Methods for Reliability Theory and Applications of Order-Restricted Inference

可靠性理论方法和阶数限制推理的应用

• 批准号: 0072207
• 负责人: Henry Block
• 金额: $ 17.1万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072207&HistoricalAwards=false
• 关键词: Methods; Reliability; Theory; Applications; Order

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.

问题是解决时，浴缸形状的故障率函数是由各种功能来描述最佳的行为。 第二个问题是混合物何时具有特定的形状，如浴缸形状。 第三个主题介绍了保序逻辑歧视，这是一个非参数广义的线性逻辑歧视考虑到顺序的限制。 第四个问题解决了寻找保序响应曲面的同时置信带，第五个主题开发了Pearson卡方检验2（k）有序表的有序扩展。 第六个主题是提出并发展了一种新的置换度量。失效率是一种用于描述系统（工程或生物）失效倾向的方法。 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，然后在老年它们往往会增加（称为磨损）。 这导致了浴缸形故障率。 对于机械或电气系统，其故障率很高，有许多早期故障。 因此，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称为老化。 通常这意味着对这些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常见现象，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的增加和胆固醇水平的增加而增加。 为了正确分析这些现象产生的数据，需要开发新的和更通用的统计方法。 研究人员正在考虑几种主要的新统计方法来建模和分析这些数据。