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IEEE Transactions on Reliability is the premiere technical journal for reliability and related disciplines. We strive to continue this reputation, so we continue to discover what makes journals great. We have discovered that IEEE journals work to have the qualities readers and authors would like to expect. Correctness and technical merit are important features of accepted manuscripts, with correctness rating as most important to the responding editors. Writing and solving real problems seem to be the least important features. The relative unimportance of these last two categories may be a concern, except that relative importance is not an indicator of absolute importance. However, a recent IEEE survey suggests that members place most value on more practical articles, which suggests that the relative importance of solving real problems should be high if we are to meet the needs of our members through our journals. [ABSTRACT FROM AUTHOR]

A complex engineering system typically consists of a group of components/subsystems in a hierarchical structure and the system is monitored at only some, not all, of these hierarchical levels. This paper investigates a Bayesian approach to system reliability prediction using multilevel incomplete data. These data are drawn simultaneously from different component/subsystem levels within the same system, thus need to be analyzed with the consideration of their overlapping nature. In this paper, a Bayesian network model is proposed for modeling the reliability of a multilevel system, where a lower level node can only be connected to one higher level node. Through Bayesian inference, the posterior distributions of lifetime parameters and conditional probabilities in the model are obtained by combining prior beliefs with lifetime data coming from different system levels. This study is also extended to include mixed data types, i.e., both pass/fail data and lifetime data. The effectiveness of the proposed approach is illustrated in a case study. [ABSTRACT FROM PUBLISHER]

A great deal of previous work has studied methods to determine system reliability. That work has defined system reliability as the probability that the production output meets a predetermined demand for a network with many workstations, each of which has random capacity determined by a discrete probability distribution. It is noteworthy that the archival work presents numerous examples, wherein entities are discrete and indivisible, while the analysis is based upon continuous flow, much like a fluid, through the network. The inconsistency, inherent in mixing discrete-entity examples with continuous-flow analysis, can result in erroneous conclusions about the system reliability. The current paper presents a rigorous discrete-analysis analytical approach, which is called the Song rule (Stochastic “Output $\geq$ demand” Networks and their Generation). Based on all examples studied in this paper, the absolute difference ratios between the previous incorrect (as published) and the correct probabilities (from the Song rule) are all greater than 23%. The proposed Song rule analysis is verified to be correct using discrete-event simulation. In addition to providing rigorous analysis for the network problems under consideration, the Song rule is a useful tool for assessing the validity of any future proposed approach for other stochastic reliability problems. [ABSTRACT FROM PUBLISHER]

Uncertain and potentially harsh operating environments are often known to alter the operational performance of a system. In order to maintain system performance while coping with varying operating environments and potential disruptions, the resilience of engineered systems is desirable. Engineering systems are often interconnected in a dimensional way inherently from basic components to subsystems to the system of systems, which poses a grand challenge for system designers to analyze the resilience of such a complex system. Moreover, further complications in the assessment of resilience in the engineering domain are attributed to time-varying system performances, random perturbation occurrences, and probable failures caused by adverse events. This paper presents a dynamic Bayesian network (DBN) approach for the modeling and predictive resilience analysis for dynamic engineered systems. With the inter-time-slice links and the conditional probability tables in a DBN, the system performance could be molded as changing in a discrete time slice, while capturing the temporal probabilistic dependencies between the variables. An industrial-based case study of an electricity distribution system is further studied to demonstrate the effectiveness of the DBN approach for resilience analysis. The approach presented in this paper hopes to aid in realizing resiliency in system designs and to pave the way toward enhancements in developing resilient engineered systems. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a system composed of mixtures of one-shot units with nonhomogeneous and time-dependent characteristics. We propose analytical expressions to predict system reliability metrics and consider a physics-statistics-based lifetime model to demonstrate the units’ failure mechanism as well as its failure process uncertainty. We design a sequence of optimum accelerated non-destructive testing (NDT) plans to predict the reliability metrics of the system and show that a well-designed sequential accelerated NDTs is an effective approach to shorten the test duration with negligible consequence on system reliability metrics. [ABSTRACT FROM PUBLISHER]

