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.     

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.     

Reliability sampling plans for the Weibull distribution under Type II progressive censoring with binomial removals

This paper presents reliability sampling plans for the Weibull distribution under Type II progressive censoring with random removals (PCR), where the number of units removed at each failure time follows a binomial distribution. To construct the sampling plans, the sample size n and the acceptance constant k are determined based on asymptotic distribution theory. The resulting sampling plans are tabulated for selected specifications under the proposed censoring scheme. Furthermore, a Monte Carlo simulation is conducted to validate the true probability of acceptance for the designed sampling plans.     

Prediction for future failures in Weibull distribution under hybrid censoring

In this paper, we consider the prediction of a future observation based on a type-I hybrid censored sample when the lifetime distribution of experimental units is assumed to be a Weibull random variable. Different classical and Bayesian point predictors are obtained. Bayesian predictors are obtained using squared error and linear-exponential loss functions. We also provide a simulation consistent method for computing Bayesian prediction intervals. Monte Carlo simulations are performed to compare the performances of the different methods, and one data analysis has been presented for illustrative purposes.     

Parameters estimation for weibull distributed lifetimes under progressive censoring with random removeals

This paper considers the estimation problem when lifetimes are Weibull distributed and are collected under a Type-II progressive censoring with random removals, where the number of units removed at each failure time follows a uniform discrete distribution. The expected time of this censoring plan is discussed and compared numerically to that under a Type II censoring without removal. Maximum likelihood estimator of the parameters and their asymptotic variances are derived.     

Design of accelerated life test plans under progressive Type II interval censoring with random removals

This paper investigates the design of accelerated life test (ALT) plans under progressive Type II interval censoring with random removals. Units’ lifetimes are assumed to follow a Weibull distribution, and the number of random removals at each inspection is assumed to follow a binomial distribution. The optimal ALT plans, which minimize the asymptotic variance of an estimated quantile at use condition, are determined. The expected duration of the test and the expected number of inspections on each stress level are calculated. A numerical study is conducted to investigate the properties of the derived ALT plans under different parameter values. For illustration purpose, a numerical example is also given.     

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.     

Exact Bayesian variable sampling plans for the exponential distribution with progressive hybrid censoring

From the exact distribution of the maximum likelihood estimator of the average lifetime based on progressive hybrid exponential censored sample, we derive an explicit expression for the Bayes risk of a sampling plan when a quadratic loss function is used. The simulated annealing algorithm is then used to determine the optimal sampling plan. Some optimal Bayes solutions under progressive hybrid and ordinary hybrid censoring schemes are presented to illustrate the effectiveness of the proposed method.     

Acceptance sampling plans under progressive interval censoring with likelihood ratio

The paper investigates the design of life test plans under progressively interval censored test. Based on the likelihood ratio, the proposed life test plans are established so that the required producer and consumer risks can be satisfied simultaneously. The advantage of the proposed method is that the developed sampling procedure depends on the likelihood ratio only so that the method can be applied to any lifetime distribution when only one parameter is unknown. A numerical study is conducted and some of the sampling plans for the Weibull lifetime distribution with different shape parameters are tabulated for illustration. Moreover, the influence of the removal schemes on the proposed sampling plans is discussed.     

Planning step-stress test plans under Type-I censoring for the log-location-scale case

In this paper, we consider a k-level step-stress accelerated life-testing (ALT) experiment with unequal duration steps τ=(τ₁, …, τ _k ). Censoring is allowed only at the change-stress point in the final stage. A general log-location-scale lifetime distribution with mean life which is a linear function of stress, along with a cumulative exposure model, is considered as the working model. Under this model, the determination of the optimal choice of τ for both Weibull and lognormal distributions are addressed using the variance–optimality criterion. Numerical results show that for a general log-location-scale distributions, the optimal k-step-stress ALT model with unequal duration steps reduces just to a 2-level step-stress ALT model.     

Optimum constant-stress life test plans for Pareto distribution under type-I censoring

The paper considers the case of constant-stress partially accelerated life testing (CSPALT) when two stress levels are involved under type-I censoring. The lifetimes of test items are assumed to follow a two-parameter Pareto lifetime distribution. Maximum-likelihood method is used to estimate the parameters of CSPALT model. Confidence intervals for the model parameters are constructed. Optimum CSPALT plans that determine the best choice of the proportion of test units allocated to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance of the maximum-likelihood estimators of the model parameters. For illustration, Monte Carlo simulation studies are presented.     

