Shuo-Jye Wu

Acceptance sampling based on truncated life tests for generalized Rayleigh distribution

Abstract 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 producers risk are discussed. Some tables are presented and the use of the tables is illustrated by a numerical example.

Inference for the extreme value distribution under progressive Type-II censoring

The extreme value distribution has been extensively used to model natural phenomena such as rainfall and floods, and also in modeling lifetimes and material strengths. Maximum likelihood estimation (MLE) for the parameters of the extreme value distribution leads to likelihood equations that have to be solved numerically, even when the complete sample is available. In this paper, we discuss point and interval estimation based on progressively Type-II censored samples. Through an approximation in the likelihood equations, we obtain explicit estimators which are approximations to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using an iterative method and examine numerically their bias and mean squared error. The approximate estimators compare quite favorably to the MLEs in terms of both bias and efficiency. Results of the simulation study, however, show that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory for both these estimators and particularly so when the effective sample size is small. We, therefore, suggest the use of unconditional simulated percentage points of these pivotal quantities for the construction of confidence intervals. The results are presented for a wide range of sample sizes and different progressive censoring schemes. We conclude with an illustrative example.

On estimation based on progressive first-failure-censored sampling

In this paper, a new life test plan called a progressive first-failure-censoring scheme is introduced. Maximum likelihood estimates, exact and approximate confidence intervals and an exact confidence region for the parameters of the Weibull distribution are discussed for the new censoring scheme. A numerical example is provided to illustrate the proposed censoring scheme. Some simulation results are presented and used to assess the performance of the proposed estimation methods developed here. The expected time required to complete the proposed life test plan is derived. Finally, a numerical study for comparing among different censoring schemes in terms of expected test time is given.

Inference in the Pareto distribution based on progressive Type II censoring with random removals

This study considers the estimation problem for the Pareto distribution based on progressive Type II censoring with random removals. The number of units removed at each failure time has a discrete uniform distribution. We are going to use the maximum likelihood method to obtain the estimator of parameter. The expectation and variance of the maximum likelihood estimator will be derived. The expected time required to complete such an experiment will be computed. Some numerical results of expected test times are carried out for this type of progressive censoring and other sampling schemes.

Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution

In this article, we study the estimation problems for the Burr type XII distribution based on progressive type II censoring with random removals, where the number of units removed at each failure time has a discrete uniform distribution. We use the method of maximum likelihood to derive the point estimators of the parameters. The main purpose of this article is to construct the exact confidence interval and region for the parameters. Finally, a numerical example is presented to illustrate the methods developed here.

Estimation for the two-parameter pareto distribution under progressive censoring with uniform removals

This study considers the estimation problem for the Pareto distribution based on progressive Type II censoring with random removals, where the number of units removed at each failure time has a uniform distribution. We use the maximum likelihood method to obtain the estimators of parameters and the distributions of the estimators are derived. We also construct the confidence intervals for the parameters and percentile of the lifetime distribution. The expected time required to complete this censoring test is computed. Some numerical results of expected test times are carried out for this type of progressive censoring and other sampling schemes.

Bayesian estimation and prediction for Weibull model with progressive censoring

This article presents the statistical inferences on Weibull parameters with the data that are progressively type II censored. The maximum likelihood estimators are derived. For incorporation of previous information with current data, the Bayesian approach is considered. We obtain the Bayes estimators under squared error loss with a bivariate prior distribution, and derive the credible intervals for the parameters of Weibull distribution. Also, the Bayes prediction intervals for future observations are obtained in the one- and two-sample cases. The method is shown to be practical, although a computer program is required for its implementation. A numerical example is presented for illustration and some simulation study are performed.

Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring

In this paper, we investigate the estimation problem concerning a progressively type-II censored sample from the two-parameter bathtub-shaped lifetime distribution. We use the maximum likelihood method to obtain the point estimators of the parameters. We also provide a method for constructing an exact confidence interval and an exact joint confidence region for the parameters. Two numerical examples are presented to illustrate the method of inference developed here. Finally, Monte Carlo simulation studies are used to assess the performance of our proposed method.

Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.

Progressively first-failure censored reliability sampling plans with cost constraint

In this article, reliability sampling plans are developed for the Weibull distribution when the life test is progressively first-failure censored. We use the maximum likelihood method to obtain the point estimators of the model parameters. We propose an approach to establish reliability sampling plans which minimize three different objective functions under the constraint of total cost of experiment and given consumers and producers risks. The results are tabulated for selected specifications under progressive first-failure censoring scheme, and the sensitivity analysis is also studied. A Monte Carlo simulation is performed to study the accuracy of large-sample approximation.