混合截尾和定时截尾试验weibull分布抽样方案的比较

混合截尾试验是定时和定数截尾的一种有用的推广。本文研究了Ｗｅｉｂｕｌｌ分布和混合截尾试验的一次抽样方案,并对可靠决策损失函数给出了贝叶斯风险的显式表达式。比较陈和林的模型（１９９９）,我们得混合截尾试验的抽样方案于定时抽样方案。     

截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文［１］给出了参数λ在先验分布为Γ（α，β）分布的假设下的Ｂａｙｅｓ估计．文［３］给出了在平方损失下的Ｂａｙｅｓ估计．本文讨论先验分布为Ｂ（ａ，ｂ）分布时，参数λ的Ｂａｙｅｓ估计．     

截尾情形下Weibull分布的最大似然估计

本文利用似然函数的单调性,分别给出了定时截尾和定数截尾情形下Weibull分布中参数最大似然估计(MLE)的数值解法.数据模拟研究表明,所给出的解法效果良好.     

截尾分布与截尾样本的统计分析

[1]中给出了样本容量n已知的(n,r）定时截尾不完全样本的分析方法。在[2]中我们讨论了n未知的（n,r）定时截尾不完全样本并较好地处理了晚截尾的接近完全样本的分析。本文中我们相应于截尾样本，引入截尾分布，通过用截尾样本拟合截尾分布而得到寿命T的整体分布。此方法无论对n已知还是n未知，对早截尾还是晚截尾的（n,r）定时截尾样本都适用。并且此方法还可推广到对其它形式的不完全样本的处理。     

定时截尾下指数分布产品可靠性抽样检验方案

本文给出了制订定时截尾下指数分布产品可靠性抽样检验方案的统计方法.检验统计量是平均寿命倒数的极大似然估计.提出了一种选择截尾时间的方法.利用分布分位数的Cornish-Fisher展开近似地确定了样本量和接收常数.模拟结果表明,本文给出的方法是可行的.     

Birnbaum—Saunders疲劳寿命分布在截尾试验情形的统计分析

本文讨论了Birnbaum-saunders疲劳寿命分布在定数截尾和定时截尾情形参数的点估计和区间估计,对所给点估计作了模拟研究。     

双参数威布尔分布下可靠性抽样检验

对于失效时间遵从双参数威布尔分布产品，本文分别提出了制订全样本下和定时截尾样本下可靠性抽样检验方案的统计方法．质量统计是不可靠度的矩估计的严格增加函数．选择截尾时间的方法被提出．利用分布分位数的Coruish-Fisher展开，佯本量和接收常数被近似地确定．模拟结果表明。本文给出的方法是可行的．     

Weibull分布定时截尾试验数据情形下可靠度的置信限

本文针对Weibull分布定时截尾型试验数据提出了一种计算可靠度置信限的方法。通过采用数据填充的方式将不完全数据虚拟成完全数据,利用完全数据情形下可靠度置信限的计算方法得到删失数据情形下可靠度的置信限。模拟研究表明本文提出的算法具有较好的计算稳定性和可操作性。     

Weibull分布恒定应力加速寿命试验的Bayes估计

对定时和定数截尾样本情形CE模型下Weibull分布场合恒定应力加速寿命试验进行了Bayes统计分析,利用Laplace方法给出了该模型的近似Bayes估计.最后通过模拟实例表明该Bayes估计是有效的.     

指数寿命定时截尾数据情形下可靠度的置信限

本文提供了一种指数寿命定时截尾寿命试验数据情形下参数的点估计方法,并在该点估计的基础上,利用Winterbottom[1]推广了的Cornish－Fisher（记为WCF）展开给出了参数的区间估计．进一步讨论了部件为指数寿命定时截尾寿命试验数据情形下系统可靠性综合问题,并通过数值模拟说明本文方法的可行性．     

Bayesian variable sampling plan for the weibull distribution with type I censoring

In this article, we study a model of a single variable sampling plan with Type I censoring. Assume that the quality of an item in a batch is measured by a random variable which follows a Weibull distributionW (λ,m), with scale parameter λ and shape parameterm having a gamma-discrete prior distribution or σ=1/λ andm having an inverse gamma-uniform prior distribution. The decision function is based on the Kaplan-Meier estimator. Then, the explicit expressions of the Bayes risk are derived. In addition, an algorithm is suggested so that an optimal sampling plan can be determined approximately after a finite number of searching steps.     

Bayesian single and double variable sampling plans for the Weibull distribution with censoring

The sampling inspection problem is one of the main research topics in quality control. In this paper, we employ Bayesian decision theory to study single and double variable sampling plans, for the Weibull distribution, with Type II censoring. A general loss function which includes the sampling cost, the time-consuming cost, the salvage value, and the after-sales cost is proposed to determine the Bayes risk and the corresponding optimal sampling plan. Explicit expressions for the Bayes risks for both single and double sampling plans are derived, respectively. Numerical examples are given to illustrate the effectiveness of the proposed method. Comparisons between single and double sampling plans are made, and sensitivity analysis is performed.     

Bayesian optimal life‐testing plan under the balanced two sample type‐II progressive censoring scheme

Joint progressive censoring schemes are quite useful to conduct comparative life‐testing experiment of different competing products. Recently, Mondal and Kundu (“A New Two Sample Type‐II Progressive Censoring Scheme,” Commun Stat‐Theory Methods; 2018) introduced a joint progressive censoring scheme on two samples known as the balanced joint progressive censoring (BJPC) scheme. Optimal planning of such progressive censoring scheme is an important issue to the experimenter. This article considers optimal life‐testing plan under the BJPC scheme using the Bayesian precision and D‐optimality criteria, assuming that the lifetimes follow Weibull distribution. In order to obtain the optimal BJPC life‐testing plans, one needs to carry out an exhaustive search within the set of all admissible plans under the BJPC scheme. However, for large sample size, determination of the optimal life‐testing plan is difficult by exhaustive search technique. A metaheuristic algorithm based on the variable neighborhood search method is employed for computation of the optimal life‐testing plan. Optimal plans are provided under different scenarios. The optimal plans depend upon the values of the hyperparameters of the prior distribution. The effect of different prior information on optimal scheme is studied.     

Optimum life testing plans in presence of hybrid censoring: A cost function approach

Hybrid censoring scheme is a combination of Type‐I and Type‐II censoring schemes. Determination of optimum hybrid censoring scheme is an important practical issue in designing life testing experiments to enhance the information on reliability of the product. In this work, we consider determination of optimum life testing plans under hybrid censoring scheme by minimizing the total cost associated with the experiment. It is shown that the proposed cost function is scale invariant for some selected distributions. Optimum solution cannot be obtained analytically. We propose a method for obtaining the optimum solution and consider Weibull distribution for illustration. We also studied the sensitivity of the optimal solution to the misspecification of parameter values and cost components through a well‐designed sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

A lifetime model with increasing failure rate

This paper deals with a new two-parameter lifetime distribution with increasing failure rate. This distribution is constructed as a distribution of a random sum of independent exponential random variables when the sample size has a zero truncated binomial distribution. Various statistical properties of the distribution are derived. We estimate the parameters by maximum likelihood and obtain the Fisher information matrix. Simulation studies show the performance of the estimators. Also, estimation of the parameters is considered in the presence of censoring. A real data set is analyzed for illustrative purposes and it is noted that the distribution is a good competitor to the gamma, Weibull, exponentiated exponential, weighted exponential and Poisson-exponential distributions for this data set.     

A Kind of the ASN' Extreme Value forMeasuring Double Sampling Plan

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