指数型产品失效率鉴定试验的Bayes方案

本文用可靠性增长方法给出了产品鉴定试验的一种Ｂａｙｅｓ方法,这种鉴定试验方法了产品研制过程中的先验信息,在确保产品质量的前提下,与传统的鉴定试验方案相比,将大大节省试验时间。     

关于元件失效率等级鉴定试验的一种贝叶斯方法

为鉴定元件失效率的等级,按目前国家标准GB1772-79规定的抽样方案,需要做大量的试验,构成人力、物力的浪费,做较高等级的鉴定甚至是不可能的.本文采用贝叶斯方法,利用大量的历史数据和工程技术人员的丰富经验确定先验分布,制定出元件失效率等级鉴定试验的一种新方案.按照这一方案,在确保产品质量的前提下,将大大节省试验时间,从而得到十分可观的经济效益。     

富集提钒工艺经济效益分析

高配比钢渣返回富集提钒是一项综合利用钒资源的新工艺．本文利用该工艺试验的原始数据，运用多元统计分析方法对新工艺的可行性给予了鉴定，并且建立了产品质量指标与其影响因素之间的数学模型。从而进行定量分析以寻求最佳生产方案，同时对工艺的综合经济效益作了评价。     

指数型产品的Bayes可靠性鉴定试验

利用可靠性增长模型确定正样产品失效率的先验分布.综合考虑由弃真和存伪风险所造成的试验损失和其他试验费用,建立可靠性鉴定试验的损失评估模型.分别用两种风险准则约束两类决策风险.根据Bayes决策理论,得到失效数和总试验时间的关系,确定使得试验损失函数值最小的鉴定方案.最后通过算例体现方法的有效性,与经典方法和其他Bayes鉴定方法相比较有其优越性.     

二项分布下的一种贝叶斯可靠性验收试验方案

为了合理利用先验信息制定可靠性验收试验方案，以降低验收试验的费用，在进行可靠性定型试验的前提下，提出了一种先验信息加工方法，并根据生产与使用双方实际所关心的风险意义，制定了产品可靠性验收试验的一种贝叶斯方案。算例结果证实，该方案在保证了生产方与使用方利益的前提下，减少了试验量，降低了验收试验费用。说明所提出的先验信息利用方式是有效的。     

工科院校高等数学作业批改方法的改革试验

长期以来，高校的数学作业批改方法基本上是沿用中小学的固定模式．本文针对传统的作业批改方法的诸多弊端论证了改革的必要性，用层次分析法对几种方案进行了决策分析，确定出一种改革新方案，并将该方案在实际教学中进行了对比试验，将取得的试验数据用数理统计方法进行分析．试验取得了圆满的成功     

R-PVC挤出粒料优化设计——介绍多指标试验设计一种方法

用优化理论指导生产试验获得的最佳方案，应该使产品质量和加工性能都好且原料成本低．本文介绍的方案特点之一是在试验设计过程中将三者紧密地联系在一起进行优选．同时，对多指标且需保证各项指标特性值应满足一定要求的试验设计，用多指标综合评分法就难于兼顾，本文介绍一种选优方法．结果，只经两轮试验就获得最佳方案，经济效应显著．     

牡丹江地区“山地资源”开发利用的优化设计

本文介绍了山地资源开发利用的优化试验方案 ,并对试验结果进行了分析。该方案取得了较好的经济、生态和社会效益。     

计算机直接试验设计

根据试验设计的原则，直接按因素－水平的实际组合随机安排若干个试验方案，按五种优良性或均匀性准则从中选出较优者，用回归分析方法分析试验结果．     

两套种作物的农艺优化教学模型研究

本文是采用回归旋转设计方法，研究两套种作物农艺优化的数学模型．利用计算机模拟仿真，优化农艺方案．示范验证表明，这种试验方法可行，优化方案应用效果显著．     

一种估计精度限制下的加速退化试验最优设计

讨论了一类步进应力的加速退化试验,在试验假定下,以退化失效分布平均寿命的极大似然估计与其真值的接近程度为标准得到一个精度限制．然后根据试验的过程得到了试验成本函数的一般表达形式．在估计精度的限制之下,最小化成本函数,以此得出试验的最优设计模型．最后,给出了一个数值例子,展示了优化设计的过程．     

Reliability tests for Weibull distribution with variational shape parameter based on sudden death lifetime data

In the traditional design of reliability tests for assuring the mean time to failure (MTTF) in Weibull distribution with shape and scale parameters, it has been assumed that the shape parameter in the acceptable and rejectable populations is the same fixed number. For the purpose of expanding applicability of the reliability testing, Hisada and Arizono have developed a reliability sampling scheme for assuring MTTF in the Weibull distribution under the conditions that shape parameters in the both populations do not necessarily coincide, and are specified as interval values, respectively. Then, their reliability test is designed using the complete lifetime data. In general, the reliability testing based on the complete lifetime data requires the long testing time. As a consequence, the testing cost becomes sometimes expensive. In this paper, for the purpose of an economical plan of the reliability test, we consider the sudden death procedure for assuring MTTF in Weibull distribution with variational shape parameter.     

