Methods for Reliability Theory and Applications of Order-Restricted Inference

提出了故障率函数的浴缸形状何时被用来描述最优行为的各种函数保持的问题。第二个问题是，混合物何时会有特定的形状，如浴缸形状。第三个主题介绍了保序Logistic判别法，它是考虑顺序限制的线性Logistic判别法的非参数推广。第四个问题解决了为等张响应面寻找同时置信带的问题，第五个问题开发了用于测试2(k个有序表)的皮尔逊卡方的序数扩展。作为第六个主题，提出并发展了一种关于排列的新度量。故障率是一种用来描述一个系统的故障倾向的方法，无论是工程上的还是生物学上的。它们是时间的函数，通常在年轻时它们很高(更有可能失败)，在中年它们很低，然后在老年它们往往会增加(称为疲惫)。这导致了浴缸形状的故障率。对于具有浴缸故障率的机械或电气系统，存在许多早期故障。因此，一个产品不应该发布，直到这个早期失败的时期过去。确保这一点的一种方法被称为老化。这通常意味着对这些产品进行一段时间的测试，直到这一关键时期结束。一个重要的考虑因素是如何最优地确定这样一个周期，这是研究人员研究的一个问题。另一个研究领域涉及许多科学问题中的一个普遍现象，即随着各种潜在实验参数的增加，实验响应往往会变得更大。例如，一个人在五年内心脏病发作的可能性将随着基线收缩压和胆固醇水平的增加而增加。为了适当地分析这些现象产生的数据，需要开发新的和更一般的统计方法。研究人员正在考虑几种主要的新统计方法来对这些数据进行建模和分析。

The question is addressed of when the bathtub shape of a failure rate function is preserved by various functions used to describe optimal behavior. A second issue is when do mixtures have specified shapes such as a bathtub shape. A third topic introduces isotonic logistic discrimination, which is developed as a nonparametric generalization of linear logistic discrimination taking into account order restrictions. The fourth question addresses finding simultaneous confidence bands for isotonic response surfaces and the fifth topic develops an ordinal extension of the Pearson chi-squared for testing 2(k ordered tables. A new metric on permutations is proposed and developed as the sixth topic. Failure rates are a method used to describe the propensity of a system, either engineering or biological, to fail. They are a function of time and typically at an early age they are high (more likely to fail), at middle age they are low, and then at an old age they tend to increase (called wearout). This gives rise to the bathtub shaped failure rate. For mechanical or electrical systems, which have a bathtub failure rate, there are many early failures. Consequently, a product should not be released until this period of early failures is past. A method of insuring this is called burn-in. Typically this means testing such products for a length of time until this critical period is over. An important consideration is how to optimally determine such a period and this is one question studied by the researchers. Another research area deals with a common phenomenon in many scientific problems where the experimental responses tend to get larger as various underlying experimental parameters are increased. For example, an individual's likelihood of heart attacks within a five-year period will increases as baseline systolic blood pressure increases and as cholesterol levels increase. In order to properly analyze the data arising from such phenomena, new and more general statistical methods need to be developed. The researchers are considering several major new statistical methods to model and analyze such data.