Cost effective scheduling of imperfect inspections in systems with hidden failures and rescue possibility

Motivated by real-world critical applications such as aircraft, medical devices, and military systems, this paper models non-repairable systems subject to a delay-time failure process involving hidden and fatal failures in two stages during their missions. A hidden failure cannot cause the system to stop functioning while a fatal failure causes the entire system loss. The system undergoes scheduled inspections for detecting the hidden failure. In the case of a positive inspection result, the system main mission is aborted and a rescue operation is started to mitigate the risk of the entire system loss. The inspections are imperfect and may produce false positive and negative failures. We propose probabilistic models for evaluating performance metrics of the system considered, including mission success probability, system survival probability, expected number of inspections during the mission, and total expected losses. Based on the evaluation models, we formulate and solve an optimization problem of finding the optimal inspection schedule on a fixed mission time horizon to minimize the total expected loss. Examples are provided to demonstrate the proposed methodology and effects of key system parameters on system performance and optimization solutions.     

Optimal maintenance of systems with Markovian mission and deterioration

We consider the maintenance of a mission-based system that is designed to perform missions consisting of a random sequence of phases or stages with random durations. A finite state Markov process describes the mission process. The age or deterioration process of the system is described by another finite state Markov process whose generator depends on the phases of the mission. We discuss optimal repair and optimal replacement problems, and characterize the optimal policies under some monotonicity assumptions. We also provide numerical illustrations to demonstrate the structure of the optimal policies.     

Reliability of repairable multi-state two-phase mission systems with finite number of phase switches

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.     

Stationary availability of a semi‐Markov system with random maintenance

We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.     

Probabilistic analysis of a series–parallel repairable system with three units and vacation

This paper studies the steady-state availability and the mean up-time of a series–parallel repairable system consisting of one master control unit, two slave units and a single repairman who operates single vacation. Under the assumption that each unit has a constant failure rate and arbitrary repair time distribution, by using the supplementary variable method and the vector Markov process theory, we obtain the explicit expressions for the steady-state probabilities of the system, the steady-state availability and the mean up-time. A special case without vacation is given. Numerical results are provided to investigate the effects of various system parameters on the steady-state availability and the mean up-time.     

M/G1/1型可修排队的强度守恒律分析

用从平稳点过程和Palm分布理论推得的强度守恒律尝试研究了寿命为一般分布的M／G1／1型可修排队系统,在求得模型稳态工作量和拟虚等待时间表达式的基础上,得到了服务台的首次故障前时间,系统可用度,平均失效概率,服务台平均失效次数和系统故障频度等．有趣的是,当寿命分布取其特例指数分布时,与文选中已知的结果完全一致．     

System availability behavior of some stationary dependent sequences

We consider the system availability behavior of a one-unit repairable system when the failure and the repair times are generated by a stationary dependent sequence of random variables. We obtain the general expression for the point availability, and discuss the nature of the availability measure for two time series models: a first-order exponential moving average process and a first-order exponential autoregressive process.     

A Bayesian model and numerical algorithm for CBM availability maximization

In this paper, we consider an availability maximization problem for a partially observable system subject to random failure. System deterioration is described by a hidden, continuous-time homogeneous Markov process. While the system is operational, multivariate observations that are stochastically related to the system state are sampled through condition monitoring at discrete time points. The objective is to design an optimal multivariate Bayesian control chart that maximizes the long-run expected average availability per unit time. We have developed an efficient computational algorithm in the semi-Markov decision process (SMDP) framework and showed that the availability maximization problem is equivalent to solving a parameterized system of linear equations. A numerical example is presented to illustrate the effectiveness of our approach, and a comparison with the traditional age-based replacement policy is also provided.     

A priority assessment multi-criteria decision model for human spaceflight mission planning at NASA

Analog missions are real-life, Earth-based science missions whose purpose is to help understand the operations, techniques, and technologies required to perform similar tasks during future human spaceflight missions. The goal of performing an analog mission is to prepare crewmembers and support teams for future space missions in a low risk, low-cost environment. Vehicle, habitat, and surface terrain simulators are used to test hardware, operations, and tasks repeatedly for analog missions. This study presents a multi-criteria decision making model that was developed for the Integrated Human Exploration Mission Simulation Facility project at Johnson Space Center to assess the priority of a set of human spaceflight mission simulators. The proposed framework integrates subjective judgments derived from the analytic hierarchy process with entropy data into a preference model to prioritize five mission simulators for the human exploration of Mars.     

Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment

As a system failure during a mission can result in considerable penalties, at some instances it is more cost-effective to terminate operation of a system than to attempt to complete its mission. This paper analyzes the optimal mission duration for systems that operate in a random environment modeled by a Poisson shock process and can be minimally repaired during a mission. Two independent sources of failures are considered and for both cases, the failures are classified as minor or terminal in accordance with the Brown-Proschan model. Under certain assumptions, an optimal time of mission termination is obtained. It is shown that, if for some reason a termination is not technically possible at this optimal time, the mission should be terminated within a specific time interval and, if this is not possible, it should not be terminated beyond this interval. Illustrative examples are presented. The influence of mission and system parameters on the mission termination interval is demonstrated.     

Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair

The series system is one of the most important and common systems in reliability theory and applications. This paper investigates availability, maintenance cost, and optimal maintenance policies of the series system with n constituting components under the general assumption that each component is subject to correlated failure and repair, imperfect repair, shut-off rule, and arbitrary distributions of times to failure and repair. Imperfect repair is modeled through the basic idea of the quasi renewal processes introduced by H. Wang, H. Pham, A quasi renewal process and its applications in imperfect maintenance, International Journal of Systems Science 27(10) (1996) 1055–1062; 28(12) (1997) 1329. System availability, mean time between system failures, mean time between system repairs, asymptotic fractional down time of the system, etc., are derived, and a numerical example is presented to compare with the existing models by R.E. Barlow, F. Proschan, Satistical Theory of Reliability of Life Testing, Holt, Renehart & Winston, NY, 1975. Then two classes of maintenance cost models are proposed and system maintenance cost rates are modeled. Finally, properties of system availability and maintenance cost rates are studied. Optimization models to optimize system availability and/or system maintenance costs are developed, and optimum system maintenance policies are discussed through a numerical example.     

离散时间单重休假两部件并联可修系统的可靠性分析

利用离散向量Markov过程方法研究了离散时间单重休假两同型部件并联可修系统.在部件寿命服从几何分布,修理时间和修理工休假时间服从一般离散型概率分布的假定下,引入修理时间和休假时间尾概率,求得了系统的稳态可用度、稳态故障频度、待修概率、修理工空闲概率和休假概率,以及首次故障前平均时间等可靠性指标.并通过具体数值实例展示了离散向量马氏链状态转移频度的具体计算方法.     

Reliability analysis of two-unit cold standby repairable systems under Poisson shocks

This paper analyses the reliability of a cold standby system consisting of two repairable units, a switch and a repairman. At any time, one of the two units is operating while the other is on cold standby. The repairman may not always at the job site, or take vacation. We assume that shocks can attack the operating unit. The arrival times of the shocks follow a homogeneous Poisson process and their magnitude is a random variable following a known distribution. Time on repairing a failed unit and the length of repairman’s vacation follow general continuous probability distributions, respectively. The paper derives a number of reliability indices: system reliability, mean time to first failure, steady-state availability, and steady-state failure frequency.     

泊松冲击下冷贮备可修系统的可靠性分析

本文研究了一类由有限个同质部件和一个修理工组成的冷贮备可修系统在随机冲击下的可靠性问题。假设冲击以泊松过程到达。当冲击到达时,它会独立地对系统中工作的部件产生影响,而不会对冷贮备部件产生影响。每次冲击的量都服从某一确定的分布,受冲击的部件以一定的概率发生故障,其故障概率是冲击量的函数,当工作的部件发生故障时,下一个冷贮备部件立即开始工作,当所有部件故障时,系统故障,故障部件按故障顺序进行修理,修理时间服从指数分布,故障部件能被修理如新。本文显式给出了系统首次故障前平均时间、稳态可用度、稳态故障频度等可靠性指标。     

Analysis of R out of N systems with several repairmen,exponential life times and phase type repair times: An algorithmic approach

An R out of N repairable system consisting of N independent components is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R − 1. A failed component is sent to a repair facility having several repairmen. Life times of working components are i.i.d random variables having an exponential distribution. Repair times are i.i.d random variables having a phase type distribution. Both cold and warm stand-by systems are considered. We present an algorithm deriving recursively in the number of repairmen the generator of the Markov process that governs the process. Then we derive formulas for the point availability, the limiting availability, the distribution of the down time and the up time. Numerical examples are given for various repair time distributions. The numerical examples show that the availability is not very sensitive to the repair time distribution while the mean up time and the mean down time might be very sensitive to the repair time distributions.     

面向多阶段任务的武器系统备件优化配置建模

资源优化配置是作战单元维修保障的关键因素.当作战单元执行单阶段任务时,讨论了部件结构为串联系统和k/n系统的任务成功概率建模问题,在此基础上,建立了k/n结构动态变化的多阶段任务系统的任务成功概率模型.在满足系统任务成功概率约束条件下,给出了防空作战单元备件携行量优化模型,并运用边际分析法进行了求解,通过示例表明了模型的正确性.     

可变环境下的离散时间单部件可修系统

研究离散时间可修系统,讨论了一个可在不同环境下工作的单部件可修系统,其所处环境的改变服从马尔可夫更新过程;利用马尔可夫更新理论,得到了系统的可用度, 故障频度和可靠度等各项指标．     

An efficient memetic algorithm for the graph partitioning problem

We consider the component testing problem of a device that is designed to perform a mission consisting of a random sequence of phases with random durations. Testing is done at the component level to attain desired levels of mission reliability at minimum cost. The components fail exponentially where the failure rate depends on the phase of the mission. The reliability structure of the device involves a series connection of nonidentical components with different failure characteristics. The optimal component testing problem is formulated as a semi-infinite linear program. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical examples.     

Reliability of several component sets with inspections at random times

We consider a random process which represents a system of components with constant failure rates and subjected to inspections at times defining a renewal process. We give an analytic method for calculating the reliability function, its Laplace transform and the mean time to failure (MTTF). These formulas are computable if the Laplace transform of the inter-arrival law of the renewal process is explicit. We also study the asymptotic behavior of the reliability and determine the asymptotic failure rate of the system.