Accelerated life testing has been widely applied to obtain the reliability information of an asset (component) at use conditions when the component is highly reliable. In accelerated life testing, tested components are exposed to stress levels more severe than usual so that more component failures can be observed in a short period of time. Most existing statistical models assume a known parametric relationship between the lifetime (or lifetime characteristic) and accelerating stresses. In this paper, we propose semiparametric modeling for the relationship between the lifetime characteristic and accelerating stresses. The proposed model is suitable for both single and multiple accelerating stress cases. A maximum penalized likelihood estimation method is developed to estimate the model parameters. A simulation study is implemented to illustrate the performance of the proposed model, and a real-world case study is conducted to demonstrate the proposed model. [ABSTRACT FROM PUBLISHER]

By combining the nonprobabilistic reliability theory with optimization design approach, this paper proposes a mixed reliability-based optimization method for the heat transfer system design with both fuzzy and interval parameters in material property, external load, and boundary condition. Fuzzy variables are used to represent subjective uncertainties associated with expert opinions; whereas, interval variables are adopted to quantify objective uncertainties with limited information. Based on the level-cut strategy, the mixed uncertain problem is transformed into a pure interval problem first. Then, a modified reliability analysis method using an interval ranking strategy and integral operation is presented to precisely assess the system safety possibility. Subsequently, a mixed reliability-based optimization model with fuzzy and interval parameters is established, which is a nested optimization problem with huge computational cost. A subinterval perturbation method is eventually presented for temperature field prediction, which can replace the inner loop optimization and improve the computational efficiency. A transient heat conduction example about a three-layer thermal structure verifies the superiority of the proposed model and method for mixed reliability analysis and optimization in practical engineering. [ABSTRACT FROM PUBLISHER]

In the process of long-term use, the uncertainty of an engineering structure often presents time-variant or dynamic characteristics due to the influence of stochastic loads and material performance degradations. In such a situation, the structural design optimization will involve an important problem of time-variant reliability-based design optimization (TRBDO). Performing TRBDO involves a nested optimization, which will lead to extremely low computational efficiency. In this paper, a single-loop approach (SLA) is proposed to convert the nested optimization in TRBDO into a sequence iterative process composed of the time-variant reliability analysis (TRA), constraint discretization, and design optimization. In each iteration step, the TRA method based on stochastic process discretization is first used to calculate the time-variant reliability of constraints; second, through introducing the concept of the target reliability index of discretized time period and proposing the corresponding algorithm, each time-variant constraint is discretized into a series of time-invariant constraints to formulate a conventional reliability-based design optimization problem. The approach exhibits a good comprehensive performance in terms of efficiency and convergence. The validity and practicality of the SLA are validated by two numerical examples and a design problem for the chassis of a self-balancing vehicle. [ABSTRACT FROM PUBLISHER]

A method is proposed in this paper to determine whether a product, a component, or a system in reliability life testing has a longer lifetime than the other. We propose two indices to compare reliability. The comparison is also distribution-free; i.e., it does not require the assumption on the lifetime distributions. A comparability index that is derived by integrating the weighted difference between the reliability functions of the two groups under comparison is named the "Better or Worse" (BOW) index. The second comparability index that is derived by calculating the overlapping area under the two distributions in comparison is named "Reliability Comparability" (RC) to quantify the degree of similarity between the two distributions. These two new indices are compared with the conventional methods currently used in the IC industries. Practical applications in lifetime-type reliability comparison are also illustrated in this paper. [ABSTRACT FROM AUTHOR]

Topological optimization is an important problem in communication networks. Exact reliability optimization methods are restricted to small problems, or specialized network topologies. For larger problems, simulation-based approaches are more practical. In simulation-based optimization, one often needs to compare the reliability of a large number of similar networks. The traditional reliability estimation & rank process is the most time consuming step of most optimization algorithms. In this paper, a novel approach is proposed to directly estimate the reliability ranking of some edge relocated networks without the need to estimate their reliabilities. In the case study considered in this paper, the proposed Synchronous Construction Ranking method achieved over 30,000 times speedup over the traditional approach using the Merge Process estimation algorithm. [ABSTRACT FROM AUTHOR]

