The reliability of a repairable system that is either improving or deteriorating depends on the system's chronological age. If such a system undergoes "minimal repair" at the occurrence of each failure so that the rate of system failures is not disturbed by the repair, then a Nonhomogeneous Poisson Process (NHPP) may be used to model the "age-dependent" reliability of the system. The Power Law Process (PLP) is a model within the class of NHPP models and is commonly used as a model for describing the failure times of a repairable system. We introduce two new models that are extensions of the PLP model: the Power Law Process Change-Point I (PLPCPI) and the Power Law Process Change-Point II (PLPCPII). These models are capable of describing the failure times of particular types of repairable systems that experience a single change in their rates of occurrence of failures. For the PLPCPI and the PLPCPII, under the assumption of a known change-point: we develop procedures for estimating the model parameters and the system intensity of failures; and predictive distributions are derived for future system failure times and the number of system failures in a future time interval. For the PLPCPI, we perform a simulation study to investigate the effect (on the estimation of the system intensity of failures at the current time) of assuming that the failure times of a repairable system follow a PLP when in reality the system failure times follow a PLPCPI. For the PLPCPI and the PLPCPII, under the assumption of an unknown change-point, we develop procedures for estimating the change-point.

ADVANCED TECHNIQUES FOR MAINTENANCE MODELING AND RELIABILITY ANALYSIS OF REPAIRABLE SYSTEMS This book covers advanced models and methodologies for reliability analysis of large, complex, and critical repairable systems that undergo imperfect maintenance actions in industries having MRO facilities and also covers real-life examples from the field of aviation. The content presented in this book is inspired by the existing limitations of the generalized renewal process (GRP) model and the problems confronted by the maintenance, repair, and operations (MRO) facilities in industries dealing with large and complex repairable systems. Through this book, the authors have attempted to equip the MRO facilities with more advanced scientific tools and techniques by addressing various limitations related to the reliability analysis of repairable systems. The book is dedicated to various imperfect maintenance-based virtual age models and methodologies to bridge various research gaps present in the available literature. A summary of deliverables is as follows: Presents the basic concepts of maintenance and provides a virtual age model that can accommodate all maintenance; Provides the basic concepts of censoring in repairable systems along with the concept of black box and failure modes. Also highlighted is how the proposed work will be useful for industries conducting failure modes and effect analysis (FMEA) and estimating the mean residual life (MRL) of repairable systems; Presents methodology that applies risk-based threshold on intensity function and provides a threshold to declare the system/component as high failure rate components (HFRCs); Identifying a system as HFRCs is an important task, but for an industry dealing with critical systems, preventing the system from being HFRC is more important, since the risk involved in such systems would be very high. Thus, the book presents a progressive maintenance policy (PMP) for repairable systems; Focusses on qualitative analysis of repair quality. Assuming repair quality as a subjective variable, the authors have presented various factors that affect the repair quality most and modeled their interdependency using Bayesian networks (BN). Audience Professional reliability engineers, reliability administrators, consultants, managers, and post-graduate students in engineering schools. The book belongs to any engineering, technical, and academic institution concerned with manufacturing, production, aviation, defense, and software industries.

The nonhomogeneous Poisson process is a widely used model for a series of events (stochastic point process) in which the rate or intensity of occurrence of points varies, usually with time. The process has the characteristic properties that the number of points in any finite set of nonoverlapping intervals are mutually independent random varialbes, and that the number of points in any of these intervals has a Poisson distribution. This paper first discusses several general methods for simulation of the one-dimensional nonhomogeneous Poisson process. Then a particular and very efficient method for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the nonhomogeneous Poisson process to the gap statistics from a random number of exponential random variables with suitably chosen parameters. Finally, a simple and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is applicable for any given rate function and is based on controlled deletion of points in a Poisson process with a rate function that dominates the given rate function.

Two algorithms for generating a non-homogeneous Poisson process with log-quadratic intensity function are implemented into computer programs and compared for relative speed, core storage requirements and fidelity. By simulating several cases of non-homogeneous Poisson processes with log-quadratic intensity functions it is shown that the Poisson-decomposition and gap statistic algorithm substantially reduces computation time from that required by an algorithm that uses a time-scale transformation of a homogeneous Poisson process. The experience gained from implementing the algorithm has led to several possibilities which are suggested for improving the efficiency of the Poisson-decomposition and gap statistic algorithm.