A mixed control chart for monitoring failure times under accelerated hybrid censoring

In an accelerated hybrid censoring scheme several stress factors can be accelerated to make the products to respond to fail more quickly than under normal operating conditions. In such situations, the control charts available in the literature cover the attribute characteristics only to monitor the performance of the process over time. This study extends the idea by proposing an optimal mixed attribute-variable control chart for Weibull distribution under an accelerated hybrid censoring scheme keeping the advantages of both attribute and variable control charts. It first monitors the number of defectives under accelerated conditions and switches to the variable control chart to investigate the mean failure times when the process stability is dubious. The performance of the proposed chart is evaluated by using run-length characteristics, and the optimality of the design parameter is achieved by minimizing the out-of-control average run length. The simulation study depicted better performance of the proposed control chart than the traditional charts in detecting shifts in the process. A real-life application is also included.KEYWORDS: Mixed control chart, attribute chart, variable chart, Weibull distribution, accelerated hybrid censoring     

Statistical analysis for competing risks model from a Weibull distribution under progressively hybrid censoring

This paper considers the statistical analysis for competing risks model under the Type-I progressively hybrid censoring from a Weibull distribution. We derive the maximum likelihood estimates and the approximate maximum likelihood estimates of the unknown parameters. We then use the bootstrap method to construct the confidence intervals. Based on the non informative prior, a sampling algorithm using the acceptance–rejection sampling method is presented to obtain the Bayes estimates, and Monte Carlo method is employed to construct the highest posterior density credible intervals. The simulation results are provided to show the effectiveness of all the methods discussed here and one data set is analyzed.     

Efficient Bayesian sampling plans for exponential distributions with random censoring

This paper considers Bayesian sampling plans for exponential distribution with random censoring. The efficient Bayesian sampling plan for a general loss function is derived. This sampling plan possesses the property that it may make decisions prior to the end of the life test experiment, and its decision function is the same as the Bayes decision function which makes decisions based on data collected at the end of the life test experiment. Compared with the optimal Bayesian sampling plan of Chen et al. (2004), the efficient Bayesian sampling plan has the smaller Bayes risk due to the less duration time of life test experiment. Computations of the efficient Bayes risks for the conjugate prior are given. Numerical comparisons between the proposed efficient Bayesian sampling plan and the optimal Bayesian sampling plan of Chen et al. (2004) under two special decision losses, including the quadratic decision loss, are provided. Numerical results also demonstrate that the performance of the proposed efficient sampling plan is superior to that of the optimal sampling plan by Chen et al. (2004).     

Estimation of the extended Weibull parameters and acceleration factors in the step-stress accelerated life tests under an adaptive progressively hybrid censoring data

ABSTRACT

Based on the tampered failure rate model under the adaptive Type-II progressively hybrid censoring data, we discuss the maximum likelihood estimators of the unknown parameters and acceleration factors in the general step-stress accelerated life tests in this paper. We also construct the exact and unique confidence interval for the extended Weibull shape parameter. In the numerical analysis, we describe the simulation procedures to obtain the adaptive Type-II progressively hybrid censoring data in the step-stress accelerated life tests and present an experimental data to illustrate the performance of the estimators.     

Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals

This paper considers the analysis of Weibull distributed lifetime data observed under Type II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their asymptotic variances are derived. The expected time required to complete the life test under this censoring scheme is investigated.     

Optimal progressive interval censoring plan under accelerated life test with limited budget

In this paper, we investigate some inference and design problems related to multiple constant-stress accelerated life test with progressive type-I interval censoring. A Weibull lifetime distribution at each stress-level combination is considered. The scale parameter of Weibull distribution is assumed to be a log-linear function of stresses. We obtain the estimates of the unknown parameters through the method of maximum likelihood, and also derive the Fisher's information matrix. The optimal number of test units, number of inspections, and length of the inspection interval are determined under D-optimality, T-optimality, and E-optimality criteria with cost constraint. An algorithm based on nonlinear mixed-integer programming is proposed to the optimal solution. The sensitivity of the optimal solution to changes in the values of the different parameters is studied.