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Applied Mathematical Modelling, Volume 37, Issue 6, 15 March 2013, Pages 4325-4336.
Soufiane Gasmi.
ESSTT, University of Tunis, BP 56, 1008 Bab Menara, Tunisia
Abstract
The log-linear intensity is often used in survival analysis of technical products with rapid deterioration. It is an extremely important intensity to characterize the probabilistic behavior of a large number of real phenomena. In this paper we develop statistical methods for an alternating repair model using a log-linear intensity. The maximum likelihood estimator is considered for determining the estimations of the model parameters. The distribution of the life times after perfect repairs and imperfect repairs are obtained. The estimation of the Fisher information matrix is given. Simultaneous confidence regions based on the likelihood ratio statistics are developed for the estimators of the parameters. The proposed model is demonstrated using the well known data on airplane air-conditioning failures from Plane 7.
Additional information
The purpose of the paper is to present statistical methods and results of an alternating repair model in which repairs alternate between good-as-new and bad-as-old.
The most commonly used models for the failure process of a repairable system are known as perfect repair or as good as new (AGAN) and minimal repair or as bad as old (ABAO).
It is well known in practice that the reality is between these two extreme cases. The repair may not yield a functioning item which is AGAN and the minimal repair assumption seems to be too pessimistic in repair strategies. From this it is seen that the imperfect repair is of great signification in practice.
