Tables of the Negative Binomial Probability Distribution

An age replacement policy requires that a unit be replaced when it attains a specified age, or at failure, whichever occurs first. The mathematical solution to the problem of what is the optimal age for replacement is well known. This paper adapts this general mathematical solution to the cases when a truncated normal, Gamma, or Weibull distribution can be assumed. Graphs are presented from which one can readily ascertain the optimal solutions for these models.     

Estimation of the Parameters of the Gamma Distribution by Sample Quantiles

This paper deals with large sample estimation of the location parameter (α₁ and the scale parameter α₂ in the gamma distribution with known shape parameter. Best linear unbiased estimates based on k sample quantiles are used. For a given k, the optimum spacings of the sample quantiles can be replaced by simpler “nearly optimum” spacings at virtually no loss of asymptotic efficiency. The theory behind the nearly optimum spacings is briefly reviewed. The major part of the paper concerns estimation of α₂ when α₂ is known. Nearly optimum spacings together with the coefficients to be used in computing the estimates are presented in a number of tables for k = 1(1) 10, and various values of the shape parameter. The paper also contains brief discussions of estimation of α₁, when α₂ is known, and simultaneous estimation of α₁ and α₂.     

Estimates of Reliability for Some Distributions Useful in Life Testing

In this paper the Rao-Blackwell and Lehmann-Scheff6 theorems are used to derive the minimum variance unbiased estimates of reliability for a number of distributions that have proved useful in life testing. Estimates are also obtained for the case of censored sample in the (one- and two-parameter) exponential case. A result of Pugh comes out as a special case of the gamma and censored one-parameter exponential model and Laurent's result as a special case of the censored twoparameter exponential model.     

On the Estimation of Safe Life When the Underlying Life Distribution Is Weibull

The problem of estimating Y ₍₁₎, the smallest of a future sample of k observations from the Weibull distribution, based on an observed sample from the same distribution, is considered. A conditional confidence interval solution is proposed for the estimation of Y ₍₁₎. The results have direct application in reliability theory, where the time until the first failure in a group of k items in service provides a measure of assurance regarding the operation of the items.     

A competing risk model for the reliability of cylinder liners in marine Diesel engines

In this paper, a competing risk model is proposed to describe the reliability of the cylinder liners of a marine Diesel engine. Cylinder liners presents two dominant failure modes: wear degradation and thermal cracking. The wear process is described through a stochastic process, whereas the failure time due to the thermal cracking is described by the Weibull distribution. The use of the proposed model allows performing goodness-of-fit test and parameters estimation on the basis of both wear and failure data. Moreover, it enables reliability estimates of the state of the liners to be obtained and the hierarchy of the failure mechanisms to be determined for any given age and wear level of the liner. The model has been applied to a real data set: 33 cylinder liners of Sulzer RTA 58 engines, which equip twin ships of the Grimaldi Group. Estimates of the liner reliability and of other quantities of interest under the competing risk model are obtained, as well as the conditional failure probability and mean residual lifetime, given the survival age and the accumulated wear. Furthermore, the model has been used to estimate the probability that a liner fails due to one of the failure modes when both of these modes act.     

The Compressibility of Single Crystals of Zinc in the Region of Positive and Negative Pressures

A new method is developed for measuring the velocity of sound in condensed materials under conditions of their shock compression, unloading, and tension, which is based on analyzing the reverberation of waves in a plane sample one of whose surfaces is in contact with a high-impedance material. This method is used to determine the dependence of the sound velocity in monocrystalline zinc on the compression/tension stress in the <001> direction in the range from -2 to 13 GPa. The lower limit of this range corresponds to approximately 25% of the maximum possible value of tension stresses in a zinc crystal of the given orientation.     

Insights into the dissolution mechanisms of detergent agglomerates: An approach to assess dissolution heterogeneity

In this work, the dissolution mechanisms of detergent agglomerates with different binders were investigated in aqueous solution. The dissolution processes of detergent agglomerates were online monitored by using in situ UV–VIS spectrophotometer and electric conductivity probe. Dissolution profiles were correlated by Weibull model to evaluate the time-dependent dissolution rate coefficient and to classify the type of dissolution rate function k_t(t). The Kullback-Leibler information distance d_K-L was proposed to assess the degree of dissolution heterogeneity. The results indicate that the sodium linear alkylbenzene sulfonates (NaLAS) and sodium carbonates (Na₂CO₃) in detergent agglomerates have different dissolution behaviors, and their dissolution rates are influenced by the type and content of binders. Moreover, detergent agglomerates using semi-solid NaLAS paste or liquid linear alkylbenzene sulfonic acid (HLAS) as binders in granulation processes follow different dissolution mechanisms in water.     

Effect of Field Stress Variance on Test to Field Correlation in Accelerated Reliability Demonstration Testing

This paper discusses the effect of field stress variance on the value of demonstrated reliability. In many cases, the acceleration factor for a reliability demonstration test is calculated based on a high percentile field stress level, typically corresponding to severe user or environmental conditions. In those cases, the actual field reliability for the population will be higher than that demonstrated by the test. This paper presents a mathematical approach to estimating ‘true’ field reliability based on the acceleration model and stress variable distribution over the product field population. This method is illustrated by an example of automotive electronics reliability demonstration testing and has a wide range of practical applications. Copyright © 2014 John Wiley & Sons, Ltd.     

