It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or un-modeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the First-Order Reliability Method (FORM). The FORM analysis requires the solution of an optimization problem however, so implementing this approach into an RBDO routine creates a double-loop optimization structure. For large problems such as Reliability-Based Topology Optimization (RBTO), numeric sensitivity analysis becomes computationally intractable. In this thesis, a general approach to the sensitivity analysis of nested functions is developed from the Lagrange Multiplier Theorem and then applied to several Reliability-Based Design Optimization problems, including topology optimization. The proposed approach is computationally efficient, requiring only a single solution of the FORM problem each iteration. / Master of Science / It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or unmodeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the First-Order Reliability Method (FORM). The FORM analysis requires the solution of an optimization problem however, so implementing this approach into an RBDO routine creates a double-loop optimization structure. For large problems such as Reliability-Based Topology Optimization (RBTO), numeric sensitivity analysis becomes computationally intractable. In this thesis, a general approach to the sensitivity analysis of nested functions is developed from the Lagrange Multiplier Theorem and then applied to several Reliability-Based Design Optimization problems, including topology optimization. The proposed approach is computationally efficient, requiring only a single solution of the FORM problem each iteration.

Yes / Bayesian Network (BN)-based methods are increasingly used in system reliability analysis. While BNs enable to perform multiple analyses based on a single model, the construction of robust BN models relies either on the conversion from other intermediate system model structures or direct analyst-led development based on experts input, both requiring significant human effort. This article proposes an architecture model-based approach for the direct generation of a BN model. Given the architectural model of a system, a systematic bottom-up approach is suggested, underpinned by failure behaviour models of components composed based on interaction models to create a system-level failure behaviour model. Interoperability and reusability of models are supported by a library of component failure models. The approach was illustrated with application to a case study of a steam boiler system.

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An attempt is made in this thesis to study some stochastic models of both reliability and inventory systems with reference to the following aspects: (i) the confidence limits with the introduction of common-cause failures. (ii) the Erlangian repair time distributions. (iii) the product interactions and demand interactions. (iv) the products are perishable. This thesis contains six chapters. Chaper 1 is introductory in nature and gives a review of the literature and the techniques used in the analysis of reliability systems. Chapter 2 is a study of component common-cause failure systems. Such failures may greatly reduce the reliability indices. Two models of such systems (series and parallel) have been studied in this chapter. The expressions such as, reliability, availability and expected number of repairs have been obtained. The confidence limits for the steady state availability of these two systems have also been obtained. A numerical example illustrates the results. A 100 (1 - a) % confidence limit for the steady state availability of a two unit hot and warm standby system has been studied, when the failure of an online unit is constant and the repair time of a failed unit is Erlangian. The general introduction of various inventory systems and the techniques used in the analysis of such systems have been explained in chapter 4. Chapter 5 provides two models of two component continuous review inventory systems. Here we assume that demand occurs according to a poisson process and that a demand can be satisfied only if both the components are available in inventory. Back-orders are not permitted. The two components are bought from outside suppliers and are replenished according to (s, S) policy. In model 1 we assume that the lead-time of the components follow an exponential distribution. By identifying the inventory level as a Markov process, a system of difference-differential equations at any time and the steady-state for the state of inventory level are obtained. Tn model 2 we assume that the lead-time distribution of one product is arbitrary and the other is exponential. Identifying the underlying process as a semi-regenerative process we find the stationary distribution of the inventory level. For both these models, we find out the performance measures such as the mean stationary rate of the number of lost demands, the demands satisfied and the reorders made. Numerical examples for the two models are also considered. Chaper 6 is devoted to the study of a two perishable product inventory model in which the products are substitutable. The perishable rates of product 1 and product 2 are two different constants. Demand for product 1 and product 2 follow two independent Poisson processes. For replenishment of product 1 (s, S) ordering policy is followed and the associated lead-time is arbitrary. Replenishment of product 2 is instantaneous. A demand for product 1 which occurs during its stock-out period can be substituted by product 2 with some probability. Expressions are derived for the stationary distribution of the inventor}' level by identifying the underlying stochastic process as a semi-regenerative process. An expression for the expected profit rate is obtained. A numerical illustration is provided and an optimal reordering level maximising the profit rate is also studied. To sum up, this thesis is an effort to improve the state the of art of (i) complex reliability systems and their estimation study (ii) muitiproduct inventory systems. The salient features of the thesis are: (i) Analysis of a two-component reliability system with common-cause failures. (ii) Estimation study of a complex system in which the repair time for both hot standby and warm standby systems are assumed to be Eriangian. (iii) A multi-product continuous review inventory system with product interaction, with a (s, S) policy. (iv) Introduction of the concept of substitutability for products. (v) Derivation of expressions for various statistical measures. (vi) Effective use of the regeneration point technique in deriving various measures for both reliability and inventory systems. (vii) Illustration of the various results by extensive numerical work. (vii) Consideration of relevant optimization problems. / Mathematical Sciences / PhD (Statistics)

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Up until 2015 the rate at which cube satellite missions achieved full mission success was only 44.1% for any organizations rst mission (academic or corporate), the success rate increases to only 62% for cube satellites launched as a second mission. This thesis suggests that there are two main sources for the high failure rate: improper veri cation, and the common use of COTS components and their reliability in a space environment. The thesis provides a means of increasing mission assurance through the use of physics of failure reliability estimation models that incorporate the intrinsic and extrinsic failures of thermal mechanical e ects as well as radiation e ects on EEE components, a design methodology is also presented that incorporates reliability modeling as well as thorough software and hardware in loop testing to prevent failure due to improper veri cation. The environment and reliability models are calculated for the on board command and data handling system of the ECOSat- II cube satellite being developed by the University of Victoria ECOSat team using NX Siemens for thermal FEA modelling, SPENVIS for radiation environment, and MATLAB for reliability calculation. / Graduate / 0544 / 0538 / cass.hussmann@gmail.com

<p>Sound maintenance strategies and planning are of crucial importance for wind power systems, and especially for offshore locations. In the last decades, an increased awareness of the impact of human living on the environment has emerged in the world. The importance of developing renewable energy is today highly recognized and energy policies have been adopted towards this development. Wind energy has been the strongest growing renewable source of energy this last decade. Wind power is now developing offshore where sites are available and benefits from strong and steady wind. However, the initial investments are larger than onshore, and operation and maintenance costs may be substantially higher due to transportation costs for maintenance and accessibility constrained by the weather.</p><p>Operational costs can be significantly reduced by optimizing decisions for maintenance strategies and maintenance planning. This is especially important for offshore wind power systems to reduce the high economic risks related to the uncertainties on the accessibility and reliability of wind turbines.</p><p>This thesis proposes decision models for cost efficient maintenance planning and maintenance strategies for wind power systems. One model is proposed on the maintenance planning of service maintenance activities. Two models investigate the benefits of condition based maintenance strategies for the drive train and for the blades of wind turbines, respectively. Moreover, a model is proposed to optimize the inspection interval for the blade. Maintenance strategies for small components are also presented with simple models for component redundancy and age replacement.</p><p>The models are tested in case studies and sensitivity analyses are performed for parameters of interests. The results show that maintenance costs can be significantly reduced through optimizing the maintenance strategies and the maintenance planning.</p>

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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.

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