Systems Failure Diagnosis and Repair Kit using Survival Signature

Abstract

A pivotal aspect of studying systems involves diagnosing its failures, referred to in this thesis as identifying the components or types of components associated with system failure. System failure diagnosis serves various purposes, including facilitating maintenance activities and informing system design. This thesis delves into the study of system failure from two distinct perspectives: determining which types of components are most likely to lead to system failure and estimating the numbers of failed components of each type at the time of system failure. While Barlow and Proschan introduced an importance measure that determines the probability of a component causing system failure based on the structure function, the complexity associated with the structure function may pose challenges in applying it to real com- plex systems. Therefore, for a general system structure containing multiple types of components, we use the concept of the survival signature introduced by Coolen and Coolen-Maturi to derive the probability of a component of a specific type failing at the system failure time, ultimately leading to system failure.

Additionally, we derive probabilities of three events related to the number of failed components of multiple types at a future moment when the system fails, based on the survival signature. First, we determine the probability of the number of failed components at system failure, given that the system will fail at a specific time t and conditioning on the number of failed components prior to system failure. Second, the probability of the number of failed components at an unknown system failure, assuming the system is functioning at a certain time, is derived. We also consider the probability of the number of failed components at system failure, assuming the system will fail in a specific future time interval. The results of the probabilities depend only on the distributions of failure times of component types and the survival signature of the system.