Verification of the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links

Two approaches to the calculation of probability of loss of assured safety (PLOAS) in temperature dependent weak link/strong link systems are described and compared on the basis of three test problems. The approaches differ in that the first approach permits a separation of epistemic and aleatory uncertainty in the calculation of PLOAS and the second approach combines epistemic and aleatory uncertainty before the calculation of PLOAS. A discrepancy in the results obtained with the test problems led to the identification of an implementation error for one of the approaches. The importance and efficacy of well-designed verification test problems are demonstrated.     

An improved modified Weibull distribution applied to predict the reliability evolution of an aircraft lock mechanism

A new improved modified Weibull distribution (IMW), which consists of two tandem failure models is proposed in this paper. The order statistics, moment estimate and maximum likelihood estimate of the new distribution are investigated. The distribution is flexible for modeling the three phases of the modified bathtub-shaped hazard function. The modified distribution allows for enhanced statistical simulation. The new distribution is analyzed and applied to two sets of known lifetime data to demonstrate the advantages of the model. To verify the practical engineering applications of the model, reliability evolution test data for an aircraft door lock mechanism are analyzed and fitted. Based on the obtained trends of the lock hook angle and lock hook distance, we predict the evolutionary data for numerous mechanism samples, thus reducing the test cost. By considering the subdistribution and removing one parameter, the fitting effect is improved over that of the traditional distribution model.     

Verification test problems for the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links

Four verification test problems are presented for checking the conceptual development and computational implementation of calculations to determine the probability of loss of assured safety (PLOAS) in temperature-dependent systems with multiple weak links (WLs) and strong links (SLs). The problems are designed to test results obtained with the following definitions of loss of assured safety: (i) failure of all SLs before failure of any WL, (ii) failure of any SL before failure of any WL, (iii) failure of all SLs before failure of all WLs, and (iv) failure of any SL before failure of all WLs. The test problems are based on assuming the same failure properties for all links, which results in problems that have the desirable properties of fully exercising the numerical integration procedures required in the evaluation of PLOAS and also possessing simple algebraic representations for PLOAS that can be used for verification of the analysis.     

Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring

This article deals with the Bayesian inference of unknown parameters of the progressively censored Weibull distribution. It is well known that for a Weibull distribution, while computing the Bayes estimates, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist. In this article it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameter has a conjugate prior distribution. As expected, when the shape parameter is unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley's approximation to compute the Bayes estimates and the Gibbs sampling procedure to calculate the credible intervals. For given priors, we also provide a methodology to compare two different censoring schemes and thus find the optimal Bayesian censoring scheme. Monte Carlo simulations are performed to observe the behavior of the proposed methods, and a data analysis is onducted for illustrative purposes.     

An application of chemometric techniques to analyze the effects of the wave function modifications on the intermolecular stretching frequencies of the hydrogen-bonded complexes

Factorial design and principal component models are used to determine how ab initio H-bond stretching frequencies depend on characteristics of the molecular orbital wave functions of acetylene–HX, ethylene–HX and cyclopropane–HX π-type hydrogen complexes with X=F, Cl, CN, NC and CCH. The results obtained for the three sets of complexes show that factorial design and principal component analyses complement each other. Factorial design calculations clearly show that these frequencies are affected mostly by inclusion of electron correlation on the calculation level. On average, their values are increased by about 25 cm⁻¹ due to a change from the Hartree–Fock (HF) to Möller–Plesset 2 (MP2) level. Valence, diffuse and polarization main effects as well as valence–diffuse, diffuse–correlation and polarization–correlation interaction effects are also important to better describe a factorial model to the H-bond stretching frequencies of these hydrogen complexes. This simplified model has been successful in reproducing the complete ab initio results, which correspond to two hundred and forty calculations. Principal component analyses applied only to hydrogen-bonded complexes whose experimental frequencies are known, has revealed that the six-dimensional original space can be accurately represented by a bidimensional space defined by two principal components. Its graphical representation reveals that the experimental intermolecular stretching frequencies are in closest agreement with the MP2/6–31+G and MP2/6–311+G ab initio results.     

荷兰生活质量指标体系及对我国的启示

荷兰是最早建立生活质量指标体系的欧洲国家之一，该体系凭借其丰富而全面的内容以及鲜明的特点证明了其宝贵的价值。文章在参考和借鉴荷兰生活质量指标体系的基础上，结合我国社会经济发展的现状，提出应围绕“以人为本、和谐社会、持续发展”的目标综合多领域、多学科优势，构建具有中国特色的生活质量指标体系。     

Modelling of fracture toughness data in the ductile to brittle transition temperature region by statistical analysis

A fracture toughness database for a ferritic 22NiMoCr37 steel forging for 12.5, 25, 50 and 100 mm thick specimens tested at nine different temperatures has been analysed statistically. The method employed uses a statistical procedure based on competing risks to evaluate the fracture toughness and quantify the probability of cleavage fracture as a function of temperature, specimen thickness and ductile crack growth. This paper describes the application of the competing risks statistical methods to the fracture toughness database obtained from the joint European Project.     

