Accession Number : ADA300996

Title :   Nonparametric Estimation for a General Repair Model.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Dorado, Crisanto ; Hollander, Myles ; Sethuraman, Jayaram

PDF Url : ADA300996

Report Date : JUN 1995

Pagination or Media Count : 33

Abstract : The construction and analysis of repair models is an important area in reliability. A commonly used model is the minimal repair model. Under this model, repair restores the state of the system to its level prior to failure. Kijima introduced repair models that could be classified as "better-than-minimal". Under Kijima's models, the system, upon repair, is functionally the same as a working system of lesser age which has never experienced failure. In this paper, we present a new approach to the modelling of better-than-minimal repair models. Using this approach, we construct a general repair model that contains Kijima's models as special cases. We also study the problem of estimating the distribution of the time to first failure of a system maintained by general repair. We make use of counting processes to show strong consistency of the estimator and prove results on weak convergence. Finally, we derive a Hall-Wellner type asymptotic confidence band for the estimator.

Descriptors :   *MATHEMATICAL MODELS, *NONPARAMETRIC STATISTICS, WEIBULL DENSITY FUNCTIONS, STOCHASTIC PROCESSES, TIME DEPENDENCE, MAXIMUM LIKELIHOOD ESTIMATION, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, FAILURE, RELIABILITY, REPAIR, SYSTEMS ANALYSIS, COVARIANCE, WEAK CONVERGENCE.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE