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.     

Design of accelerated life test sampling plans with a nonconstant shape parameter

Accelerated life test sampling plans (ALTSPs) provide information quickly on the lifetime distribution of products by testing them at higher-than-usual stress level to induce early failures and reduce the testing efforts. In the traditional design of ALTSPs for Weibull distribution, it is assumed that the shape parameter remains constant over all stress levels. This paper extends the existing design of ALTSPs to Weibull distribution with a nonconstant shape parameter and presents two types of ALTSPs; time-censored and failure-censored. Optimum ALTSPs which satisfy the producer’s and consumer’s risk requirements and minimize the asymptotic variance of the test statistic for deciding the lot acceptability are obtained. The properties of the proposed ALTSPs and the effects of errors in pre-estimate of the design parameters are also investigated.     

Weibull 分布基于恒加试验尺度参数估计

对 Weibull 分布场合恒加寿命试验的参数估计进行了讨论,在现有参数估计的基础上作了进一步改进,从而使改进后的参数估计更优.     

对数正态分布场合有非常数尺度参数恒加试验的参数估计

讨论了对数正态分布场合有非常数尺度参数恒加寿命试验的参数估计，导出了基于全样本和定数截尾样本恒加试验的点估计和近似区间估计。