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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.

Due to changes of the thermal environment, thermal stresses are produced in structures. Two approaches based on the stochastic process theory are used to describe this phenomenon. The structure is idealized as a long hollow viscoelastic cylinder. Two sites are considered: Barrow (AK) and Yuma (AZ). First passage concepts are applied to characterize the reliability of the system. Crossings are assumed to follow either the behavior of the Poisson process or Markov process. In both cases, the distribution of the time to first passage is taken to be the exponential distribution. Because the material is viscoelastic, statistically and time varying barriers (strengths) with Normal, Log-Normal, or Neibull distributions are considered. Degradation of the barriers by aging and cumulative damage are incorporated in the analysis. / Ph. D. / incomplete_metadata

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.

A thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy, School of Statistics and Actuarial Science, Faculty of Science University of Witwatersrand, Johannesburg. February 2017. / The work done in this thesis on finite planning horizon inspection models has demonstrated that with the advent of powerful computers these days it is possible to easily find an optimal inspection schedule when the lifetime distribution is known. For the case of system time to failure following a uniform distribution, a result for the maximum number of inspections for the finite planning models has been derived. If the time to failure follows an exponential distribution, it has been noted that periodically carrying out inspections may not result in maximization of expected profit. For the Weibull distributions family (of which the exponential distribution is a special case), evenly spreading the inspections over a given finite planning horizon may not lead to any serious prejudice in profit. The case of inspection models where inspections are of non-negligible duration has also been explored. The conditions necessary for inspections that are evenly spread over the entire planning horizon to be near-optimal when system time to failure either follows a uniform distribution or exponential distribution have been explored. Finite and infinite planning horizon models where inspections are imperfect have been researched on. Interesting observations on the impact of Type I and Type II errors in inspection have been made. These observations are listed on page 174. A clear and easy to implement road map on how to get an optimal inspection permutation in problems first discussed by Zuckerman (1989) and later reviewed by Qiu (1991) for both the undiscounted and discounted cases has been given. The only challenge envisaged when a system has a large number of components is that of computer memory requirements - which nowadays is fast being overcome. In particular, it has been clearly demonstrated that the impact of repair times and per unit of time repair costs on the optimal inspection permutation cannot be ignored. The ideas and procedures of determining optimal inspection permutations which have been developed in this thesis will no doubt lead to huge cost savings especially for systems where the cost of inspecting components is huge. / XL2018

