper we consider the determination of Bayesian life test acceptance sampling plans for finite lots when the underlying lifetime distribution is the two parameter exponential. It is assumed that the prior distribution is the natural conjugate prior, that the costs associated with the actions accept and reject are known functions of the lifetimes of the items, and that the cost of testing a sample is proportional to the duration of the test. Type 2 censored sampling is considered where a sample of size n is observed only until the rth failure occurs and the decision of whether to accept or reject the remainder of the lot is made on the basis of the r observed lifetimes. Obtaining the optimal sample size and the optimal censoring number are difficult problems when the location parameter of the distribution is restricted to be non-negative. The case when the positivity restriction on the location parameter is removed has been investigated. An example is provided for illustration.     

Optimum Design for Type-I Step-stress Accelerated Life Tests of Two-parameter Weibull Distributions

In this article, we focus on the general k-step step-stress accelerated life tests with Type-I censoring for two-parameter Weibull distributions based on the tampered failure rate (TFR) model. We get the optimum design for the tests under the criterion of the minimization of the asymptotic variance of the maximum likelihood estimate of the pth percentile of the lifetime under the normal operating conditions. Optimum test plans for the simple step-stress accelerated life tests under Type-I censoring are developed for the Weibull distribution and the exponential distribution in particular. Finally, an example is provided to illustrate the proposed design and a sensitivity analysis is conducted to investigate the robustness of the design.     

Variables acceptance reliability sampling plan for items subject to inverse Gaussian degradation process

Until now, in the literature, a variety of acceptance reliability sampling plans have been developed based on different life test plans. In most of the reliability sampling plans, the decision procedures to accept or reject the corresponding lot are developed based on the lifetimes of the items observed on tests, or the number of failures observed during a pre-specified testing time. However, frequently, the items are subject to degradation phenomena and, in these cases, the observed degradation level of the item can be used as a decision statistic. In this paper, we develop a variables acceptance sampling plan based on the information on the degradation process of the items, assuming that the degradation process follows the inverse Gaussian process. It is shown that the developed sampling plan improves the reliability performance of the items conditional on the acceptance in the test and that the lifetimes of items after the reliability sampling test are stochastically larger than those before the test. A study comparing the proposed degradation-based sampling plan with the conventional sampling plan which is based on a life test is also performed.KEYWORDS: Variables sampling plan, degradation test, inverse Gaussian process, mixture distribution, stochastic ordering     

A likelihood ratio test of quasi-independence for sparse two-way contingency tables

We consider a likelihood ratio test of independence for large two-way contingency tables having both structural (non-random) and sampling (random) zeros in many cells. The solution of this problem is not available using standard likelihood ratio tests. One way to bypass this problem is to remove the structural zeroes from the table and implement a test on the remaining cells which incorporate the randomness in the sampling zeros; the resulting test is a test of quasi-independence of the two categorical variables. This test is based only on the positive counts in the contingency table and is valid when there is at least one sampling (random) zero. The proposed (likelihood ratio) test is an alternative to the commonly used ad hoc procedures of converting the zero cells to positive ones by adding a small constant. One practical advantage of our procedure is that there is no need to know if a zero cell is structural zero or a sampling zero. We model the positive counts using a truncated multinomial distribution. In fact, we have two truncated multinomial distributions; one for the null hypothesis of independence and the other for the unrestricted parameter space. We use Monte Carlo methods to obtain the maximum likelihood estimators of the parameters and also the p-value of our proposed test. To obtain the sampling distribution of the likelihood ratio test statistic, we use bootstrap methods. We discuss many examples, and also empirically compare the power function of the likelihood ratio test relative to those of some well-known test statistics.     

Optimal step-stress test under type I progressive group-censoring with random removals

Some traditional life tests result in no or very few failures by the end of test. In such cases, one approach is to do life testing at higher-than-usual stress conditions in order to obtain failures quickly. This paper discusses a k-level step-stress accelerated life test under type I progressive group-censoring with random removals. An exponential failure time distribution with mean life that is a log-linear function of stress and a cumulative exposure model are considered. We derive the maximum likelihood estimators of the model parameters and establish the asymptotic properties of the estimators. We investigate four selection criteria which enable us to obtain the optimum test plans. One is to minimize the asymptotic variance of the maximum likelihood estimator of the logarithm of the mean lifetime at use-condition, and the other three criteria are to maximize the determinant, trace and the smallest eigenvalue of Fisher's information matrix. Some numerical studies are discussed to illustrate the proposed criteria.     

Exact Bayesian Variable Sampling Plans for the Exponential Distribution Based on Type-I and Type-II Hybrid Censored Samples

A sampling plan with a polynomial loss function for the exponential distribution is considered. From the distribution of the maximum likelihood estimator of the mean of an exponential distribution based on Type-I and Type-II hybrid censored samples, we obtain an explicit expression for the Bayes risk of a sampling plan with a quadratic loss function. Some numerical examples and comparisons are given to illustrate the effectiveness of the proposed method, and a robustness study reveals that the proposed optimal sampling plans are quite robust.     

Interval censored sampling plans for the log-logistic lifetime distribution

The log-logistic distribution is one of the popular distributions in life-testing applications. This article develops an acceptance sampling procedure for the log-logistic lifetime distribution based on grouped data when the shape parameter is given. Both producer and consumer risks are considered to develop the ordinary, approximate and simulated sampling plans. Some of the proposed sampling plans are tabulated; moreover, those three types of sampling plans are compared with each other under the same censoring rates. The use of these tables is illustrated by an example.     

New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions

In this paper, we consider the Birnbaum–Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.     

Optimal Bayesian sampling plans for exponential distributions based on hybrid censored samples

We study variable sampling plans for exponential distributions based on type-I hybrid censored samples. For this problem, two sampling plans based on the non-failure sample proportion and the conditional maximum likelihood estimator are proposed by Chen et al. [J. Chen, W. Chou, H. Wu, and H. Zhou, Designing acceptance sampling schemes for life testing with mixed censoring, Naval Res. Logist. 51 (2004), pp. 597–612] and Lin et al. [C.-T. Lin, Y.-L. Huang, and N. Balakrishnan, Exact Bayesian variable sampling plans for the exponential distribution based on type-I and type-II censored samples, Commun. Statist. Simul. Comput. 37 (2008), pp. 1101–1116], respectively. From the theoretic decision point of view, the preceding two sampling plans are not optimal due to their decision functions not being the Bayes decision functions. In this article, we consider the decision theoretic approach, and the optimal Bayesian sampling plan based on sufficient statistics is derived under a general loss function. Furthermore, for the conjugate prior distribution, the closed-form formula of the Bayes decision rule can be obtained under either the linear or quadratic decision loss. The resulting Bayesian sampling plan has the minimum Bayes risk, and hence it is better than the sampling plans proposed by Chen et al. (2004) and Lin et al. (2008). Numerical comparisons are given and demonstrate that the performance of the proposed Bayesian sampling plan is superior to that of Chen et al. (2004) and Lin et al. (2008).