Reliability Analysis And Optimal Maintenance Planning For Repairable Multi-Component Systems Subject To Dependent Competing Risks

Modern engineering systems generally consist of multiple components that interact in a complex manner. Reliability analysis of multi-component repairable systems plays a critical role for system safety and cost reduction. Establishing reliability models and scheduling optimal maintenance plans for multi-component repairable systems, however, is still a big challenge when considering the dependency of component failures. Existing models commonly make prior assumptions, without statistical verification, as to whether different component failures are independent or not. In this dissertation, data-driven systematic methodologies to characterize component failure dependency of complex systems are proposed. In CHAPTER 2, a parametric reliability model is proposed to capture the statistical dependency among different component failures under partially perfect repair assumption. Based on the proposed model, statistical hypothesis tests are developed to test the dependency of component failures. In CHAPTER 3, two reliability models for multi-component systems with dependent competing risks under imperfect assumptions are proposed, i.e., generalized dependent latent age model and copula-based trend-renewal process model. The generalized dependent latent age model generalizes the partially perfect repair model by involving the extended virtual age concept. And the copula-based trend renewal process model utilizes multiple trend functions to transform the failure times from original time domain to a transformed time domain, in which the repair conditions can be treated as partially perfect. Parameter estimation methods for both models are developed. In CHAPTER 4, based on the generalized dependent latent age model, two periodic inspection-based maintenance polices are developed for a multi-component repairable system subject to dependent competing risks. The first maintenance policy assumes all the components are restored to as good as new once a failure detected, i.e., the whole system is replaced. The second maintenance policy considers the partially perfect repair, i.e., only the failed component can be replaced after detection of failures. Both the maintenance policies are optimized with the aim to minimize the expected average maintenance cost per unit time. The developed methodologies are demonstrated by using applications of real engineering systems

Reasoning About the Reliability of Multi-version, Diverse Real-Time Systems

This paper is concerned with the development of reliable real-time systems for use in high integrity applications. It advocates the use of diverse replicated channels, but does not require the dependencies between the channels to be evaluated. Rather it develops and extends the approach of Little wood and Rush by (for general systems) by investigating a two channel system in which one channel, A, is produced to a high level of reliability (i.e. has a very low failure rate), while the other, B, employs various forms of static analysis to sustain an argument that it is perfect (i.e. it will never miss a deadline). The first channel is fully functional, the second contains a more restricted computational model and contains only the critical computations. Potential dependencies between the channels (and their verification) are evaluated in terms of aleatory and epistemic uncertainty. At the aleatory level the events ''A fails" and ''B is imperfect" are independent. Moreover, unlike the general case, independence at the epistemic level is also proposed for common forms of implementation and analysis for real-time systems and their temporal requirements (deadlines). As a result, a systematic approach is advocated that can be applied in a real engineering context to produce highly reliable real-time systems, and to support numerical claims about the level of reliability achieved

Reliability demonstration for safety-critical systems

This paper suggests a new model for reliability demonstration of safety-critical systems, based on the TRW Software Reliability Theory. The paper describes the model; the test equipment required and test strategies based on the various constraints occurring during software development. The paper also compares a new testing method, Single Risk Sequential Testing (SRST), with the standard Probability Ratio Sequential Testing method (PRST), and concludes that: • SRST provides higher chances of success than PRST • SRST takes less time to complete than PRST • SRST satisfies the consumer risk criterion, whereas PRST provides a much smaller consumer risk than the requirement

Reliability analysis of components subject to degradation failure with in-service inspections

Maintaining the reliability of components or systems that are subject to degradation failures is an old and challenging problem. The traditional way to deal with this problem has been to systematically replace parts so that certain reliability, and possibly cost, criteria are satisfied. More recently, new technologies have been developed that allow nondestructive inspections of increasing precision. Thus, replacements may be based now on observations made at these inspections. In a first model, we consider the important case where degradation and failure result from the growth of a crack that has developed within the component of interest, this growth being assumed deterministic. A probabilistic model is presented for the fatigue reliability and cost analysis of such components subject to periodic nondestructive inspections. Some figures of merit considered include the hazard function, an approximation of the cost per unit of service time, and the mean time between failures. A numerical example is given that focuses on the effect of inspections on the hazard function. This model is then extended in order both to handle the possible stochasticity of different parameters, and to allow the dynamic scheduling of inspections from observations. The model is not restricted to the crack growth type degradation. Finally, a computer code with an interface between the Fortran and S-plus languages is developed so that important quantities like the probabilities of failure, of replacements, or the hazard function are calculated in the case where the degradation law parameters are random. The code also provides graphs for the failure time density and the hazard function. Thus, for these functions, the effect of modifying model inputs may be appreciated both numerically and graphically. Numerical examples are given for two crack growth degradation cases, where the growth obeys Paris Law

Feedback and time are essential for the optimal control of computing systems

The performance, reliability, cost, size and energy usage of computing systems can be improved by one or more orders of magnitude by the systematic use of modern control and optimization methods. Computing systems rely on the use of feedback algorithms to schedule tasks, data and resources, but the models that are used to design these algorithms are validated using open-loop metrics. By using closed-loop metrics instead, such as the gap metric developed in the control community, it should be possible to develop improved scheduling algorithms and computing systems that have not been over-engineered. Furthermore, scheduling problems are most naturally formulated as constraint satisfaction or mathematical optimization problems, but these are seldom implemented using state of the art numerical methods, nor do they explicitly take into account the fact that the scheduling problem itself takes time to solve. This paper makes the case that recent results in real-time model predictive control, where optimization problems are solved in order to control a process that evolves in time, are likely to form the basis of scheduling algorithms of the future. We therefore outline some of the research problems and opportunities that could arise by explicitly considering feedback and time when designing optimal scheduling algorithms for computing systems