Past research into the phenomenon of reliability growth has emphasised modeling a major reliability characteristic in terms of a specific parametric function. In addition, the time-to-failure distribution of the system was generally assumed to be exponential. The result was that in most cases the improvement was modeled as a nonhomogeneous Poisson process with intensity λ(t). Major differences among models centered on the particular functional form of the intensity function. The popular Duane model, for example, assumes that λ(t) = β(1 – α)t ⁻ᵅ. The inability of any one family of distributions or parametric form to describe the growth process resulted in a multitude of models, each directed toward answering problems encountered with a particular test situation. This thesis proposes two new growth models, neither requiring the assumption of a specific function to describe the intensity λ(t). Further, the first of the models only requires that the time-to-failure distribution be unimodal and that the reliability become no worse as development progresses. The second model, while requiring the assumption of an exponential failure distribution, remains significantly more flexible than past models. Major points of this Bayesian model include: (1) the ability to encorporate data from a number of test sources (e.g. engineering judgement, CERT testing, etc.), (2) the assumption that the failure intensity is stochastically decreasing, and (3) accountability of changes that are incorporated into the design after testing is completed. These models were compared to a number of existing growth models and found to be consistently superior in terms of relative error and mean-square error. An extension to the second model is also proposed that allows system level growth analysis to be accomplished based on subsystem development data. This is particularly significant, in that, as systems become larger and more complex, development efforts concentrate on subsystem levels of design. No analysis technique currently exists that has this capability. The methodology is applied to data sets from two actual test situations.

Three fundamental problems of mechanical reliability are addressed. (1) computing the probability of failure, p(f), of a component having design factors with known statistical distributions and a limit state with a closed form algebraic expression (2) computing the probability of failure of a component having design factors with known distributions and a limit state which can only be expressed by a computer algorithm, and (3) deriving safety check expressions in a "design by reliability" approach. An algorithm for generating estimates of p(f) is presented. The method is an extension of, and demonstrated to be a significant improvement to, the widely used Rackwitz-Fiessler (R-F) method--a fast and efficient numerical method for performing reliability analysis. Comparisons were made for numerous examples, it was found that the error in p(f), using the proposed method, is typically about half of the error in R-F estimates. A method was proposed for computing p(f) when the relationship between design factors can be defined only using a computer algorithm, e.g., finite element analysis. A second order polynomial is constructed, using a simple curve fitting routine, to approximate the limit state in the neighborhood of the design point (i.e., a point close to the most likely value of the design variables at failure). Then the R-F method can be applied easily. It is demonstrated that this scheme is much faster than the Monte Carlo method in producing reasonable estimates of p(f). Methods of deriving safety check expressions for design codes and design criteria documents are studied. A Level I format employing partial safety factors derived from Level II methods is used to construct the safety check expressions which are suitable for code development. The procedures are demonstrated using numerous examples which include the problems where the limit states are complicated, i.e., the limit states are not explicitly defined.