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published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

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In this dissertation, the synthesis of system reliability from the reliabilities of the componentry constituting the system is considered. For the purpose of contextual elucidation, major emphasis is accorded to complex missile systems. / Ph. D.

In this dissertation the estimation of reliability for a developmental process generating attribute type data is examined. It is assumed that the process consists of m stages, and the probability of failure is constant or decreasing from stage to stage. Several models for estimating the reliability at each stage of the developmental process are examined. In the classical area, Barlow and Scheuer's model, Lloyd and Lipow's model and a cumulative maximum likelihood estimation model are investigated. In the Bayesian area A.F.M. Smith's model, an empirical Bayes model and a cumulative beta Bayes model are investigated. These models are analyzed both theoretically and by computer simulation. The strengths and weaknesses of each are pointed out, and modifications are made in an attempt to improve their accuracy. The constrained maximum likelihood estimation model of Barlow and Scheuer is shown to be inaccurate when no failures occur at the final stage. Smith's model is shown to be incorrect and a corrected algorithm is presented. The simulation results of these models with the same data indicate that with the exception of the Barlow and Scheuer's model they are all conservative estimators. When reliability estimation with growth is considered, it is reasonable to emphasize data obtained at recent stages and de-emphasize data from the earlier stages. A methodology is developed using geometric weights to improve the estimates. This modification is applied to the cumulative MLE model, Lloyd and Lipow's model, Barlow and Scheuer's model and cumulative beta Bayes model. The simulation results of these modified models show considerable improvement is obtained in the cumulative MLE model and the cumulative beta Bayes model. For Bayesian models, in the absence of prior knowledge, the uniform prior is usually used. A prior with maximum variance is examined theoretically and through simulation experiments for use with the cumulative beta Bayes model. These results show that the maximum variance prior results in faster convergence of the posterior distribution than the uniform prior. The revised Smith's model is shown to provide good estimates of the unknown parameter during the developmental process, particularly for the later stages. The beta Bayes model with maximum variance prior and geometric weights also provides good estimates.

Uncertainties in engineering design exist due to the random nature of loads and materials, lack of knowledge, and imperfect modelling of design parameters. Conventional design methods based on deterministic procedures do not always yield designs having consistent safety. In recent years considerable research has been conducted in the use of probability theory for modelling uncertainties in engineering designs and several probabilistic design formats have been developed. Probability based design methods provide a unified procedure applicable to all construction materials, all loads, and all types of uncertainties. Code committees are currently working on the development of the new design codes for various construction materials such as steel, concrete, and wood based on probabilistic concepts. The objective of this study is to study a probability based design format for wood members. Reliability analysis of wood structural elements such as beams, columns, and beam-columns is conducted, and the risk level is measured by the reliability or safety index, β. Wood members subjected to dead plus live load and dead plus snow load combinations are considered. After conducting a reliability analysis of current designs, a target reliability index is selected. The reliability index is then used in conjunction with the predetermined load factors and load combinations to determine resistance factors. Finally, a design format is proposed for Load and Resistance Factor Design for wood structures. / M.S.

An efficient reliability technique has been developed based on Response Surface Methodology (RSM) in conjunction with the First Order Second Moment (FOSM) reliability method. The technique is applied when the limit state function cannot be obtained explicitly in terms of the design variables, i.e., when the analysis is performed using numerical techniques such as finite elements. The technique has proven to be efficient because it can handle problems with large numbers of design variables and correlated as well as nonnormal random variables. When compared with analytical results, the method has shown excellent agreement. The technique contains a sensitivity analysis scheme which can be used to reduce the computation time resulting in nearly the same accuracy. This technique allows the extension of most finite element codes to account for probabilistic analysis, where statistical variations can be added to the design variables. An explicit solution for rocket motors consisting of propellant and steel case under environmental temperature variations is compared to the RSM technique. The method is then used for the analysis of rocket motors subjected to mechanical loads for which the stress analysis is performed using the finite element method. The technique is also applied to study the reliability of a laminated composite plate with geometric nonlinearity subjected to static and time dependent loadings. Different failure modes were considered as well as different meshes. Results have shown that when the relative size of the element is introduced into the probabilistic model, the same reliability value is obtained regardless of the number of elements in the mesh. This is good because it allows the technique to be used for problems where the failure region is unknown. / Ph. D.