Planning progressive type-I interval censoring life tests with competing risks

[[abstract]]In this article, we investigate some reliability and quality problems when the competing risks data are progressive type-I interval censored with binomial removals. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher's information matrix. The optimal lengths of the inspection intervals are determined under two different criteria. The reliability sampling plans are established under given producer's and customer's risks. A Monte Carlo simulation is conducted to evaluate the performance of the estimators, and also some numerical results are presented.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]電子

Maximum likelihood estimation for life distributions with competing failure modes

Systems which are placed on test at time zero, function for a period and die at some random time were studied. Failure may be due to one of several causes or modes. The parameters of the life distribution may depend upon the levels of various stress variables the item is subject to. Maximum likelihood estimation methods are discussed. Specific methods are reported for the smallest extreme-value distributions of life. Monte-Carlo results indicate the methods to be promising. Under appropriate conditions, the location parameters are nearly unbiased, the scale parameter is slight biased, and the asymptotic covariances are rapidly approached

Empirical Likelihood Ratio Tests for Homogeneity of Distributions of Component Lifetimes from System Lifetime Data with Known System Structures

In system reliability, practitioners may be interested in testing the homogeneity of the component lifetime distributions based on system lifetimes from multiple data sources for various reasons, such as identifying the component supplier that provides the most reliable components. In the first part of the dissertation, we develop distribution-free hypothesis testing procedures for the homogeneity of the component lifetime distributions based on system lifetime data when the system structures are known. Several nonparametric testing statistics based on the empirical likelihood method are proposed for testing the homogeneity of two or more component lifetime distributions. The computational approaches to obtain the critical values of the proposed test procedures are provided. The performances of the proposed empirical likelihood ratio test procedures are evaluated and compared to the nonparametric Mann-Whitney $U$ test and some parametric test procedures. The simulation results show that the proposed test procedures provide comparable power performance under different sample sizes and underlying component lifetime distributions, and they are powerful in detecting changes in the shape of the distributions. In collecting system lifetime data, censoring is often adopted due to time and budget constraints. In the second part of the dissertation, we consider the situation where the system lifetime data from two different kinds of systems are subjected to Type-II censoring, and we are interested in testing the homogeneity of distributions of component lifetimes from Type-II censored system lifetime data with known system structures. Based on the Mann-Whitney $U$ test and empirical likelihood ratio tests developed for testing the homogeneity of distributions of component lifetimes with complete system lifetime data, we propose different non-parametric test procedures using the idea of permutation of the censored system lifetimes. We consider a restricted assumption on the equality of the censored lifetimes to reduce the permutations required in the computation. The computational approaches to obtain the critical values of the proposed test procedures are provided using the Monte Carlo method. A practical example is used to illustrate the proposed test procedures. Then, the power performances of the proposed test procedures are evaluated and compared using a Monte Carlo simulation study. The simulation results show that the proposed test procedures provide good power performance for Type-II censored system lifetime data under different scenarios. Finally, summaries of the major contributions of the thesis and concluding remarks are provided. Some possible future research directions are also discussed

Optimal Progressive Group-Censoring Plans for Chen Distribution under Cost Constraint

[[abstract]]In this paper, the optimal design of a progressively group-censored life test with the restriction of experimental budget is developed for the Chen distribution is considered. The maximum likelihood estimates, approximate confidence intervals for the parameters based on progressively group-censored sample are obtained. Wu et al.’s (2008a) approach is used to determine the number of test units, the number of inspections and the length of inspection interval of a life test under a pre-determined budget of experiment such that the determinant of the asymptotic variances-covariance matrix of estimators of parameters is minimum. A numerical example is presented and the sensitivity analysis is also studied.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Optimal Experimental Planning of Reliability Experiments Based on Coherent Systems