Network analysis is an important approach to model real-world systems. System reliability, and system unreliability are two related performance indices useful to measure the quality level of a supply-demand system. For a binary-state network without flow, the system unreliability is the probability that the system can not connect the source and the sink. Extending to a limited-flow network in the single-commodity case, the arc capacity is stochastic, and the system capacity (i.e. the maximum flow) is not a fixed number. The system unreliability for (d + 1), the probability that the upper bound of the system capacity equals d, can be computed in terms of upper boundary points. An upper boundary point is the maximal system state such that the system fulfills the demand. This paper concentrates on a multicommodity limited-flow network (MLFN) in which multicommodity are transmitted through unreliable nodes and arcs. Nevertheless, the system capacity is not suitable to be treated as the maximal sum of the commodity because each commodity consumes the capacity differently. We define the system capacity as a demand vector if the system fulfills at most such a demand vector. The main problem of this paper is to measure the quality level of a MLFN. We propose a new performance index, the probability that the upper bound of the system capacity equals the demand vector subject to the budget constraint, to evaluate the quality level of a MLFN. A branch-and-bound algorithm based on minimal cuts is presented to generate all upper boundary points in order to compute the performance index. The computational complexity of the proposed algorithm is analyzed. [ABSTRACT FROM AUTHOR]

This paper discusses some of the difficulties in the paper: "A BDD-based algorithm for reliability analysis of phased-mission systems" by X. Zang, H. Sun, and K. S. Trivedi. [ABSTRACT FROM AUTHOR]

This paper presents a generalized periodic imperfect preventive maintenance (PM) model for a system with age-dependent failure type. The imperfect PM model proposed in this study incorporates improvement factors vis-à-vis the hazard-rate function, and effective age. As failures occur, the system experiences one of the two types of failure: type-I failure (minor), and type-II failure (catastrophic). Type-I failures are rectified with minimal re- pair. In a PM period, the system is preventively maintained following the occurrence of a type-II failure, or at age T, whichever takes place first. At the Nth PM, the system is replaced. An approach that generalizes the existing studies on the periodic PM policy is proposed. Taking age-dependent failure type into consideration, the objective consists of determining the optimal PM & replacement schedule that minimize the expected cost per unit of time, over an infinite horizon. [ABSTRACT FROM AUTHOR]

In modern industries, there is intense pressure to continuously reduce costly, unscheduled maintenance of complex systems. To obtain high availability with reduced life cycle total ownership costs, classical maintenance policies are not optimal. Indeed, these polices do not allow us to perform maintenance only when it is necessary because they are not able to forecast system damage states in the future. To predict precisely the future system damage state, it is necessary to take into account how and where the system will be used. To build incremental damage models, this paper presents a generic methodology and formalism based on the system decomposition in three levels: environment, mission, and process. Predictions are performed via a sequence of known mission parameters, and environmental conditions. This allows for mission and maintenance planning by taking into account the predicted system damages over time. [ABSTRACT FROM AUTHOR]

This paper combines two distinct areas of research, namely software reliability growth modeling, and efficacy studies on software testing methods. It begins by proposing two software reliability growth models with a new approach to modeling. These models make the basic assumption that the intensity of failure occurrence during the testing phase of a piece of software is proportional to the s-expected probability of selecting a failure-causing input. The first model represents random testing, and the second model represents partition testing. These models provide the s-expected number of failures over a period, which in turn is used in analyzing the failure detection abilities of testing strategies. The specific areas of investigation are • conditions that enable partition testing yielding optimal results, and • comparison between partition testing and random testing in terms of efficacy [ABSTRACT FROM AUTHOR]

Extrapolating reliability from accelerated tests for technologies without field data always carries the risk that the accelerated tests do not show the mechanisms which dominate at operating conditions. In statistical terminology, such accelerated testing carries a risk of confounding. For linear models, there is theory which allows one to determine which models are confounded with others. This paper develops analogous theory for a simple kind of confounding model, evanescent processes, when kinetics is used as the basis of modeling accelerated testing. A heuristic for identifying simple evanescent processes that can give rise to disruptive alternatives (alternative models that reverse the decision which would be made based on modeling to date) is outlined. Then, we develop activity mapping, a tool for quantitatively identifying the parameter values of that evanescent process which can result in disruptive alternatives. Finally, we see how activity mapping can be used to identify experiments which help reveal such disruptive evanescent processes. [ABSTRACT FROM AUTHOR]

