Previous research on event log data analysis has primarily focused on identifying critical and frequent events, as well as qualitatively assessing correlations between event occurrences. However, the probabilistic behavior of frequently occurring events over time remains poorly understood. Through an in-depth exploratory analysis, we reveal that the (log) inter arrival times of events follow some mixture distributions with two modes, suggesting the presence of transitions between latent states. To better understand the data-generating mechanism underlying these frequent events, we employ Markov Modulated Renewal Processes (MMRPs), a type of hidden Markov model, to capture the patterns exhibited in the inter-arrival times between successive events. Due to limitations in record precision, some inter-arrival times are recorded as zero. To address this issue, we propose a simple data imputation algorithm to generate non zero inter-arrival times, facilitating inference on the inter-arrival time distributions and the underlying MMRPs. The effectiveness of the algorithm is validated using synthetic data. Finally, we evaluate the proposed model on real manufacturing system data, uncovering key insights into system states.

PRIMEX (PRIME-based Graph Encoding and Extraction for Information Fusion) is a novel framework designed to enhance distributed information fusion while minimizing communication overhead and computational complexity. Traditional information graph (IG)-based approaches require frequent synchronization and large-scale graph updates, leading to significant communication demands. PRIMEX overcomes these challenges by encoding information pedigree of state estimates as products of distinct prime numbers, allowing fusion to be performed using lightweight arithmetic operations such as greatest common divisor (GCD) for redundancy removal and least common multiple (LCM) for data integration. This eliminates the need for transmitting complex graph structures and instead leverages prime factorization-based queries to efficiently identify shared information, significantly improving scalability. PRIMEX is particularly well-suited for edge computing environments and decentralized systems, where reducing communication, computation, and memory overhead is crucial. By supporting federated learning principles, PRIMEX enhances system adaptability while preserving data privacy, making it a practical solution for scalable, distributed information fusion in applications such as autonomous systems, multi-agent networks, and large-scale sensing platforms.

This article pioneers an order statistics framework for analyzing systems reliability with dependent components, uniquely integrating survival signature computation and order statistics-derived probabilistic expressions. A Copula-based dependence modeling approach is utilized to characterize interdependencies within the system. Comparative analyses are conducted between the proposed framework and three established reliability assessment methodologies: structure function-based method; signature-based method; and survival signature-based method.

Consider a system consisting of multistate components that perform the same function, and each component occupies a location in the system. The deterioration processes of components differ due to different workloads, usage rates, or environmental stresses that are associated with the locations. This article proposes a condition-based maintenance policy, in which the component reallocation (CR) with distinct assignments of components to locations and the preventive replacement of system are dynamically implemented based on the system state. A Markov decision process (MDP) is formulated to optimize the proposed condition-based multi-CR maintenance policy by determining the actions for each system state that minimize the expected long-run system maintenance cost. In the current studies on the MDP for maintenance optimization, the actions mainly include component replacement, imperfect repair, and system replacement. In this article, including CRs of distinct assignments as actions and considering multiple times of CRs increase the action space of the MDP significantly. An enumeration-based value iteration algorithm and a genetic-algorithm-based value iteration algorithm are proposed. Numerical experiments on$k$-out-of-$n$:G systems and Monte Carlo simulation tests show the effectiveness of CRs on reducing the system maintenance cost and extending system lifetime and provide structural insights on the optimal maintenance policy.

A real system may go through several states ranging from full performance to complete failure, carrying out infinite partial performances during service time. This article portrays such a nonbinary state of systems via the fuzzy membership function. Then, the relation between the system reliability under the binary state and that under the fuzzy state is deduced, on which a multitype component allocation problem (MCAP) is investigated to search for the optimal permutation of different types of components to maximize the fuzzy system reliability. After that, we inherit the exploration ability of genetic algorithm (GA) and the exploitation ability of Birnbaum importance (BI) to propose a fuzzy-BI-based two-stage approach combined with GA in order to deal with the MCAP under fuzzy state assumption efficiently and accurately. The k-out-of-n systems in both low and high dimensions are presented to illustrate the effectiveness of the proposed algorithm and demonstrate the similarity and difference between the MCAP under binary state and that under fuzzy state. The experimental results showcase that the proposed approach outperforms the existing state-of-the-art approaches for MCAP.

