Some Studies On Allocation Of Redundancy And Stochastic Dependence Of Sample Spcaings

Stochastic comparison is a well-used way to deal with the stochastic problems, which sums up the comparison of uncertainty cases in living to some stochastic comparison of random variables, and offers all sorts of criteria for statistics, reliability theory, actuary science and auction theory, etc. many fields. One part of this dissertation focus on using stochastic comparison to study the ways of the redundancy allocation on the component level which can have the system bolstered best. The other part studies the dependence among sample spacings, and the problem that if it can forecast any conditions of one sample spacing from the length of another one has been the focus of attention of many authors in the past two decades years.For the problem of the ways of allocation, a special stochastic order is first introduced (it is not appropriate to say the word "a special stochastic order" here, which is used just for convenience, please refer to Chapter 2 for details), the so-called stochastic precedence order, for which owns some special properties for the larruping way of the definition, often can offer more useful warrant for a choice or decision-making. As an important way to optimize the reliability of a system, the problem of the redundancy allocation have attracted many attentions from many authors since a long time, and many interesting works have got for the system level and the component level. For example, a famous result introduced in the monograph by Barlow & Proschan (1981) says that, for a coherent system, the allocation on the component level is always more effective than that on the system level. Definitely, when the allocation way equals to the way of parallel, the former increases more reliability for the system than the latter, and when the allocation way equals to the way of the series, the former decreases more reliability against the system than the latter. In this dissertation, many stochastic orders as different criteria are used to compare the ways of redundancy allocation, where we first study the case that the way of the allocation equals to the parallel, and then, the case that the way equals to the convolution is studied. In the discussion for the dependence of the sample spacings, we proved that TP2 (RR2) dependence between a general spacing and a non-adjacent order statistic may be characterized by DLR (ILR) property of the parent distribution, and TP2 dependence between any pair of consecutive spacings may be characterized by DLR aging property of the population. Furthermore, TP2 dependence between any two consecutive spacings in multiple outliers exponential models is also derived. In addition, some applications in reliability and business auction are presented as well.