Masked system life test data arises when the exact component which causes the system failure is unknown. Instead, it is assumed that there are two observable quantities for each system on the life test. These quantities are the system life time, and the set of components that contains the component leading to the system failure. The component leading to the system failure may be either completely unknown (general masking), isolated to a subset of system components (partial masking), or exactly known (no masking). In the dependent masked system life test data, it is assumed that the probability of masking may depend on the true cause of system failure. Masking is usually due to limited resources for diagnosing the cause of system failures, as well as the modular nature of the system. In this paper, we present point, and interval maximum likelihood, and Bayes estimators for the reliability measures of the individual components in a multi-component system in the presence of dependent masked system life test data. The life time distributions of the system components are assumed to be geometric with different parameters. Simulation study will be given in order to 1) compare the two procedures used to derive the estimators for the reliability measures of system components, 2) study the influence of the masking level on the accuracy of the estimators obtained, and 3) study the influence of the masking probability ratio on the accuracy of the estimators obtained. [ABSTRACT FROM AUTHOR]

The k-out-of-n secret sharing schemes are effective, reliable, and secure methods to prevent a secret or secrets from being lost, stolen, or corrupted. The circular sequential k-out-of-n congestion (CSknC) system [3], based upon this type of secret sharing scheme, is presented for reconstructing secret(s) from any k servers among n servers in circular, sequential order. When a server is connected successfully, it will not be reconnected in later rounds until the CSknC system has k distinct, successfully connected servers. An optimal server arrangement in a CSknC system is determined in [3] where n servers have known network connection probabilities for two states, i.e., congested, and successful. In this paper, we present: i) a generalized access structure congestion (GΓC) system that is based upon the generalized secret sharing scheme, and ii) an efficient connection procedure for the GΓC system in terms of the minimal number of server connection attempts. The k-out-of-n secret sharing schemes are considered as simple cases of the generalized secret sharing schemes. It implies that the GΓC system is a more general system than the CSknC system. We established an iterative connection procedure for the new system. Simulation results are used to demonstrate that the iterative connection procedure is more efficient in terms of minimizing the number of connection attempts. [ABSTRACT FROM AUTHOR]

Over the last several decades, many Software Reliability Growth Models (SRGM) have been developed to greatly facilitate engineers and managers in tracking and measuring the growth of reliability as software is being improved. However, some research work indicates that the delayed S-shaped model may not fit the software failure data well when the testing-effort spent on fault detection is not a constant. Thus, in this paper, we first review the logistic testing-effort function that can be used to describe the amount of testing-effort spent on software testing. We describe how to incorporate the logistic testing-effort function into both exponential-type, and S-shaped software reliability models. The pro- posed models are also discussed under both ideal, and imperfect debugging conditions. Results from applying the proposed models to two real data sets are discussed, and compared with other traditional SRGM to show that the proposed models can give better pre- dictions, and that the logistic testing-effort function is suitable for incorporating directly into both exponential-type, and S-shaped software reliability models. [ABSTRACT FROM AUTHOR]

Stringent in-service and operating requirements oblige marine diesel engines to possess high levels of reliability and availability. To achieve the desired reliability and availability levels, it is necessary to carry out costly maintenance activity on the cylinder liners, the wear on which is a major factor in causing diesel engine failure. This paper presents a s-based methodology that can be used to carry out a condition-based estimate of liner reliability with respect to failure through excessive wear, and to plan condition-based maintenance activity. The wear process is described through an ad hoc cumulative damage model, and the reliability of the liners is estimated on the basis of wear measures, and predictions of wear increase. The approach proposed allows reducing maintenance costs without noticeably affecting liner reliability. In fact, it gives the probability of inspecting or replacing liners only when there is a high likelihood that their wear level will exceed the wear limit before the next inspection date. The proposed model, and planning procedure have been applied to a data set consisting of wear measures of the cylinder liners of two SULZER RTA 58 engines equipping twin ships of the Grimaldi Group. [ABSTRACT FROM AUTHOR]

This paper proposes efficient methods to assess the reliability of phased-mission systems (PMS) considering both imperfect fault coverage (IPC), and common-cause failures (CCF). The IPC introduces multimode failures that must be considered in the accurate reliability analysis of PMS. Another difficulty in analysis is to allow for multiple CCF that can affect different subsets of system components, and which can occur s-dependently. Our methodology for resolving the above difficulties is to separate the consideration of both IPC and CCF from the combinatorics of the binary decision diagram-based solution, and adjust the input and output of the program to generate the reliability of PMS with LPC and CCF. According to the separation order, two equivalent approaches are developed. The applications and advantages of the approaches are illustrated through examples. PMS without IPC and/or CCF appear as special cases of the approaches. [ABSTRACT FROM AUTHOR]

