Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17 (1988), 1857–1870] considered a hybrid censoring scheme and obtained the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution along with an exact lower confidence bound. Childs et al. [Exact likelihood inference based on Type‐I and Type‐II hybrid censored samples from the exponential distribution, Ann Inst Statist Math 55 (2003), 319–330] recently derived an alternative simpler expression for the distribution of the MLE. These authors also proposed a new hybrid censoring scheme and derived similar results for the exponential model. In this paper, we propose two generalized hybrid censoring schemes which have some advantages over the hybrid censoring schemes already discussed in the literature. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under these generalized hybrid censoring schemes. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

屏蔽数据在新型截尾样本下系统的可靠性分析

当系统含有屏蔽数据时,在具有随机移走逐步增加型截尾模型下,讨论了部件寿命服从双参数指数分布的串联系统可靠性估计问题。设随机移走系统数服从二项分布,利用极大似然方法,Bayes理论及方法,推导出双参数指数部件参数、系统可靠性函数、失效率函数及移走概率的极大似然估计和Bayes估计。并利用Monte Carlo方法对两种估计结果进行了比较,表明Bayes估计较极大似然估计效果更优。     

Estimating the point availability with right‐censored data

The point availability of a one‐unit system at a specified time is defined as the probability that the component is operating at that time. When both operating time and repair time are subject to random (right) censorship, we propose an asymptotic nonparametric approach for constructing confidence intervals for the point availability of the system. The technique is based on the fact that a product limit estimator converges to a Gaussian process. The method is also extended to finding confidence intervals for the point availability of a complex system using the δ‐Method. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 119–127, 1999     

Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint

By running life tests at higher stress levels than normal operating conditions, accelerated life testing (ALT) quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant‐stress testing, a unit is tested at a fixed stress level until failure or the termination time point of test, whereas step‐stress testing allows the experimenter to gradually increase the stress levels at some prefixed time points during the test. In this work, the optimal k‐level constant‐stress and step‐stress ALTs are compared for the exponential failure data under complete sampling and Type‐I censoring. The objective is to quantify the advantage of using the step‐stress testing relative to the constant‐stress one. Assuming a log‐linear life–stress relationship with the cumulative exposure model for the effect of changing stress in step‐stress testing, the optimal design points are determined under C/D/A‐optimality criteria. The efficiency of step‐stress testing to constant‐stress one is then discussed in terms of the ratio of optimal objective functions based on the information matrix. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013     

Statistical analysis for masked system life data from Marshall‐Olkin Weibull distribution under progressive hybrid censoring

This paper considers the statistical analysis of masked data in a series system, where the components are assumed to have Marshall‐Olkin Weibull distribution. Based on type‐I progressive hybrid censored and masked data, we derive the maximum likelihood estimates, approximate confidence intervals, and bootstrap confidence intervals of unknown parameters. As the maximum likelihood estimate does not exist for small sample size, Gibbs sampling is used to obtain the Bayesian estimates and Monte Carlo method is employed to construct the credible intervals based on Jefferys prior with partial information. Numerical simulations are performed to compare the performances of the proposed methods and one data set is analyzed.     

不同损失函数下指数-泊松分布的Bayes估计

基于定数截尾样本,在熵损失、Linex损失和刻度平方损失函数下,给出了指数-泊松分布参数的Bayes估计,并证明了所给估计都是容许的。最后给出了随机模拟例子,对所给估计结果的优良性进行了分析比较。     

逐步Ⅰ型混合截尾试验下Burr部件的可靠性分析

在逐步Ⅰ型混合截尾试验下,研究了Burr部件寿命参数及可靠性指标的极大似然估计和Bayes估计.利用简单迭代方法,给出了寿命参数和可靠性指标的极大似然估计的数值解.然后利用Lindely Bayes近似算法得到了平方损失下寿命参数以及可靠性指标的Bayes估计.最后,运用Monte-Carlo方法对各估计结果作了模拟比较,结果表明Bayes估计较极大似然估计的误差小.     

Estimating reliability of components with increasing failure rate using series system data

The maximum likelihood estimator (MLE) for a distribution function with increasing failure rate is derived, based on a collection of series system data. Applications can arise in industries where operating environments make available only such system-level data, due to system configuration or type-II censoring. The estimator can be solved using isotonic regression. For the special case in which systems contain one component, the estimator is equivalent to the restricted maximum likelihood estimator of Marshall and Proschan [9]. The MLE is illustrated using emergency diesel generator failure data from the nuclear industry. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 115–123, 1998     

Monitoring censored lifetime data with a weighted‐likelihood scheme

Lifetime experiments are common in many research areas and industrial applications. Recently, process monitoring for lifetime observations has received increasing attention. However, some existing methods are inadequate as neither their in control (IC) nor out of control (OC) performance is satisfactory. In addition, the challenges associated with designing robust and flexible control schemes have yet to be fully addressed. To overcome these limitations, this article utilizes a newly developed weighted likelihood ratio test, and proposes a novel monitoring strategy that automatically combines the likelihood of past samples with the exponential weighted sum average scheme. The proposed Censored Observation‐based Weighted‐Likelihood (COWL) control chart gives desirable IC and OC performances and is robust under various scenarios. In addition, a self‐starting control chart is introduced to cope with the problem of insufficient reference samples. Our simulation shows a stronger power in detecting changes in the censored lifetime data using our scheme than using other alternatives. A real industrial example based on the breaking strength of carbon fiber also demonstrates the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 631–646, 2017     

Designing acceptance sampling schemes for life testing with mixed censoring

Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time‐consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004