Qingqing Zhai

Reliability of demand-based phased-mission systems subject to fault level coverage

In many real-world applications, a mission may consist of several different tasks or phases that have to be accomplished in sequence. Such systems are referred to as phased-mission systems (PMS). In this paper we consider the demand-based PMS with parallel structure, where the system components function in parallel with different capacities in each phase of the mission and the mission is successful if and only if the total system capacity meets the predetermined mission demand in each phase. The reliability of the demand-based PMS (DB-PMS) with parallel structure subject to fault-level coverage (FLC) is first studied using a multi-valued decision diagram (MDD) based technique. The traditional MDD is modified to accommodate the FLC mechanism and new MDD construction and evaluation procedures are proposed for DB-PMS. To reduce the size of the MDD, an alternative construction procedure applying the branching truncation method and new reduction rules are further proposed. An upwards algorithm is put forward to evaluate the reliability of DB-PMS subject to FLC. The proposed approaches are illustrated through examples.

A preventive maintenance policy based on dependent two-stage deterioration and external shocks

This paper proposes a preventive maintenance policy for a single-unit system whose failure has two competing and dependent causes, i.e., internal deterioration and sudden shocks. The internal failure process is divided into two stages, i.e. normal and defective. Shocks arrive according to a non-homogeneous Poisson process (NHPP), leading to the failure of the system immediately. The occurrence rate of a shock is affected by the state of the system. Both an age-based replacement and finite number of periodic inspections are schemed simultaneously to deal with the competing failures. The objective of this study is to determine the optimal preventive replacement interval, inspection interval and number of inspections such that the expected cost per unit time is minimized. A case study on oil pipeline maintenance is presented to illustrate the maintenance policy.

Binary decision diagram-based reliability evaluation of k-out-of-(n + k) warm standby systems subject to fault-level coverage:

Warm standby sparing is a fault-tolerance technique that attempts to improve system reliability while compromising the system energy consumption and recovery time. However, when the imperfect fault coverage effect (an uncovered component fault can propagate and cause the whole system to fail) is considered, the reliability of a warm standby sparing can decrease with an increasing level of the redundancy. This article studies the reliability of a warm standby sparing subject to imperfect fault coverage, in particular, fault level coverage where the coverage probability of a component depends on the number of failed components in the system. The suggested approach is combinatorial and based on a generalized binary decision diagrams technique. The complexity for the binary decision diagram construction is analyzed, and several case studies are given to illustrate the application of the approach.

Measurement errors in degradation-based burn-in

Burn-in is an effective tool to improve product reliability and reduce field failure costs before a product is sold to customers. As many products are becoming highly reliable, traditional burn-in that tests a batch of a product until most weak units fail requires an unaffordable testing duration. If the product failure can be associated with an underlying degradation process and a weak unit degrades faster than a normal one, then degradation-based burn-in can be implemented. Due to such various factors as human errors and limited precision of the measurement device, measurement errors are often inevitable. Ignoring measurement errors in the degradation observations would lead to inferior burn-in decisions. This study uses the Wiener process to model the underlying degradation and considers Gaussian measurement errors in the observations. Two burn-in models with different cost structures are studied and the optimal cutoff level for each model is obtained analytically. The relation between the two models is discussed, leading to a new cost model.

Multi-Valued Decision Diagram-Based Reliability Analysis of

To improve the system reliability while conserving the limited system resources, cold standby sparing is often used. In computing tasks, because active components fail randomly, and the standby component has to pick up the mission task whenever required, scheduled backups are often implemented to save the completed portions of the task. The backups can facilitate an effective system recovery where the standby component can take over the mission task from the last backup point instead of resuming the mission task from the very beginning. This paper considers a k-out-of- n cold standby system subject to scheduled backups, where k components are online and operating, with the remaining components waiting in the unpowered, cold standby mode. Whenever an online component fails, a cold standby component is activated to take over the mission task from the last backup point. The backup intervals are deterministic, but can be even or uneven. As the component may fail due to an imperfect switching from the standby state to the fully powered up state, the switching failure is also considered in the system model. A multi-valued decision diagram (MDD)-based analytical approach is proposed to evaluate the reliability of the considered system, and its complexity is analyzed. The proposed method is applicable to systems with non-identical components following arbitrary lifetime distributions. Examples are given to illustrate the MDD-based method. The correctness and efficiency of the proposed method are verified using Monte Carlo simulations.