Numerous stochastic models for repairable systems have been developed by assuming different time trends, and repair effects. In this paper, a new general repair model based on the repair history is presented. Unlike the existing models, the closed-form solutions of the reliability metrics can be derived analytically by solving a set of differential equations. Consequently, the confidence bounds of these metrics can be easily estimated. The proposed model, as well as the estimation approach, overcomes the drawbacks of the existing models. The practical use of the proposed model is demonstrated by a much-discussed set of data. Compared to the existing models, the new model is convenient, and provides accurate estimation results. [ABSTRACT FROM AUTHOR]

The system capacity of a deterministic flow network is the maximum flow from the source to the destination. In a single-commodity stochastic-flow network (branches all have several possible capacities, and may fail), the system reliability, the probability that the maximum flow is larger than or equal to a given demand, is an important performance index to measure the quality level of a network. In a two-commodity stochastic-flow network, different types of commodities are transmitted through the same network simultaneously, and compete for the capacities. We concentrate on the reliability problem for such a network subject to the budget constraint. This paper defines firstly the system capacity as a pattern. We propose a performance index, the probability that the system capacity is less than or equal to a given pattern subject to the budget constraint, to evaluate the system performance. A simple algorithm based on minimal cuts is proposed to generate all maximal vectors meeting the demand and budget constraints. The performance index can then be computed in terms of all such maximal vectors. [ABSTRACT FROM AUTHOR]

Planned replacement policies are used to reduce the incidence of system failures, or to return a failed system to work. New better than used aging classes are commonly used in reliability theory to model situations in which the lifetime of a new unit is ‘better’ than the lifetime of a used one. The purpose of this paper is to establish comparisons of expected failure times of an age (block) replacement policy, and a renewal process with no planned replacements when the lifetime of the unit is NBUE. As we will see, age and block replacement policies improve the stochastic behavior compared with the renewal process with no planned replacements when the underlying distribution is NBUE. Some interpretations, applications, and a discussion about some related results are included. [ABSTRACT FROM AUTHOR]

Dependability evaluation is a fundamental step in distributed control system design. However, the current depend- ability evaluation methods are not appropriate due to the level of complexity of such systems. Given the ineffectiveness of these methods, we propose the Safe-SADT formalism for dependability evaluation (SADT stands for Structured Analysis and Design Techniques). This formalism allows the explicit formalization of functional interaction, the identification of the characteristic values affecting complex system dependability, the quantification of RAMS parameters (Reliability, Availability, Maintainability, and Safety) for the system's operational architecture, and the validation of the operational architecture in terms of the dependability objectives and constraints required by the functional specifications. The results presented in this paper are limited to RAMS quantification. [ABSTRACT FROM AUTHOR]

In this paper, we develop a generalized multi-state degraded system reliability model subject to multiple competing failure processes, including two degradation processes, and random shocks. The operating condition of the multi-state systems is characterized by a finite number of states. We also present a methodology to generate the system states when there are multi- failure processes. The model can be used not only to determine the reliability of the degraded systems In the context of multi-state functions, but also to obtain the states of the systems by calculating the system state probabilities. Several numerical examples are given to Illustrate the concepts. [ABSTRACT FROM AUTHOR]

This paper deals with a new reliability model for nonrepairable systems, the Hyperbolic. A decreasing hazard rate approaching a value greater than zero is its distinctive characteristic. Potentially, many mechanisms of failure can produce mortality laws of Hyperbolic type. The "Deterioration", "Stress-Strength", and "Shocks" failure models discussed here are such models. To make the use of the Hyperbolic model easier, the maximum likelihood estimators of its parameters are given. They can be calculated without any difficulty, and appear to be acceptable for practical technological applications. Finally, two applicative examples are given. These examples exhibit that when the mechanism of failure is one of the types discussed, the Hyperbolic model shows a better fit compared with other alternative reliability models, like Gamma, and Weibull. [ABSTRACT FROM AUTHOR]