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

Reliability-based design optimization (RBDO) is one of the most crucial techniques in complex and reliability-critical engineering systems. This has been a research hotspot over the past few decades. RBDO allows us to take into consideration the uncertainties from various sources, during the early design stage. It provides a design that satisfies various constraints as well as the reliability of the designed system performing the expected functions. Such capabilities can serve as countermeasures against the foreseeable uncertainties in the manufacturing or application process. Following a short preliminary overview of RBDO as well as the canonical strategies, this article sets out to review how surrogate models have been explored to streamline RBDO. This is done through a systematic study, outlining their respective advantages as well as disadvantages, and discussing the problems that need to be solved.

Optimal reliability design (ORD) problem is challenging and fundamental to the study of system reliability. For a system with u components/stages where each of them can be set in m possible reliability levels, state-of-the-art linear reformulation models of ORD problem require O(um) binary variables, O(mn) continuous variables together with either O(mn) inequality constraints or O(um) equality constraints. Using the special property of prime factorization and adopting the logarithmic expression technique, in this article, we propose a novel linear reformulation model of the ORD problem requiring O(um) binary variables, O(mn n! ) continuous variables, and very few linear constraints. This theoretic reduction in variables and constraints can lead to significant savings in computational efforts. Our numerical experiments further confirm the drastic reduction in computational time for solving ORD problems in large size.

The papers in this special section focus on the topic of crisis management - from events such as nuclear accidents to the COVID-19 pandemic. Discusses the impact such events have on society, the economy, the environment, and politics.

The semiconductor manufacturing is one of the most sophisticated processes in modern industries. It contains hundreds of complex operations, and this makes semiconductor reliability a challenging task especially in recent years that integrated circuits (ICs) have been broadly used at much wider areas including the health cares, automotive, and aerospace applications, where safety is the major concern. To make things worse, due to the shorter product life cycles and severe competitions, time-consuming reliability tests become unacceptable. The industries are in urgent need of a fast and effective way to quickly assess reliability risks. Under all these stringent limitations and the high reliability targets, we propose a consolidated approach that consists of an efficient and effective reliability baseline (BL) management system and a test scheme developed based on sequential probability ratio test (SPRT). To ensure a trustworthy setting for the SPRT test scheme, we apply the Bayesian approach to continuously update the BL database. An integrated flow chart is introduced to elucidate our proposed methodology. It is the first time SPRT is applied on reliability risk assessments with two unknown parameters. Several actual cases from semiconductor arena are reported to demonstrate the merits and powers of our proposed methodology. From these real cases, as a side benefit, we show the wide applicability of our method, which does not limit to reliability but on yield and functionality checks as well. To facilitate the use of our method by field practitioners, we do the best to explain derivations in a plain manner and provide analysis codes in R (in Supplementary Material) to make our approach as portable as possible.

This paper develops a maintenance policy for a multicomponent system subject to hidden failures. Components of the system are assumed to suffer from hidden failures, which can only be detected at inspection. The objective of the maintenance policy is to determine the inspection intervals for each component such that the long-run cost rate is minimized. Due to the dependence among components, an exact optimal solution is difficult to obtain. Concerned with the intractability of the problem, a heuristic method named “base interval approach” is adopted to reduce the computational complexity. Performance of the base interval approach is analyzed, and the result shows that the proposed policy can approximate the optimal policy within a small factor. Two numerical examples are presented to illustrate the effectiveness of the policy.

As we live in a highly technological world, surrounded by the Internet, biological technologies, high-speed trains and sophisticated aircraft, new energy sources, new social movement, wide wealth gap between the rich and poor groups and countries, political and religious differences, and so on, we have to face many new challenges which may either improve or threaten our living environment. All these ever-increasing challenges add new risks, and are in the scope of reliability for sustainability. However, the traditional approach of reliability, which looks into the failure free operation of systems, is far too simple, and has to be re-examined.

Presents an editorial on the activities and major areas of development in the reliability industry and with the publication from 1999 through 2015.

Recounts the career and contributions of Susan Hong Xu.

