Statistics and risk in the nuclear industry

Nuclear power, after a decade of being ignored, is again becoming an option—perhaps the preferred option—for future power generation in Britain. Can it be done safely? As importantly, can existing plant be decommissioned safely? Granville Tunnicliffe Wilson has worked on a series of statistical projects with the nuclear industry, stretching over a period of 30 years. He looks at the part statistics has played in past safety assurance and the questions that are now being asked about its role. He also reveals past cases where operators failed to follow valid statistical indicators of plant failure.     

Sequential Series Systems and Their Risk Assessments

System reliability models are critical in both theory and engineering. Although there are many system reliability models, they still cannot cover some practical situations. In this article, three sequential series systems are introduced in terms of some real backgrounds. An order profile for the system working is also introduced, because it can be used to describe the working component contribution for the system clearly. As the systems become more and more complicated and important, the safety issue is a hot topic. Risk analysis is one of the important ways for safety studies and implements. The formulae for some risk measures for the sequential systems are presented from a safety point of view. A numerical example is given to illustrate the details of the procedure and formulae.     

Monte Carlo Simulation of Numerical Integration

A Monte Carlo simulation program based on accompanying probability theory is developed and implemented to examine the trustworthiness of certain methods used in numerical integration. The power and reliability of an approximation process are defined. Using the simulation, estimated power and reliability values are obtained for the Trapezoidal rule, for Simpson’s rule, and for Romberg integration in conjunction with several frequently used stopping rules. The above-mentioned approximation processes are then analyzed and compared within the context of these two fundamental notions.     

Early stopping by using stochastic curtailment in a three-arm sequential trial

Summary. Interim analysis is important in a large clinical trial for ethical and cost considerations. Sometimes, an interim analysis needs to be performed at an earlier than planned time point. In that case, methods using stochastic curtailment are useful in examining the data for early stopping while controlling the inflation of type I and type II errors. We consider a three-arm randomized study of treatments to reduce perioperative blood loss following major surgery. Owing to slow accrual, an unplanned interim analysis was required by the study team to determine whether the study should be continued. We distinguish two different cases: when all treatments are under direct comparison and when one of the treatments is a control. We used simulations to study the operating characteristics of five different stochastic curtailment methods. We also considered the influence of timing of the interim analyses on the type I error and power of the test. We found that the type I error and power between the different methods can be quite different. The analysis for the perioperative blood loss trial was carried out at approximately a quarter of the planned sample size. We found that there is little evidence that the active treatments are better than a placebo and recommended closure of the trial.     

煤矿企业安全氛围量表开发研究

采用标准化的量表开发程序,对煤矿企业安全氛围量表进行研究.通过文献分析、高管访谈与专家反馈确定量表的初始项目池,通过预测试样本的项目分析与探索性因子分析对量表题项进行精炼,通过大样本数据的验证性因子分析与回归分析对量表有效性进行确认.研究表明,煤矿企业安全氛围包括7个维度,即安全意识、管理允诺、监管者行为、安全政策、安全交流、安全培训和风险准备.本研究的开发过程不仅规范、可靠,得到的量表结构亦具有较高的信度和效度,能够为煤矿企业安全氛围管理提供理论指导和测量工具.     

多边价格指数中的价格异方差问题与CPD法的改进

CPD法是国际比较项目（ICP）中应用的一种重要的多边价格比较方法,多边价格比较方法的可靠性直接影响ICP公布的各国购买力平价数据的可信度。本文从理论上系统地分析了CPD法中存在的价格异方差问题,引入一种消除异方差的WLS估计方法。然后以2011年ICP居民实际消费支出各大类商品的价格数据为例,实证说明WLS估计的CPD法能显著提高各国购买力平价数据的可靠性;相对而言,存在异方差的CPD法会系统性高估发展中国家的居民实际消费支出水平。     

Impact of safety monitoring on error probabilities of binary efficacy outcome analyses in large phase III group sequential trials

In phase III clinical trials, some adverse events may not be rare or unexpected and can be considered as a primary measure for safety, particularly in trials of life-threatening conditions, such as stroke or traumatic brain injury. In some clinical areas, efficacy endpoints may be highly correlated with safety endpoints, yet the interim efficacy analyses under group sequential designs usually do not consider safety measures formally in the analyses. Furthermore, safety is often statistically monitored more frequently than efficacy measures. Because early termination of a trial in this situation can be triggered by either efficacy or safety, the impact of safety monitoring on the error probabilities of efficacy analyses may be nontrivial if the original design does not take the multiplicity effect into account. We estimate the actual error probabilities for a bivariate binary efficacy-safety response in large confirmatory group sequential trials. The estimated probabilities are verified by Monte Carlo simulation. Our findings suggest that type I error for efficacy analyses decreases as efficacy-safety correlation or between-group difference in the safety event rate increases. In addition, although power for efficacy is robust to misspecification of the efficacy-safety correlation, it decreases dramatically as between-group difference in the safety event rate increases.     

