Methods for Reliability Theory and Applications of Order-Restricted Inference

讨论了各种用于描述最优行为的函数在何种情况下保持故障率函数的浴盆形状。第二个问题是混合物何时具有特定的形状，例如浴缸形状。第三个主题介绍了等压逻辑判别，它是考虑顺序限制的线性逻辑判别的非参数推广。第四个问题涉及寻找等渗响应面的同时置信带，第五个主题发展了检验2(k)有序表的皮尔逊卡方的有序扩展。作为第六个主题，提出并发展了一个关于排列的新度量。故障率是一种用于描述系统（工程或生物）失败倾向的方法。它们是时间的函数，通常在早期它们很高（更容易失败），在中年它们很低，然后在老年它们倾向于增加（称为疲劳）。这就产生了浴缸形的故障率。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，在这段早期失败的时期过去之前，不应该发布产品。一种确保这一点的方法被称为老化。通常情况下，这意味着要对这类产品进行一段时间的测试，直到这个关键时期结束。一个重要的考虑因素是如何最佳地确定这样一个时期，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，实验响应趋于变大。例如，一个人在五年内心脏病发作的可能性会随着基线收缩压的升高和胆固醇水平的升高而增加。为了恰当地分析这些现象产生的数据，需要发展新的和更普遍的统计方法。研究人员正在考虑几种主要的新统计方法来模拟和分析这些数据。

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.