This paper proposes a method by which material in- homogeneity may be taken into account in a reliability calculation. The method employs Monte-Carlo simulation; and introduces a material strength index, and a standard deviation of material strength to model the variation in the strength of a component throughout its volume. The method is compared to conventional load-strength interference theory. The results are identical for the case of homogeneous material, but reliability is shown to reduce for the same load as the component volume increases. The case of a tensile bar is used to explore the variation of reliability with component volume. [ABSTRACT FROM AUTHOR]

Summary and Conclusions - This paper presents four models for optimizing the reliability of embedded systems considering both software and hardware reliability under cost constraints, and one model to optimize system cost under multiple reliability constraints. Previously, most optimization models have been developed for hardware-only or software-only systems by assuming the hardware, if any, has perfect reliability. In addition, they assume that failures for each hardware or software unit are statistically independent. In other words, none of the existing optimization models were developed for embedded systems (hardware and software) with failure dependencies. For our work, each of our models is suitable for a distinct set of conditions or situations. The first four models maximize reliability while meeting cost constraints, and the fifth model minimizes system cost under multiple reliability constraints. This is the first time that optimization of these kinds of models has been performed on this type of system. We demonstrate and validate our models for an embedded system with multiple applications sharing multiple resources. We use a Simulated Annealing optimization algorithm to demonstrate our system reliability optimization techniques for distributed systems, because of its flexibility for various problem types with various constraints. It is efficient, and provides satisfactory optimization results while meeting difficult-to-satisfy constraints. [ABSTRACT FROM AUTHOR]

This paper proposes two alternative policies for preventive replacement of a component, which shows sign of occurrence of a fault, and operates for some random time with degraded performance, before its final failure. The time between fault occurrence and component failure is termed as delay time. The first policy, namely age replacement during delay time policy (ARDTP), recommends replacement of a faulty component on failure or preventive replacement of the same after a fixed lime during, its delay time. It considers the performance degradation during delay lime to develop an age replacement policy. It Is also shown that the policy is a feasible proposition for a component that has positive (nonnegative) performance degradation during its CFR (IFR) delay time. The second policy, OARDTP, extends ARDTP to opportunistic age replacement policy where a faulty component is replaced at the first available randomly occurring maintenance opportunity, after a fixed time from occurrence of fault, or on failure. The time between opportunities (TBO) is considered to be exponentially distributed. This policy reduces the number of forced shutdowns, which is essential to ARDTP. It is shown that the second policy is superior to the first policy if the cost of a preventive replacement with forced shutdown is more than the preventive replacement cost during an opportunity. The policies are appropriate for complex process plants, where the tracking of the entire service life of each component is difficult. Their implementation requires tracking of components' delay time only, and estimation of mean time to occurrence of faults. The policies are relatively insensitive to estimation error in failure replacement cost. As their implementation requires immediate capturing of fault occurrence information, they are particularly attractive to organizations where operators are involved in the maintenance of machines. [ABSTRACT FROM AUTHOR]

Mechanical characterization of electronic devices is often quite uneasy; most of the techniques used require a contact with the sample under study. In this paper, we propose an optical noncontact interferometric imaging method to study the thermomechanical behavior of running devices, and In particular, to deduce the corresponding elastic strain energy. This analysis will permit us to localize the zones of fragility of the device. Results obtained on a power MOS transistor to detect the region of maximum elastic strain energy an presented. It is in particular adapted in microelectronics a applications to detect stress accumulation due to dilation coefficient mismatches when assembling microchips. [ABSTRACT FROM AUTHOR]

This paper discusses contact discontinuity of electromechanical switches, and presents a model that considers the effect of vibration-induced inertial force on operational reliability. Using this model, the operational reliability of a switch with a specific contact assembly can be assessed for given vibration conditions. Under the vibration conditions, a minimum contact spring force functioning of the switch, while the magnitude of contact uncertainty determines the need of an additional force to ensure operational reliability. With reduced contact uncertainty, the operational reliability of switches approaches either 0 or 1, solely depending upon the design & operational conditions. In this model, the parameters of c', b,& σ/μ need to be determined either empirically, or experimentally before the model can be used for reliability assessment. To theoretically determine those parameters, Hertz contact with randomly distributed surface asperities needs to be considered. Finally, although this model starts from a log-normal distribution of electrical contact the approach can be applied to other distributions, such as the inverse Gaussian and Weibull distributions. [ABSTRACT FROM AUTHOR]