In industrial engineering and manufacturing, assessing the reliability of a product or system is an important topic. Life-testing and reliability experiments are commonly used reliability assessment methods to gain sound knowledge about product or system lifetime distributions. Usually, a sample of items of interest is subjected to stresses and environmental conditions that characterize the normal operating conditions. During the life-test, successive times to failure are recorded and lifetime data are collected. Life-testing is useful in many industrial environments, including the automobile, materials, telecommunications, and electronics industries. There are different kinds of life-testing experiments that can be applied for different purposes. For instance, accelerated life tests (ALTs) and censored life tests are commonly used to acquire information in reliability and life-testing experiments with the presence of time and resource limitations. Statistical inference based on the data obtained from a life test and effectively planning a life-testing experiment subject to some constraints are two important problems statisticians are interested in. The experimental design problem for a life test has long been studied; however, the experimental planning considering putting the experimental units into systems for a life-test has not been studied. In this thesis, we study the optimal experimental planning problem in multiple stress levels life-testing experiments and progressively Type-II censored life-testing experiments when the test units can be put into coherent systems for the experiment. Based on the notion of system signature, a tool in structure reliability to represent the structure of a coherent system, under different experimental settings, models and assumptions, we derive the maximum likelihood estimators of the model parameters and the expected Fisher information matrix. Then, we use the expected Fisher information matrix to obtain the asymptotic variance-covariance matrix of the maximum likelihood estimators when $n$-component coherent systems are used in the life-testing experiment. Based on different optimality criteria, such as $D$-optimality, $A$-optimality and $V$-optimality, we obtain the optimal experimental plans under different settings. Numerical and Monte Carlo simulation studies are used to demonstrate the advantages and disadvantages of using systems in life-testing experiments

Analysis Of Type-II Progressively Hybrid Censored Competing Risks Data

A Type-II progressively hybrid censoring scheme for competing risks data is introduced, where the experiment terminates at a pre-specified time. The likelihood inference of the unknown parameters is derived under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. The maximum likelihood estimators of the unknown parameters are obtained in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes

Bayesian accelerated life tests: exponential and Weibull models

Reliability life testing is used for life data analysis in which samples are tested under normal conditions to obtain failure time data for reliability assessment. It can be costly and time consuming to obtain failure time data under normal operating conditions if the mean time to failure of a product is long. An alternative is to use failure time data from an accelerated life test (ALT) to extrapolate the reliability under normal conditions. In accelerated life testing, the units are placed under a higher than normal stress condition such as voltage, current, pressure, temperature, to make the items fail in a shorter period of time. The failure information is then transformed through an accelerated model commonly known as the time transformation function, to predict the reliability under normal operating conditions. The power law will be used as the time transformation function in this thesis. We will first consider a Bayesian inference model under the assumption that the underlying life distribution in the accelerated life test is exponentially distributed. The maximal data information (MDI) prior, the Ghosh Mergel and Liu (GML) prior and the Jeffreys prior will be derived for the exponential distribution. The propriety of the posterior distributions will be investigated. Results will be compared when using these non-informative priors in a simulation study by looking at the posterior variances. The Weibull distribution as the underlying life distribution in the accelerated life test will also be investigated. The maximal data information prior will be derived for the Weibull distribution using the power law. The uniform prior and a mixture of Gamma and uniform priors will be considered. The propriety of these posteriors will also be investigated. The predictive reliability at the use-stress will be computed for these models. The deviance information criterion will be used to compare these priors. As a result of using a time transformation function, Bayesian inference becomes analytically intractable and Markov Chain Monte Carlo (MCMC) methods will be used to alleviate this problem. The Metropolis-Hastings algorithm will be used to sample from the posteriors for the exponential model in the accelerated life test. The adaptive rejection sampling method will be used to sample from the posterior distributions when the Weibull model is considered

Bayesian Life Test Planning for the Log-Location-Scale Family of Distributions

This paper describes Bayesian methods for life test planning with censored data from a log-location-scale distribution, when prior information of the distribution parameters is available. We use a Bayesian criterion based on the estimation precision of a distribution quantile. A large sample normal approximation gives a simplified, easy-tointerpret, yet valid approach to this planning problem, where in general no closed form solutions are available. To illustrate this approach, we present numerical investigations using the Weibull distribution with Type II censoring. We also assess the effects of prior distribution choice. A simulation approach of the same Bayesian problem is also presented as a tool for visualization and validation. The validation results generally are consistent with those from the large sample approximation approach