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• A repairable multi-state two-phase mission system with finite number of phase switches is proposed. • The probability density function for the time to first failure of the two-phase mission system is presented. • Some reliability indexes, such as the point-wise and interval availabilities, are given. In this article, a repairable multi-state two-phase mission system with finite number of phase switches is considered. System states can be divided into a subset of working states and a subset of failed states, and the system can be repaired from the failed subset to the working subset. However, when the number of switches between two phases exceeds a specified integer, the system will be permanently damaged and cannot be repaired any more. The closed-form formulas of the probability density function of the time to first failure of the system, the point-wise availability, the interval availability and other reliability indexes are obtained by using the theory of aggregated stochastic processes. Finally, a detailed example of lithium-ion batteries is given to illustrate the proposed model and obtained results. [ABSTRACT FROM AUTHOR]

Highlights • Three types of thresholds including alarm line and two different failure thresholds are used to model the system reliability. • Two degradation process models, Wiener-Gamma and Gamma-Gamma, are developed. • Explicit formulas for the system reliability in terms of duration thresholds for the degradation models are presented. Abstract Stochastic degradation process models are developed in terms of cumulative degradation signals of systems under three types of thresholds including alarm line and two different failure thresholds. One of the failure thresholds corresponds to the degradation amount, and the other corresponds to the duration. We assume that the degradation process can be separated into two distinctive stages by a change-point which is the first passage time of the degradation process with respect to the alarm line. For simplicity, the first stage is regarded as an age-dependent (or non-stationary) Wiener process or an age-dependent (or non-stationary) Gamma process, and the second stage is regarded as an age-dependent (or non-stationary) Gamma process; thus, two special degradation models, Wiener-Gamma and Gamma-Gamma, are constructed. Specially, two-stage stationary Wiener-Gamma and Gamma-Gamma models can be viewed as special cases. The system reliability is defined as the probability that the degradation signals do not exceed a failure threshold and the duration of exceeding the alarm line is less than the duration threshold. Some reliability results including two cases in terms of duration thresholds (constants and random variables) are derived. The moments of lifetime are also given based on the results. In addition, simulation is carried out to verify the given results. And some numerical examples are presented to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

Different regimes, for example, different seasons, bull market/bear market, multiple missions etc., affect the performance of systems or products greatly in the real world. Thus, a dynamic reliability model, with cyclic multiple mission periods, is developed for non-repairable discrete state systems in this paper. By taking Laplace transforms and aggregated stochastic theory for describing the conditional probabilities of transitions among different mission periods and system states, we obtain closed form solutions of some reliability indexes and distributions of sojourn times with perfect and imperfect function. Three models of valve systems are considered in details based on different reliability structures, and a numerical example of marine reactor safety water injection system is also presented by applying our proposed methods for two special cases: (i) when the mission durations are fixed and; (ii) when the mission durations have exponential distributions. [ABSTRACT FROM AUTHOR]

• A new balanced system with auto-balancing mechanisms is studied. • A new balanced system model is analyzed with the theory of aggregated stochastic process and semi-Markov process. • Formulas for the expectation lifetime and point-wise availabilities of the proposed systems are given. Reliability analysis of balanced systems has become one of the hot and significant topics in the reliability research field. As a new view for the research of balanced system, balanced mechanisms bring much room for research. Based on most practical systems, an auto-balancing mechanism for a multi-state balanced system composed of two subsystems is innovatively proposed for both theoretical and practical demands in this paper. The auto-balancing mechanism is activated to correct the temporary upcoming unbalance of system by adjusting the performance states of each subsystem and to ensure that the performance state difference between the two subsystems of the balanced system do not exceed a balance limitation. The aggregated stochastic processes and semi-Markov processes are used to obtain the reliability measures, and the related expressions of the expectation lifetime and point-wise availabilities of the system are derived. Finally, a numerical example is given to illustrate the results obtained in the paper. The model and the results presented in the paper can be used in reliability, transportation planning, supply chain management, and other areas. [ABSTRACT FROM AUTHOR]

Reliability analysis of balanced system has become a key factor for the safe operation of some important equipment and the perfect completion of some important missions. As some real systems consisting of several subsystems with different levels of performance and under degradation processes when in operations are relatively common, they have received widely concerned in the recent years, but are rarely in the new reliability research field of balanced systems, the researches on the balanced systems by considering multi-state are rare, and even few researches are in combination with degradation processes. In this paper, a new balanced system for the multi-state system under degradation processes by considering new failure criteria is put forth. The system consists of two subsystems and fails when either subsystem enters into absorbing states, a new model is proposed and applied to two special cases by assuming that the thresholds of the sojourn time in upcoming unbalanced subsets are constant and random variables respectively, and this paper is the first to extend balanced systems into competing risks. The related expressions of the reliability indexes are derived by employing the theory of aggregated stochastic processes. Finally, numerical examples are presented and some future research topics are also discussed. [ABSTRACT FROM AUTHOR]

• Developing degradation-based and duration-based mission abort policies based on a two-stage degradation process. • Deriving mission reliability and system survivability under the proposed stochastic failure process and mission abort policies. • Investigating the optimal mission abort policies balancing the tradeoff between mission reliability and system survivability. • Providing a detailed comparison of the cost-saving performance of the two proposed abort policies numerically. Various safety-critical systems such as aircrafts, submarines and space stations are required to perform missions continually in harsh environment. To enhance the survivability of such systems, a mission can be aborted when the mission completion becomes problematic and a rescue procedure is immediately initiated. This paper investigates the optimal mission abort policy based on a two-stage Gamma process which can be separated into normal and defective stages. Degradation-based abort policy where a mission is aborted if the system degradation level is higher than a threshold and duration-based abort policy where a mission is aborted if the duration in defective stage is larger than a threshold are considered. The mission success probability and system survivability under these two policies are evaluated and the optimal mission abort thresholds balancing the tradeoff between the mission success probability and system survivability are investigated. A numerical example on an unmanned aerial vehicle (UAV) is presented to illustrate the applicability of the proposed abort policies. [ABSTRACT FROM AUTHOR]

Markov history-dependent repairable systems refer to the Markov repairable systems in which some states are changeable and dependent on recent evolutional history of the system. In practice, many Markov history-dependent repairable systems are subjected to neglected failures, i.e., some failures do not affect system performances if they can be repaired promptly. In this paper, we develop a model based on the theory of aggregated stochastic processes to describe the history-dependent behavior and the effect of neglected failures on the Markov history-dependent repairable systems. Based on the developed model, instantaneous and steady-state availabilities are derived to characterize the reliability of the system. Four reliability-related time distributions, i.e., distribution for the k th working period, distribution for the k th failure period, distribution for the real working time in an effective working period, distribution for the neglected failure time in an effective working period, are also derived to provide a more comprehensive description of the system's reliability. Thanks to the power of the theory of aggregated stochastic processes, closed-form expressions are obtained for all the reliability indexes and time distributions. Finally, the developed indexes and analysis methods are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]