Nonparametric methods for imperfect repair models

• Other Authors: Presnell, Brett Douglas.
• Format: Others
• Language: English
• Subjects: Statistics
• Online Access: http://purl.flvc.org/fsu/lib/digcoll/etd/3161993

Under the imperfect repair model of Brown and Proschan (1983), a failed item is replaced by a new item (perfect repair) with probability p, and with probability 1 $-$ p, a minimal repair is performed; that is, the failed item is replaced by a working item of the same age. This procedure is repeated at each subsequent failure. Block, Borges, and Savits (1985) extend this model by allowing p to be a function of the age of the item. In both of these models, imperfect repairs are thus assumed to be minimal. Whitaker and Samaniego (1989) propose an estimator for the life distribution, F, of a new item, when either of these processes is observed until the time of the $m\sp{\rm th}$ perfect repair. === In this dissertation, we extend to the case of possibly discontinuous F, a result of Block, Borges, and Savits identifying the distribution of the waiting time until the first perfect repair. We then use a martingale approach to rederive and extend the weak convergence results of Whitaker and Samaniego. These results are used to derive asymptotic confidence bands for F, and an extension of the Wilcoxon two-sample test for data collected under these models. Finally, we propose a test of the minimal repair assumption, and the limiting distribution of the proposed test statistic is derived. === Source: Dissertation Abstracts International, Volume: 51-02, Section: B, page: 0831. === Major Professors: Myles Hollander; Jayaram Sethuraman. === Thesis (Ph.D.)--The Florida State University, 1989.