A fair result in foul weather

The Duckworth–Lewis method for adjusting targets in rain-interrupted one-day cricket matches is used throughout the world, but, as Frank Duckworth explains, he originally came to statistics from physics via metallurgy, and only thought of applying statistical methods to sport when their power became apparent to him during his career in the nuclear energy industry     

Modified branching process for the reliability analysis of complex systems: Multiple-robot systems

Current design practice is usually to produce a safety system which meets a target level of performance that is deemed acceptable by the regulators. Safety systems are designed to prevent or alleviate the consequences of potentially hazardous events. In many modern industries the failure of such systems can lead to whole system breakdown. In reliability analysis of complex systems involving multiple components, it is assumed that the components have different failure rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed generating function (GF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. Moreover, when the system failure results in fatalities it is desirable for the system to achieve an optimal rather than adequate level of performance given the limitations placed on available resources. This paper concerns with developing a modified branching process joint with generating function to handle reliability evaluation of a multi-robot complex system. The availability of the system is modeled to compute the failure probability of the whole system as a performance measure. The results help decision-makers in maintenance departments to analyze critical components of the system in different time periods to prevent system breakdowns.     

Sample size determination of steel's nonparametric many-one test

We derive sample size formulas for the many-one test of Steel (1959) when the all-pairs power is preassigned. In this large sample approach we replace, similar to Noether (1987), the unknown variances and also the unknown correlation coefficients in the power expressions by their known values under the null hypotheses. We then obtain least favorable configurations for one-and two-sided comparisons. The reliability of our formulas is examined in computer simulations for different alternatives with various distributions.     

Joint Integrated Importance Measure for Multi-State Transition Systems

Joint reliability importance (JRI) evaluates the interaction of two components in contributing to the system reliability in a system. Traditional JRI measures mainly concern the change of the system reliability caused by the interactive change of the reliabilities of the two components and seldom consider the probability distributions, transition rates of the object component states, and system performance. This article extends the JRI concept of two components from multi-state systems to multi-state transition systems and mainly focuses on the joint integrated importance measure (JIIM) which considers the transition rates of component states. Firstly, the concept and physical meaning of JIIM in binary systems are described. Secondly, the JIIM for deterioration process (JIIMDP) and the JIIM for maintenance process (JIIMMP) in multi-state systems are studied respectively. The corresponding characteristics of JIIMDP and JIIMMP for series and parallel systems are also analyzed. Finally, an application to an offshore electrical power generation system is given to demonstrate the proposed JIIM.     

A new futility test approach in clinical interim data monitoring

Sequential monitoring of efficacy and safety data has become a vital component of modern clinical trials. It affords companies the opportunity to stop studies early in cases when it appears as if the primary objective will not be achieved or when there is clear evidence that the primary objective has already been met. This paper introduces a new concept of the backward conditional hypothesis test (BCHT) to evaluate clinical trial success. Unlike the regular conditional power approach that relies on the probability that the final study result will be statistically significant based on the current interim look, the BCHT was constructed based on the hypothesis test framework. The framework comprises a significant test level as opposed to the arbitrary fixed futility index utilized in the conditional power method. Additionally, the BCHT has proven to be a uniformly most powerful test. Noteworthy features of the BCHT method compared with the conditional power method will be presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Hypotheses testing for generalized order statistics with simple order restrictions on model parameters under the alternative

In applications of generalized order statistics as, for instance, reliability analysis of engineering systems, prior knowledge about the order of the underlying model parameters is often available and may therefore be incorporated in inferential procedures. Taking this information into account, we establish the likelihood ratio test, Rao's score test, and Wald's test for test problems arising from the question of appropriate model selection for ordered data, where simple order restrictions are put on the parameters under the alternative hypothesis. For simple and composite null hypothesis, explicit representations of the corresponding test statistics are obtained along with some properties and their asymptotic distributions. A simulation study is carried out to compare the order restricted tests in terms of their power. In the set-up considered, the adapted tests significantly improve the power of the associated omnibus versions for small sample sizes, especially when testing a composite null hypothesis.     