Many importance measures have been proposed with respect to the diverse considerations of system performance, reflecting different probabilistic interpretations and potential applications. This paper studies importance measures in reliability, including their definitions, probabilistic interpretations, properties, computations, and comparability. It categorizes importance measures into the structure, reliability, and lifetime types based on the knowledge for determining them. It covers importance measures of individual components, and ones of pairs and groups of components. It also investigates importance measures in consecutive-k-out-of-nsystems.

To identify the critical components or sets of components in a system, various importance measures have been proposed with different probabilistic perspectives and applications. Many of these importance measures are actually related to each other in some ways. This paper summarizes the importance measures in reliability, and presents relations and comparisons among them, focusing on their interrelations to the B-importance, the dominant relations among them, the dual relations, their performances in typical systems, and their computations. The early versions of the importance measures are for binary coherent systems, while the recent research is not limited to this type of system. This paper investigates the extensions of importance measures in noncoherent systems, multistate systems, continuum systems, and repairable systems.

This study proposes Bayesian methods for planning optimal simple step-stress accelerated life tests. The Bayesian approach is an attractive alternative to the maximum likelihood method when there is uncertainty in the planning values of the model parameters. The uncertainty in the planning values is described by a joint prior distribution of the model parameters. The optimization criterion is defined as minimization of the pre-posterior variance of the logarithm of a quantile life at the normal stress condition. Two optimization algorithms, one based on Monte Carlo integration, and the other based on large-sample approximation, are developed to find the optimal plans. Nonparametric kernel smoothing technique is adopted in both algorithms to reduce the computational time. The proposed Bayesian approach is also extended to the design of three-level step-stress accelerated life tests. Effects of prior and sample size on the optimal plans are also investigated. Results indicate that both the prior, and the sample size affect the optimal Bayesian plans. And under certain conditions, the Bayesian approach, and the maximum likelihood approach provide very similar optimal plans.

Discusses the aftermath of the earthquake and the tsunami that struck Japan in March 2011 and how the fears about nuclear power may affect its future.

The paper by Hwang (IEEETrans.Reliability, vol. 54, no.1, p. 169-172, 2005) presented structural importance measures in terms of cutsets or pathsets, and investigated how they are related. Hwang's paper has made contributions to importance measures. However, several errors which cause confusions are found in the paper. This note is to clarify these errors, and discuss the suspicions.

In a MOS structure, the generation of hot carrier interface states is a critical feature of the item's reliability. On the nano-scale, there are problems with degradation in transconductance, shift in threshold voltage, and decrease in drain current capability. Quantum mechanics has been used to relate this decrease to degradation, and device failure. Although the lifetime, and degradation of a device are typically used to characterize its reliability, in this paper we model the distribution of hot-electron activation energies, which has appeal because it exhibits a two-point discrete mixture of logistic distributions. The logistic mixture presents computational problems that are addressed in simulation.

The author makes two modifications to his original paper (see ibid., vol.55, no.4, p.569-70, Dec. 2006).

While teaching is an important component of engineering education, few widely adopted objective measures for evaluating teaching have emerged in our institutions of higher learning. The most frequently used measure nationally is the teaching questionnaire. This editorial does not attempt to analyse the much debated topic of whether teaching questionnaires are capable of measuring teaching effectiveness. What this paper does is quantify the relationship between class size and scores on teaching questionnaires. We report here, for the first time, that 1) compared to larger classes, course ratings are higher for classes of size 20 or less, and course ratings decrease when the class size increases within this small class group and 2) course ratings are independent of class size when the class size is larger than 20. This editorial is based on data from end-of-term teaching appraisals obtained from the archives at the Texas A&M University College of Engineering for all three semesters each year, beginning with Spring 1998 and continuing until Fall 2002

Complex systems are less compatible internally, and with other systems, which reduces reliability. To restate, two primary principles must be kept in mind: keep the system simple, and make the system compatible with others. These two guidelines will help maintain the desired reliability.

We introduce the system of consecutive failures with sparse d which is a natural extension of consecutive-k systems. Then a series of generalizations of consecutive-k systems are discussed, such as consecutive-k-out-n:F systems with sparse d, M consecutive-k-out-of-n:F systems with sparse d, and (n, f, k) :F systems with sparse d. We present the formulation for the system reliability of these generalized consecutive-k systems with various component settings in terms of the finite Markov chain imbedding idea, along with two numerical examples.

