Hazard rate ordering of the second-order statistics from multiple-outlier PHR samples

In this paper, we compare the hazard rate functions of the second-order statistics arising from two sets of independent multiple-outlier proportional hazard rates (PHR) samples. It is proved that the submajorization order between the sample size vectors together with the supermajorization order between the hazard rate vectors imply the hazard rate ordering between the corresponding second-order statistics from multiple-outlier PHR random variables. The results established here provide theoretical guidance both for the winner's price for the bid in the second-price reverse auction in auction theory and fail-safe system design in reliability. Some numerical examples are also provided for illustration.     

Why Frequency is Not Well Defined for Engineering Systems with Nonexponential Failure Times

Dr. Yellman proposes to define frequency as “a time‐rate of events of a specified type over a particular time interval.” We review why no definition of frequency, including this one, can satisfy both of two conditions: (1) the definition should agree with the ordinary meaning of frequency, such as that less frequent events are less likely to occur than more frequent events, over any particular time interval for which the frequencies of both are defined; and (2) the definition should be applicable not only to exponentially distributed times between (or until) events, but also to some nonexponential (e.g., uniformly distributed) times. We make the simple point that no definition can satisfy (1) and (2) by showing that any definition that determines which of any two uniformly distributed times has the higher “frequency” (or that determines that they have the same “frequency,” if neither is higher) must assign a higher frequency number to the distribution with the lower probability of occurrence over some time intervals. Dr. Yellman's proposed phrase, “time‐rate of events … over a particular time interval” is profoundly ambiguous in such cases, as the instantaneous failure rates vary over an infinitely wide range (e.g., from one to infinity), making it unclear which value is denoted by the phrase “time‐rate of events.”     

公益诉讼费用分担方式的构建

公益诉讼费用是公益诉讼必然面临的问题,其合理与否极大地关系着人们享受法律保障的程度。但公益诉讼往往诉讼成本高,导致公益诉讼难以取得理想的预期效果,而现行的诉讼费用分担方式并不能完全适应公益诉讼的发展需要。因此,应从被告方分担、受益者分担、国家分担三方面入手,通过设立公益诉讼奖励基金以及费用移转支付的方式,建立起一个与公益诉讼理念相契合的公益诉讼费用分担方式。     

Social Cognitive Factors,Support, and Engagement: Early Adolescents’ Math Interests as Precursors to Choice of Career

The authors examined the central hypothesis that students’ early perceptions of support and sense of engagement in math classes and math activities strongly influence the broadening or narrowing of their math interest. The focus was on the first wave of qualitative data collected from 5th‐, 7th‐, and 9th‐grade students during the 2007–2008 academic year as part of a longitudinal study. Findings indicate the importance of using group work and extrinsic motivation in middle school math classes to broaden interest; peer classroom behavior was often a detractor of math interest.     

超声波提取胡椒中有效成分条件优化

试验研究温度、时间、超声波频率对超声波-食用乙醇提取胡椒有效成分的影响,以胡椒粗提取物的提取率为指标,正交实验确定较适宜提取条件为,温度55℃、时间55 min,超声波频率60 KHz,胡椒粗提取物的提取率为4.29%.     

利益分析视角下的公路班线客运集约化发展研究

公路班线客运集约化改革的难点在于利益关系的协调。在广泛调研和深入访谈的基础上，结合班线客运发展历程及现状，从利益分析的视角剖析了政府、企业、个体之间的利益诉求、利益冲突及利益博弈的内在机理，指出挂靠关系下企业与个体之间的利益争夺是集约化发展难以推进的根源。研究提出以当前利益分配格局为均衡点的“实收配股”集约化发展改革方案，同时强调政府应转变职能定位、完善相关政策，防止形成市场封锁或垄断。     

区域碳锁定的判定研究--以云南省为例

通过建立包括陆地、湿地和海洋的碳承载力、碳超载率的计算模型，采用供需平衡法建立了区域碳锁定时间和趋势的判定模型。以有着“植物王国”和“基因宝库”之称以及水电资源相对丰富的云南省为例，对该省的碳锁定时间、趋势进行了实证研究。实证分析结果显示，云南省自2002年后开始出现了碳锁定现象且趋势越来越严重，若不进行强有力的外界干扰，这种趋势将一直延续下去。结合即使“十一·五”低碳目标的完成也没能减轻云南省碳锁定加剧的趋势，提出把减轻碳超载、控制能源消费总量、提升碳承载力纳入低碳经济发展的目标管理。     

Testing dominance of biometric functions

The hazard rate (HR) and mean residual lifetime are two of the most practical and best-known functions in biometry, reliability, statistics and life testing. Recently, the reversed HR function is found to have interesting properties useful in additional areas such as censored data and forensic science. For these three biometric functions, we propose testing methods that they take on a known functional form against that they dominate or are dominated by this known form. This goodness-of-fit-type testing is wider in applications and more interesting than the long-standing testing procedures for exponentiality against the monotonicity of these functions or even the change point problems. This is so since we can test against any choice of the survival distribution and not just exponentiality. For this general testing, we present easy to implement tests and generalize them into classes of statistics that could lead to more powerful and efficient testing.     

A bootstrap control chart for inverse Gaussian percentiles

The conventional Shewhart-type control chart is developed essentially on the central limit theorem. Thus, the Shewhart-type control chart performs particularly well when the observed process data come from a near-normal distribution. On the other hand, when the underlying distribution is unknown or non-normal, the sampling distribution of a parameter estimator may not be available theoretically. In this case, the Shewhart-type charts are not available. Thus, in this paper, we propose a parametric bootstrap control chart for monitoring percentiles when process measurements have an inverse Gaussian distribution. Through extensive Monte Carlo simulations, we investigate the behaviour and performance of the proposed bootstrap percentile charts. The average run lengths of the proposed percentage charts are investigated.