Multi-Valued Decision Diagram-Based Reliability Analysis of <formula formulatype="inline"><tex Notation="TeX">$k$</tex> </formula>-out-of-<formula formulatype="inline"><tex Notation="TeX">$n$</tex> </formula> Cold Standby Systems Subject to Scheduled Backups

Abstract

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 -out-of-cold standby system subject to scheduled backups, where 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.Index Terms--out-of-cold standby, scheduled backup, multi-valued decision diagram, imperfect switch. ABBREVIATIONS MDDMulti-valued decision diagram CDF Cumulative distribution function NNSN Number of non-sink nodes Manuscript

Maintenance optimization of a two‐component series system considering masked causes of failure

“…We assume the lifetime of both actuator and mechanical valve follow Weibull distribution, which has been widely adopted to describe the lifetime of mechanical and electronic systems and shows good performance. 36,37 The lifetime CDF of the actuator is 𝐹 1 (𝑡) = 1 − exp[−(𝑡∕12.7) 3.3 ] (unit of time: 10 5 cycles), and the lifetime CDF of the mechanical valve is 𝐹 2 (𝑡) = 1 − exp[−(𝑡∕8.6) 2.1 ] (unit of time: 10 5 cycles). All these parameters can be obtained based on real failure time data with some statistical methods.…”

“…A solenoid may fail due to coil failure of the actuator, or the mechanical valve failure. We assume the lifetime of both actuator and mechanical valve follow Weibull distribution, which has been widely adopted to describe the lifetime of mechanical and electronic systems and shows good performance 36, 37 . The lifetime CDF of the actuator is $$F_1(t)=1-\exp [-(t/12.7)^{3.3}]$$ (unit of time: 10 5 cycles), and the lifetime CDF of the mechanical valve is $$F_2(t)=1-\exp [-(t/8.6)^{2.1}]$$ (unit of time: 10 5 cycles).…”

Preventive replacement policy of a system considering multiple maintenance actions upon a failure

“…In addition, a mechanical valve can be preventively replaced when its virtual age reaches a threshold. We assume the PDF of the valve lifetime follows a Weibull distribution, which has been widely adopted to describe the lifetime of a mechanical system and shows good performance 47, 48 . The shape parameter and scale parameter are respective $$m=2.5$$ and $$\eta =40$$, which can be obtained based on real failure time data by maximizing likelihood function 49–51 .…”

“…We assume the PDF of the valve lifetime follows a Weibull distribution, which has been widely adopted to describe the lifetime of a mechanical system and shows good performance. 47,48 The shape parameter and scale parameter are respective 𝑚 = 2.5 and 𝜂 = 40, which can be obtained based on real failure time data by maximizing likelihood function. [49][50][51] In our study, we use a Beta distribution to model the random quality of the imperfect repair, and the parameters are set as respective 𝛼 = 4 and 𝛽 = 2.…”

A new efficient algorithm for finding all d -minimal cuts in multi-state networks

“…These methods exploit a variety of tools for system reliability modeling and analysis. The widely adopted tools mainly include Monte-Carlo simulation [16,17], universal generating function (UGF) [18][19][20][21][22][23][24][25], multi-valued decision diagram (MDD) [26][27][28][29][30][31][32][33], and minimal cut (MC) vectors/minimal path (MP) vectors to level d (named d-MCs/d-MPs) [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Monte-Carlo simulation is an effective modeling tool, and provides a general method for analyzing multi-state systems.…”