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This paper models repairable computing systems performing a mission that is successful if the system can accomplish a specified amount of work within the allowed mission time or deadline. During the mission the system is subject to a sequence of full and incremental data backup procedures to facilitate an effective system recovery and avoid repeating the entire mission work from the very beginning when a system failure happens. The repair time is fixed while the system time-to-failure can follow any arbitrary type of distributions. This paper makes novel contributions by first developing a new numerical algorithm to evaluate mission success probability and expected completion time of the considered repairable real-time computing systems subject to mixed full and incremental backups. Correctness of the proposed evaluation algorithm is verified using Monte Carlo simulations. We make another new contribution by formulating and solving the backup schedule optimization problem that finds the full and incremental backup frequencies maximizing the mission success probability. Through illustrative examples, effects of different parameters (including the system time-to-failure distribution parameter, maximum allowed mission time, data backup and retrieval times, storage availability, repair time and efficiency) on the mission success probability and expected completion time as well as on the optimal backup schedule solution are investigated.

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Abstract Variance-based sensitivity analysis has been widely studied and asserted itself among practitioners. Monte Carlo simulation methods are well developed in the calculation of variance-based sensitivity indices but they do not make full use of each model run. Recently, several works mentioned a scatter-plot partitioning method to estimate the variance-based sensitivity indices from given data, where a single bunch of samples is sufficient to estimate all the sensitivity indices. This paper focuses on the space-partition method in the estimation of variance-based sensitivity indices, and its convergence and other performances are investigated. Since the method heavily depends on the partition scheme, the influence of the partition scheme is discussed and the optimal partition scheme is proposed based on the minimized estimator׳s variance. A decomposition and integration procedure is proposed to improve the estimation quality for higher order sensitivity indices. The proposed space-partition method is compared with the more traditional method and test cases show that it outperforms the traditional one.

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Importance measures have been widely studied and applied in reliability and safety engineering. This paper presents a general formulation of moment-independent importance measures and several commonly discussed importance measures are unified based on Minkowski distance (MD). Moment-independent importance measures can be categorized into three classes of MD importance measures, i.e. probability density function based MD importance measure, cumulative distribution function based MD importance measure and quantile based MD importance measure. Some properties of the proposed MD importance measures are investigated. Several new importance measures are also derived as special cases of the generalized MD importance measures and illustrated with some case studies.

Cold Standby Systems Subject to Scheduled Backups

This paper studies the defense and attack strategies for a system with a common bus performance-sharing mechanism that is subject to intentional attacks. The performance-sharing mechanism allows any surplus performance of a component to be transmitted to other components in the system via the common bus. A practical example of such a system is the power system. The system may fail due to internal causes, such as component degradation, as well as intentional attacks, such as acts of terrorism. The defender allocates its resources to maximize the systems reliability by protecting the common bus and the components. The attacker allocates its resources to minimize the systems reliability by attacking the common bus and the components. We propose a framework to model both the reliability and the defense-attack contest for a general common bus system. Based on this framework, we investigate the optimal defense and attack strategies for a system with identical components in a two-stage min–max game.

Optimization of Full versus Incremental Periodic Backup Policy

We propose an inspection and replacement policy for a single component system that successively executes missions with random durations. The failure process of the system can be divided into two states, namely, normal and defective, following the delay time concept. Inspections are carried out periodically and immediately after the completion of each mission (random inspections). The failed state is always identified immediately, whereas the defective state can only be revealed by an inspection. If the system fails or is defective at a periodic inspection, then replacement is immediate. If, however, the system is defective at a random inspection, then replacement will be postponed if the time to the subsequent periodic inspection is shorter than a pre-determined threshold, and immediate otherwise. We derive the long run expected cost per unit time and then investigate the optimal periodic inspection interval and postponement threshold. A numerical example is presented to demonstrate the applicability of the proposed maintenance policy.