Optimum step-stress accelerated degradation test for Wiener degradation process under constraints

To assess a product's reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.     

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As a new reliability test plan, generalized progressive hybrid censoring can improve test efficiency by allowing experimenters to observe a pre-specified number of failure samples before the final termination point. Based on a class of widely used life distribution in life data analysis --- generalized exponential distribution, this paper discusses its parameters inference issue under generalized progressive hybrid censoring scheme. EM Algorithm is used to estimate parameters of the considered model. Simulation studies and a real-data analysis are carried out to illustrate the performance of finite sample for the proposed procedure.     

Optimal plan for Wiener constant-stress accelerated degradation model

This paper explores inferential procedures for the Wiener constant-stress accelerated degradation model under degradation mechanism invariance. The exact confidence intervals are obtained for the parameters of the proposed accelerated degradation model. The generalized confidence intervals are also proposed for the reliability function and pth quantile of the lifetime at the normal operating stress level. In addition, the prediction intervals are developed for the degradation characteristic, lifetime and remaining useful life of the product at the normal operating stress level. The performance of the proposed generalized confidence intervals and the prediction intervals is assessed by the Monte Carlo simulation. Furthermore, a new optimum criterion is proposed based on minimizing the mean of the upper prediction limit for the degradation characteristic at the design stress level. The exact optimum plan is also derived for the Wiener accelerated degradation model according to the proposed optimal criterion. The proposed interval procedures and optimum plan are the free of the equal testing interval assumption. Finally, two examples are provided to illustrate the proposed interval procedures and exact optimum plan. Specifically, based on the degradation data of LEDs, some interval estimates of quantities related to reliability indicators are obtained. For the degradation data of carbon-film resistors, the optimal allocation of test units is derived in terms of the proposed optimal criterion.     

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.     

Design of component reliability test plan for a series system having time dependent testing cost with the presence of covariates

Consider a series system with n different components. Assume that the lifetime of \(i\text {-}th\) component follows exponential distribution with parameter \( \lambda _{i}(\mathbf {x}), \ \mathbf {x} \in \mathbb {R}^{k} \) is a covariate vector, \( 1\le i \le n \). For example, \( \mathbf {x} \) may be (temperature, pressure, humidity), so that \( \mathbf {x} \in \mathbb {R}^{3} \) represents a three dimensional covariate vector. Assume that each \( \lambda _{i}(\mathbf {x}),1\le i \le n \), is distinct and depends upon \( \mathbf {x} \) through linear relationship. Prior information available in the form of upper bounds on \( \lambda _{i}(\mathbf {x}) \) are also incorporated in the design. We propose to obtain optimal reliability test plan based on maximum likelihood estimator of system reliability. A non-linear integer optimization problem is formulated for minimizing the maximum of total expected cost involved in testing satisfying usual probability requirements (Type-I and Type-II error constraints). In addition, it is also established through simulation that the derived sampling plan meets the specified producer’s and consumer’s risks as well. A sensitivity analysis is carried out to study the effect of various input parameters on maximum total expected testing cost. Finally, a qualitative analysis is presented at the end to discuss the nature of sampling plan derived. Several numerical examples are discussed to illustrate our test plan, and it is observed that the proposed plan has significant potential to reduce the total number of components to be tested for failure. It is noted that the number of components to be tested for failure is reduced by about 96% as compared to the existing test plans in the literature.     

Feasible generalized monotone line search SQP algorithm for nonlinear minimax problems with inequality constraints

In this paper, the nonlinear minimax problems with inequality constraints are discussed, and a sequential quadratic programming (SQP) algorithm with a generalized monotone line search is presented. At each iteration, a feasible direction of descent is obtained by solving a quadratic programming (QP). To avoid the Maratos effect, a high order correction direction is achieved by solving another QP. As a result, the proposed algorithm has global and superlinear convergence. Especially, the global convergence is obtained under a weak Mangasarian–Fromovitz constraint qualification (MFCQ) instead of the linearly independent constraint qualification (LICQ). At last, its numerical effectiveness is demonstrated with test examples.