Reliability has become a greater concern in recent years, because high-tech industrial processes with ever increasing levels of sophistication comprise most engineering systems today. To keep pace with this rapidly developing field, this paper provides a broad overview of recent research on reliability optimization problems and their solution methodologies. In particular, we address issues related to: 1) universal generating-function-based optimal multistate system design; 2) percentile life employed as a system performance measure; 3) multiobjective optimization of reliability systems, especially with uncertain component-reliability estimations; and 4) innovation and improvement in traditional reliability optimization problems, such as fault-tolerance mechanism and cold-standby redundancy-involved system design. New developments in optimization techniques are also emphasized in this paper, especially the methods of ant colony optimization and hybrid optimization. We believe that the interesting problems that are reviewed here are deserving of more attention in the literature. To that end, this paper concludes with a discussion of future challenges related to reliability optimization

A tree heuristic is presented for solving the general redundancy allocation problem in reliability optimization. The tree heuristic can obtain several local optima by branching off the main searching path when some criterions are satisfied. Then, the best local optima is selected for the final solution. The tree heuristic is a simple, efficient, iterative heuristic for any integer nonlinear programming problems with increasing constraint functions. Iterative heuristics are normally trapped in a local optimum. However, the tree heuristic can overcome local optima by branching the solution path. The experiments show that the proposed heuristic is very efficient in terms of solution quality, and computation time.

The effect of a 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.

This paper provides: an overview of the methods that have been developed since 1977 for solving various reliability optimization problems; applications of these methods to various types of design problems; and heuristics, metaheuristic algorithms, exact methods, reliability-redundancy allocation, multi-objective optimization and assignment of interchangeable components in reliability systems. Like other applications, exact solutions for reliability optimization problems are not necessarily desirable because exact solutions are difficult to obtain, and even when they are available, their utility is marginal. A majority of the work in this area is devoted to developing heuristic and metaheuristic algorithms for solving optimal redundancy-allocation problems.

This paper presents a search method based on lexicographic order, and an upper bound on the objective function, for solving redundancy allocation problems in coherent systems. Such problems generally belong to the class of nonlinear integer programming problems with separable constraints and nondecreasing functions. For illustration, 3 types of problems are solved using our method. Numerical investigation shows the performance of the method for large problems.

This paper presents an overview of yield, reliability, burn-in, cost factors, and fault coverage as practiced in the semiconductor manufacturing industry. Reliability and yield modeling can be used as a foundation for developing effective stress burn-in, which in turn can warranty high-quality semiconductor products. Yield models are described and their advantages and disadvantages are discussed. Both yield reliability relationships and relation models between yield and reliability are thoroughly analyzed in regard to their importance to semiconductor products.

A system of N statistically identical machines is modeled using renewal theory through a unique architecture and state space. The model is very useful in evaluating flexible manufacturing systems (FMS) in particular. Each machine consists of multiple part types that are subject to individual failure. A multiple stage repair process composed of integrable sojourn time distributions requires access to spare parts to repair down machines. A performability measure is used to gauge system effectiveness for this partially degradable system, and an example is given.

A process for reliability-related quality programming is developed to fill existing gaps in software design and development so that a quality programming plan can be achieved. The tradeoffs among system reliability improvement, resource consumption, and other relevant constraints through the management phase are investigated. A software reliability-to-cost relation is developed both from a software reliability-related cost model and from software redundancy models with common-cause failures. A generic N-component redundancy model is also developed. The software reliability optimization problems can be formulated into a mixed-integer programming problem.>

Stochastic models for system effectiveness are developed for a multiple-component human-machine system. System effectiveness is defined as the combined measure of availability and reliability at each task-arrival time, when transient human operator behavior is considered in conjunction with the machine state. Because factors such as fatigue, stress, and learning affect the human operator over time, all probability measures for successful human performance are considered to be time-dependent. Performance evaluation models for a generic military system are developed. The modeling techniques can also be used for large-scale, man-machine systems that consist of modern computers and processors.>