Interval Reliability,Corrections and Developments of “Reliability Measures of Semi-Markov Systems with General State Space”

This paper present the interval reliability of a semi-Markov systems in general state space in continuous and discrete-time cases. We get also, as a particular case the interval reliability for the alternating renewal process. This is a continuation of the paper Limnios (Methodol Comput Appl Probab 14(4):895–917, 2012) where the interval reliability is referred as interval availability and also Propositions 2.1 and 3.1 below replace Propositions 3.4 and 5.3 respectively.     

Non-Probabilistic Structural Reliability Analysis Integrating the PSO and the Kriging Model北大核心CSCD

针对复杂结构可靠性分析中面临的隐式功能函数和小样本问题,提出了一种粒子群优化和Kriging模型相结合的结构非概率可靠性分析方法。采用多维椭球描述结构不确定参数,运用粒子群优化对模型相关参数进行求解,并构建隐式功能函数的Kriging模型进行可靠性分析。三个算例结果表明所提方法有效可行,精度和效率均优于基于Kriging模型的非概率可靠性分析方法。     

Reliability and efficiency of algorithms for computing the significance of the Mann–Whitney test

Motivated by recent applications of the Mann–Whitney U test to large data sets we took a critical look at current methods for computing its significance. Surprisingly, we found that the two fastest and most popular tools for exact computation of the test significance, Dinneen and Blakesley’s and Harding’s, can exhibit large numerical errors even in moderately large datasets. In addition, another method proposed by Pagano and Tritchler also suffers from a similar numerical instability and can produce inaccurate results. This motivated our development of a new algorithm, mw-sFFT, for the exact computation of the Mann–Whitney test with no ties. Among the class of exact algorithms that are numerically stable, mw-sFFT has the best complexity: O(m ² n) versus O(m ² n ²) for others, where m and n are the two sample sizes. This asymptotic efficiency is also reflected in the practical runtime of the algorithm. In addition, we also present a rigorous analysis of the propagation of numerical errors in mw-sFFT to derive an error guarantee for the values computed by the algorithm. The reliability and efficiency of mw-sFFT make it a valuable tool in compuational applications and we plan to provide open-source libraries for it in C++ and Matlab.     

Reliability inference of stress–strength model for the truncated proportional hazard rate distribution under progressively Type-II censored samples

This paper considers the reliability inference for the truncated proportional hazard rate stress–strength model based on progressively Type-II censoring scheme. When the stress and strength variables follow the truncated proportional hazard rate distributions, the maximum likelihood estimation and the pivotal quantity estimation of stress–strength reliability are derived. Based on the percentile bootstrap sampling technique, the 95% confidence interval of stress–strength reliability is obtained, as well as the related coverage percentage. Moreover, based on the Fisher Z transformation and the modified generalized pivotal quantity, the 95% modified generalized confidence interval for the stress–strength reliability is obtained. The performance of the proposed method is evaluated by the Monte Carlo simulation. The numerical results show that the pivotal quantity estimators performs better than the maximum likelihood estimators. At last, two real datasets are analyzed by the proposed methodology for illustrative purpose. The results of real example analysis show that our model can be applied to the practical problem, the truncated proportional hazard rate distribution can fit the failure data better than other distributions, and the algorithms in this paper are suitable to handle the small sample data.     

Is reliability a new science? A paper from the panel session held at the 10th International Conference on Mathematical Methods in Reliability

The 10th International Conference on Mathematical Methods in Reliability, MMR 2017, held in Grenoble, France during July 3‐7, entailed a panel discussion entitled “Is reliability a new science?” with Mark Brown, Regina Liu, William Meeker, Sheldon Ross, and Nozer Singpurwalla as panelists. Bill Meeker also doubled as a chair and as a moderator of the panel. The panel discussion was spawned by the recent appearance of a book by Professor Paolo Rocchi, Docent Emeritus of IBM, titled “Reliability is a new science: Gnedenko was right” published by Springer in 2017. The panel discussion was well attended and enthusiastically received and could serve as a forerunner to other such panel discussions at future MMR conferences. This paper presents some elements from the lively debate generated by this discussion.     

Asymptotically Optimal in Reliability Circuits in Two Bases Under Failures of 0 (<Emphasis Type="Italic">k</Emphasis> − 1) Type at the Outputs of Elements

We consider a problem of the realization of k-valued logics functions (k ≥ 3) by circuits in two bases: in the Rosser–Turkett basis and in its dual basis. We assume that the basis gates are exposed to faults at outputs: only of type 0 or only of type k ? 1, and they pass into faulty states independently of each other. We describe a constructive method for the synthesis of an asymptotically optimal reliable circuit for almost any function of k-valued logic, we found the upper and lower bounds of circuits unreliability and the class of functions for which the lower bounds are true.