A powerful equation is derived for determining the probability of safe/failure states dependent on random variables, following a homogeneous Poisson process in a finite domain. The equation is generic & gives the probability of all types of relative configurations of the random variables governing reliability. The significance of the derived equation stems from the fact that the reliability problems only, or to a simple function of the relative distances between the locations of the random variables. Many intractable reliability problems can be solved easily using the derived equation which reduces complex reliability problems to problems with trivial solutions. The power of the equation is illustrated by the derivation of a number of important special cases, and numerous applications: i) determining the probability of existence of a set of minimum intervals between the locations of random variables in a finite interval, ii) determining the number density envelope of the random variables which prevents clustering within a critical distance, and iii) a closed-form relationship for determining reliability during shock loading. The new equation is at the basis of a new reliability measure which consists of a combination of a set of specified minimum free gaps before/between random variables in a finite interval, and a minimum specified probability with which they must exist. The new reliability measure is at the heart of a technology for setting quantitative reliability requirements based on minimum failure-free operating periods (MFFOP). The equation is applied to cases where failure is triggered because of clustering of two ore more demands, forces, or manufacturing/material flaws following a homogeneous Poisson process in a specified time interval/length. A number of important applications have also been considered related to the conditional case (a homogeneous Poisson process conditioned on the number of random variables in a finite interval). Solutions have been provided for common problems related to: i) collisions of demands from a given number of customers using a particular equipment for a specified time; ii) overloading of supply systems from a given number of consumers connecting independently & randomly, and iii) analysis of random failures following a homogeneous Poisson process where only the number of failures is known, but not the actual failure times. In the paper, it is demonstrated that even for a small number of random variables in a finite interval, the probability of clustering of two or more random variables is surprisingly high, and should always be accounted for in risk assessments. [ABSTRACT FROM AUTHOR]

This paper proposes a suite of approaches to solve the survivable routing problem with shared protection. We first define in mathematics the maximum extent of resource sharing for a protection path given the corresponding working path according to the current network link-state. Then the problem of solving the least-cost working & protection path-pair (in terms of the sum of the cost) is formulated into an Integer Linear Programming process. Due to the dependency of the protection path on its working path, however, the formulation is not scalable with the network size, and takes an extract effort to solve. Therefore, we introduce two heuristic algorithms, called Iterative Two-Step-Approach (ITSA) & Maximum Likelihood Relaxation (MLR), which aim to explore the approximating eptimal solutions with less computation time. We evaluate the performance of the proposed schemes, and make a comparison with some reported counterparts. The simulation results show that the ITSA scheme, with a properly defined tolerance to optimality, can achieve the best performance at the expense of more computation time. On the other hand, MLR delivers a compromise between computation efficiency & performance. [ABSTRACT FROM AUTHOR]

The effect of repair of a complex system can usually be approximated by the following two types: minimal repair for which the system is restored to its functioning state with minimum effort, or perfect repair for which the system is replaced or repaired to a good-as-new state. When both types of repair are possible, an important problem is to determine the repair policy; that is, the type of repair which should be carried out after a failure. In this paper, an optimal allocation problem is studied for a monotonic failure rate repairable system under some resource constraints. In the first model, the numbers of minimal & perfect repairs are fixed, and the optimal repair policy maximizing the expected system lifetime is studied. In the second model, the total amount of repair resource is fixed, and the costs of each minimal & perfect repair are assumed to be known. The optimal allocation algorithm is derived in this case. Two numerical examples are shown to illustrate the procedures. [ABSTRACT FROM AUTHOR]

The transient behavior of a system with operational and repair times distributed following phase-type distributions is studied. These times are alternated in the evolution of the system, and they form 2 separate geometric processes. The stationary study of this system when the repair times form a renewal process has been made [3]. This paper also considers that operational times are partitioned into two well-distinguished classes successively accupied: good, and preventive. An algorithmic approach is performed to determine the transition probabilities for the Markov process which governs the system, and other performance measures beyond those in [3] are calculated in a well-structured form. The results are applied to a numerical example, and the transient quantities are compared with the ones obtained in the stationary case. The computational implementation of the mathematical expressions formulated are performed using the Matlab program. [ABSTRACT FROM AUTHOR]