Estimators for Reliability Measures in Geometric Distribution Model Using Dependent Masked System Life Test Data

Abstract

Masked system life test data arises when the exact component which causes the system failure is unknown. Instead, it is assumed that there are two observable quantities for each system on the life test. These quantities are the system life time, and the set of components that contains the component leading to the system failure. The component leading to the system failure may be either completely unknown (general masking), isolated to a subset of system components (partial masking), or exactly known (no masking). In the dependent masked system life test data, it is assumed that the probability of masking may depend on the true cause of system failure. Masking is usually due to limited resources for diagnosing the cause of system failures, as well as the modular nature of the system. In this paper, we present point, and interval maximum likelihood, and Bayes estimators for the reliability measures of the individual components in a multi-component system in the presence of dependent masked system life test data. The life time distributions of the system components are assumed to be geometric with different parameters. Simulation study will be given in order to 1) compare the two procedures used to derive the estimators for the reliability measures of system components, 2) study the influence of the masking level on the accuracy of the estimators obtained, and 3) study the influence of the masking probability ratio on the accuracy of the estimators obtained