信息不对称、议价能力测度与中国水果出口定价——基于双边随机边界模型

议价能力是影响出口定价的重要因素。运用双边随机边界模型,对信息不对称条件下中国水果出口议价能力及其对最终出口定价的影响效应进行实证分析。研究结果表明:进出口国双方掌握的信息程度对最终出口定价具有重要影响,同时进口国相对于出口国掌握着更多的信息并具有更强的议价能力;出口国被迫接受一个低于理论价格的价格,最终形成的实际出口价格相对于公正的理论价格低0.92%;年度效应和国别效应分析发现,长期以来实际出口价格低于理论价格,水果出口议价能力没有得到提升。为提高水果出口议价能力,政府部门应搭建出口信息平台,及时提供全方位的信息服务,并鼓励提高水果出口商的组织化程度,通过集体议价的方式与进口商展开谈判。     

Alpha power Weibull distribution: Properties and applications

In this paper, a new lifetime distribution is defined and studied. We refer to the new distribution as alpha power Weibull distribution. The importance of the new distribution comes from its ability to model monotone and non monotone failure rate functions, which are quite common in reliability studies. Various properties of the proposed distribution are obtained including moments, quantiles, entropy, order statistics, mean residual life function, and stress-strength parameter. The maximum likelihood estimation method is used to estimate the parameters. Two real data sets are used to illustrate the importance of the proposed distribution.     

The inverse power Lindley distribution in the presence of left-censored data

In this study, classical and Bayesian inference methods are introduced to analyze lifetime data sets in the presence of left censoring considering two generalizations of the Lindley distribution: a first generalization proposed by Ghitany et al. [Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64 (2013), pp. 20–33], denoted as a power Lindley distribution and a second generalization proposed by Sharma et al. [The inverse Lindley distribution: A stress–strength reliability model with application to head and neck cancer data, J. Ind. Prod. Eng. 32 (2015), pp. 162–173], denoted as an inverse Lindley distribution. In our approach, we have used a distribution obtained from these two generalizations denoted as an inverse power Lindley distribution. A numerical illustration is presented considering a dataset of thyroglobulin levels present in a group of individuals with differentiated cancer of thyroid.     

Distribution of the product of a pair of independent two-sided power variates

ABSTRACT

The distributions of algebraic functions of random variables are important in theory of probability and statistics and other areas such as engineering, reliability, and actuarial applications, and many results based on various distributions are available in the literature. The two-sided power distribution is defined on a bounded range, and it is a generalization of the uniform, triangular, and power-function probability distributions. This paper gives the exact distribution of the product of two independent two-sided power-distributed random variables in a computable representation. The percentiles of the product are then computed, and a real data application is given.     

Zero acceptance number quick switching system for compliance sampling

The zero acceptance number plan is invariably used for compliance sampling and safety inspection of products. The disadvantage of such a plan is that its discriminating power between good and bad lots is poor. This paper presents a quick switching system that has zero acceptance numbers, with a provision for the resubmission of lots not accepted during normal inspection. The proposed system is found to require a smaller average sample size, and possesses greater discriminating power.     

A COM-Poisson-type generalization of the negative binomial distribution

ABSTRACT

This paper introduces a generalization of the negative binomial (NB) distribution in analogy with the COM-Poisson distribution. Many well-known distributions are particular and limiting distributions. The proposed distribution belongs to the modified power series, generalized hypergeometric and exponential families, and also arises as weighted NB and COM-Poisson distributions. Probability and moment recurrence formulae, and probabilistic and reliability properties have been derived. With the flexibility to model under-, equi- and over-dispersion, and its various interesting properties, this NB generalization will be a useful model for count data. An application to empirical modeling is illustrated with a real data set.     

On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample

The power function distribution is often used to study the electrical component reliability. In this paper, we model a heterogeneous population using the two-component mixture of the power function distribution. A comprehensive simulation scheme including a large number of parameter points is followed to highlight the properties and behavior of the estimates in terms of sample size, censoring rate, parameters size and the proportion of the components of the mixture. The parameters of the power function mixture are estimated and compared using the Bayes estimates. A simulated mixture data with censored observations is generated by probabilistic mixing for the computational purposes. Elegant closed form expressions for the Bayes estimators and their variances are derived for the censored sample as well as for the complete sample. Some interesting comparison and properties of the estimates are observed and presented. The system of three non-linear equations, required to be solved iteratively for the computations of maximum likelihood (ML) estimates, is derived. The complete sample expressions for the ML estimates and for their variances are also given. The components of the information matrix are constructed as well. Uninformative as well as informative priors are assumed for the derivation of the Bayes estimators. A real-life mixture data example has also been discussed. The posterior predictive distribution with the informative Gamma prior is derived, and the equations required to find the lower and upper limits of the predictive intervals are constructed. The Bayes estimates are evaluated under the squared error loss function.