This thesis explores methodologies of modeling and evaluating the operational performance of a typical aeroengine having field experience over two decades. Upon failure, the engine is repaired and restored to flight worthy condition and hence comes under the purview of repairable systems. Operational performance of the engine is being measured in terms of five functions of time, namely, M(t), which is the expected number of system failures in the time interval [0,t]; system failure rate m(t), which is an unconditional quantity and is simply the derivative of M(t); ρ(t), the conditional failure intensity given the history of a system Ht, which is nothing but limdt→1 Prob(System fails in [t,t + dt] |Ht); and M′(t) and m′(t), which are 0 dt conditional entities analogous to M(t) and m(t) defined in the same spirit as that of ρ(t), the details of which are given in the third chapter of the thesis. These functions are being estimated using field failure-repair data of 418 aeroengines, where the observations on time between failures are being measured in number of flying hours logged in between failures, and the corresponding repair duration is being measured in number of calendar days. To start with, using the superimposed renewal process model the above quantities M(t), m(t), m′(t), M′(t) and ρ(t) are estimated both in the frequentist as well as the Bayesian framework. Subsequently repair times have been incorporated into the model and analysed using both frequentist and Bayesian approaches. Next, the model of Lawless and Thiagarajah (1996) which incorporates both renewal and time trend, has been generalized to include repair time as well, and a comprehensive methodology of Bayesian model selection under this model has been developed. After introducing the research problem in the first chapter, the engineering system description leading to the identification of the failure modes, repair practice and the variables of interest is taken up in the following chapter at the outset, as a pre-requisite to the stochastic modeling and the statistical analysis that to follow in the remainder of the thesis. As the first stochastic model, the number of system failures in a given time interval is modeled as a superimposed renewal process with the constituent independent renewal processes running in different component sockets having Weibull inter failure times. This model is first empirically validated using the field failure data and then using this model, the five quantities of interest as mentioned above viz. M(t), m(t), ρ(t), M′(t) and m′(t) are analysed from a frequentist maximum likelihood perspective. A Bayesian analysis of the same follows in the subsequent chapter. Next, the repair effect is incorporated into the superimposed renewal process model by considering the Weibull parameters of inter failure times of the constituent renewal processes running in independent component sockets as a polynomial in the last repair time. The nature of this polynomial relationships are empirically deter-mined and the Weibull assumption is validated through a test of hypothesis. Different polynomial relationships lead to consideration of several models, with the correct ones chosen through a series of likelihood ratio tests. Next based on the appropriate models a maximum likelihood analysis of M(t), ρ(t) and M′(t) has been carried out. Like the simple superimposed renewal process model, Bayesian analysis of this model incorporating repair times is carried out in the following chapter. In the Bayesian setup however, the problem of model selection could be kept unrestricted to non-nested models as well (unlike the previous chapter, where only nested models could be considered), and a comprehensive model selection exercise has been carried out with the aid of intrinsic Bayes factors and training data sets. The last but one chapter presents a generalised model of Lawless and Thiagarajah (1996) for performance evaluation of aeroengines that incorporate renewals, time trends and the repair characteristics. Here also since the primary problem is one of model selection, the entire analysis like in the preceding chapter has been carried out under the Bayesian frame-work. The final chapter concludes the thesis by comparing the empirical results obtained in the previous five chapters, summarising the main contributions of the thesis and providing directions for future research.

Consider life testing of J-component series systems that are subjected to stress levels that are steeper than that at normal usage condition. The objective of performing such life tests, commonly known as Accelerated Life Testing (ALT) in the literature, is to collect observations on system failure times within a limited time frame. The accelerated observations are then used to infer on the component and system reliability metrics at usage stress. In this thesis, the existing literature is first extended by considering the general case of K stress variables, as opposed to the usual consideration of a single stress variable. Next, a general model assuming that the component log-lifetimes belong to an arbitrary location-scale family of distributions, is formulated. The location parameters are assumed to depend on the stress variables through a general stress translation function, while the scale parameters are assumed to be independent of the stress variables. This formulation covers the standard lifetime distributions as well as well-known stress translation functions as special cases. Bayesian methodologies are then developed for four special cases of the proposed general model, viz., exponentials, Weibulls with equal shape parameter, Weibulls with distinct shape parameters and log-normals with distinct scale parameters. For exponential and Weibull models, the priors on lifetime parameters are assumed to be log-concave and independent of each other. The resulting univariate conditional posterior of each lifetime parameter given the rest, is shown to be log-concave. This facilitates Gibbs sampling from the joint posterior of lifetime parameters. Propriety of the joint posteriors with Laplacian uniform priors on stress coefficients are also proved under a suitable set of sufficient conditions. For the log-normal model, the observed data is first augmented with log-lifetimes of un-failed components to form complete data. A Gibbs sampling scheme is then developed to generate observations from the joint posterior of lifetime parameters, through the augmented data and a conjugate prior for the complete data. In all four cases, Bayesian predictive inference techniques are used to study component and system reliability metrics at usage stress. Though this thesis mainly deals with Bayesian inference of accelerated data of series systems, maximum likelihood analysis for the log-normal component lifetimes is also performed via an expectation-maximization (EM) algorithm and bootstrap, which are not available in the literature. The last part of this thesis deals with construction of optimal Bayesian designs for accelerated life tests of J-component series systems under Type-I censoring scheme. Optimal ALT plans for a single stress variable are obtained using two different Bayesian D-optimality criteria for exponentially distributed component lives. A detailed sensitivity analysis is carried out to investigate the effect of different planning inputs on the optimal designs as well.