Threshold toughness of polymers in the ductile to brittle transition region by different approaches

The fracture behavior of polymers in the ductile-to-brittle region is neither completely brittle nor entirely ductile. Besides, scatter in toughness results impairs the situation. Consequently, conventional methods based exclusively either on linear elastic fracture mechanics theory (LEFM) or on non-linear elastic fracture mechanics theory (NLEFM) are not suitable. It was demonstrated previously, that Weibull statistical method could be successfully used to determine the toughness threshold of polymers displaying ductile-to-brittle behavior. The present study compares the threshold toughness value determined by the statistical approach with other critical values calculated following other different suitable approaches: Low temperature plane strain fracture toughness, Plastic zone corrected fracture toughness, Stable and unstable propagation combined model, J extrapolated at zero stable propagation value, and Quasi J-R curve. The analysis was carried out on data points taken from fracture tests performed on polypropylene homopolymer, PPH, and on a blend of PPH and an elastomeric polyolefin, PPH/POes. The results of this analysis indicate that statistical, stable and unstable propagation combined model, and the J extrapolated at zero stable propagation value methods yield to very similar toughness threshold values being practically equivalent. In this case, threshold value was slightly smaller than the minimum J displayed by the experimental replicas, suggesting that it is an actual representative material toughness. Among these methodologies, the Statistical Method is applicable even if stable crack growth is difficult to determine. On the other hand, the methodologies based on LEFM tended to underestimate the fracture toughness, being very conservative while Quasi J-R curve method based on NLEFM overestimated the PPH/POes toughness value.     

An approach for using risk assessment in risk-informed decisions on plant-specific changes to the licensing basis

This paper discusses an acceptable approach that the US Nuclear Regulatory Commission staff has proposed for using Probabilistic Risk Assessment in making decisions on changes to the licensing basis of a nuclear power plant. First, the overall philosophy of risk-informed decision-making, and the process framework are described. The philosophy is encapsulated in five principles, one of which states that, if the proposed change leads to an increase in core damage frequency or risk, the increases must be small and consistent with the intent of the Nuclear Regulatory Commission's Safety Goal Policy Statement. The second part of the paper discusses the use of PRA to demonstrate that this principle has been met. The discussion focuses on the acceptance guidelines, and on comparison of the PRA results with those guidelines. The difficulties that arise because of limitations in scope and analytical uncertainties are discussed and approaches to accommodate these difficulties in the decision-making are described.     

The different roles of proximity in multiple informal network relationships: evidence from the cluster of high technology applied to cultural goods in Tuscany

The role of proximity in innovation and inter-organisational networks has received increasing attention over the past decade. Despite the rich literature, most contributions principally focus on only one type of relationship and mainly consider formal relationships such as R&;D partnerships, EU projects or patents. The aim of the study is to investigate the role of various forms of proximity in multiple informal inter-organisational relationships. The article focuses on two research questions: (i) How do the various forms of proximity influence the formation of different informal relationships? and (ii) What is the impact of social ties on relationships for innovation? ERGM is applied to measure the different impact of the proximities on three network relationships operating in the cluster of High Technology applied to Cultural Goods. The results underline the heterogeneous impact of various forms of proximity on the different relationships and the strong impact of social ties on innovation.     

数字散斑相关技术在高分子材料蠕变测试中的应用

将数字散斑相关计算与压痕硬度测试相结合,探讨在洛氏硬度计上测试高分子材料的蠕变性。首先使用CCD连续采集压头移动图像,然后进行散斑计算,根据计算结果绘制出压头位移-时间曲线,据此建立压入深度与时间、材料的蠕变与时间以及应力与时间之间的关系式,最后通过线性拟合得到被测材料的蠕变指数。通过对高密度尼龙、有机玻璃及环氧树脂的试验证实,该方法是可行的,试验得到三种材料的蠕变指数分别为0.12、0.012、0.07。试验中还发现,根据深度计算的硬度值与通过表盘读出的硬度值是不同的,在比较不同高分子材料的硬度时,前者比后者更合理。     

Accidents in the construction industry in the Netherlands: An analysis of accident reports using Storybuilder

As part of an ongoing effort by the Ministry of Social Affairs and Employment of the Netherlands, a research project is being undertaken to construct a causal model for occupational risk. This model should provide quantitative insight into the causes and consequences of occupational accidents. One of the components of the model is a tool to systematically classify and analyse reports of past accidents. This tool ‘Storybuilder’ was described in earlier papers. In this paper, Storybuilder is used to analyse the causes of accidents reported in the database of the Dutch Labour Inspectorate involving people working in the construction industry. Conclusions are drawn on measures to reduce the accident probability. Some of these conclusions are contrary to common beliefs in the industry.