Maintenance is constantly challenged with increasing productivity by maximizing up-time and reliability while at the same time reducing expenditure and investment. In the last few years it has become evident through the development of maintenance concepts that maintenance is more than just a non-productive support function, it is a profit- generating function. In the past decades, hundreds of models that address maintenance strategy have been presented. The vast majority of those models rely purely on mathematical modeling to describe the maintenance function. Due to the complex nature of the maintenance function, and its complex interaction with other functions, it is almost impossible to accurately model maintenance using mathematical modeling without sacrificing accuracy and validity with unfeasible simplifications and assumptions. Analysis presented as part of this thesis shows that stochastic simulation offers a viable alternative and a powerful technique for tackling maintenance problems. Stochastic simulation is a method of modeling a system or process (on a computer) based on random events generated by the software so that system performance can be evaluated without experimenting or interfering with the actual system. The methodology developed as part of this thesis addresses most of the shortcomings found in literature, specifically by allowing the modeling of most of the complexities of an advanced maintenance system, such as one that is employed in the airline industry. This technique also allows sensitivity analysis to be carried out resulting in an understanding of how critical variables may affect the maintenance and asset management decision-making process. In many heavy industries (e.g. airline maintenance) where high utilization is essential for the success of the organization, subsystems are often of a rotable nature, i.e. they rotate among different systems throughout their life-cycle. This causes a system to be composed of a number of subsystems of different ages, and therefore different reliability characteristics. This makes it difficult for analysts to estimate its reliability behavior, and therefore may result in a less-than-optimal maintenance plan. Traditional reliability models are based on detailed statistical analysis of individual component failures. For complex machinery, especially involving many rotable parts, such analyses are difficult and time consuming. In this work, a model is proposed that combines the well-established Weibull method with discrete simulation to estimate the reliability of complex machinery with rotable subsystems or modules. Each module is characterized by an empirically derived failure distribution. The simulation model consists of a number of stages including operational up-time, maintenance down-time and a user-interface allowing decisions on maintenance and replacement strategies as well as inventory levels and logistics. This enables the optimization of a maintenance plan by comparing different maintenance and removal policies using the Cost per Unit Time (CPUT) measure as the decision variable. Five different removal strategies were tested. These include: On-failure replacements, block replacements, time-based replacements, condition-based replacements and a combination of time-based and condition-based strategies. Initial analyses performed on aircraft gas-turbine data yielded an optimal combination of modules out of a pool of multiple spares, resulting in an increased machine up-time of 16%. In addition, it was shown that condition-based replacement is a cost-effective strategy; however, it was noted that the combination of time and condition-based strategy can produce slightly better results. Furthermore, a sensitivity analysis was performed to optimize decision variables (module soft-time), and to provide an insight to the level of accuracy with which it has to be estimated. It is imperative as part of the overall reliability and life-cycle cost program to focus not only on reducing levels of unplanned (i.e. breakdown) maintenance through preventive and predictive maintenance tasks, but also optimizing inventory of spare parts management, sometimes called float hardware. It is well known that the unavailability of a spare part may result in loss of revenue, which is associated with an increase in system downtime. On the other hand increasing the number of spares will lead to an increase in capital investment and holding cost. The results obtained from the simulation model were used in a discounted NPV (Net Present Value) analysis to determine the optimal number of spare engines. The benefits of this methodology are that it is capable of providing reliability trends and forecasts in a short time frame and based on available data. In addition, it takes into account the rotable nature of many components by tracking the life and service history of individual parts and allowing the user to simulate different combinations of rotables, operating scenarios, and replacement strategies. It is also capable of optimizing stock and spares levels as well as other related key parameters like the average waiting time, unavailability cost, and the number of maintenance events that result in extensive durations due to the unavailability of spare parts. Importantly, as more data becomes available or as greater accuracy is demanded, the model or database can be updated or expanded, thereby approaching the results obtainable by pure statistical reliability analysis.

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The College of Engineering at the University of Central Florida (UCF) required a data set containing the Bachelor of Science in Engineering (BSE) graduates from 1970 on, to be updated each semester. The data set was created in 1984, through the use of the Statistical Analysis System/Full-Screen Product (SAS/FSP), a computer system which allows for easy access to and editing of data values, and the use of SAS programming for statistical analysis of the data set. The data set presently (1985) contains 1483 observations each with 70 variables, such as personal information (age, social security number, ethnic origin), degree information (junior college attended, grade point average, honors), post-graduate information (master and doctorate degrees, first job after graduation), and test results (CLAST, SAT, GRE). The current data was obtained through the Department of institutional Research and transcripts. Because this data set will be in use a long time, a manual has been written that contains a detailed description of (a) the data set and all its variables, (b) the use of the full-screen product with a tutorial, (c) the use of the questionnaires, and (d) the method used to collect data. Five tests were performed on four semesters of graduates, equaling 301 observations. The math and overall grade point averages (GPAs) for transfer and time-shortened-degree (TSD) students were tested against the math and overall GPAs of the general UCF BSE population. It was discovered that the math and overall GPAs of the graduates who received Associate of Arts degrees from Florida community colleges before entering UCF lowered significantly at UCF. The tests also suggested a possible difference in academic approaches between the community college and UCF, and there should be more than just a recognition of the drop in math and overall GPA. The TSD graduates did not perform as well in the math and overall curriculum as might be expected. Recommendations for manual testing, updating of the data set, and further testing with SAS are included.