Preventive replacement policies for parallel systems with deviation costs between replacement and failure
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Preventive replacement policies for parallel systems with deviation costs between replacement and failure Xufeng Zhao1 · Satoshi Mizutani2 · Mingchih Chen3 · Toshio Nakagawa2 Accepted: 9 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In order to balance the deviation time between replacement and failure, a new notion of cost named as deviation cost is taken into account for planning replacement policies. We firstly take up a standard parallel system with n identical units and model replacement policies that are done at planned time and at periodic times. Next, we model again the above replacement policies when the number of units is a random variable that has a Poisson distribution. Thirdly, replacement policies are planned preventively at the completion of random working times. Optimum number of units is scheduled for a total working interval that is constantly and randomly given. Finally, we give reliability functions of k-out-of-n systems for extensions of parallel systems. We give analytical discussions for the above replacement policies and illustrate numerical examples when the failure time of each unit has an exponential distribution. Keywords Preventive replacement · Parallel system · Working times · Failure · Reliability
1 Introduction It has been well known that a system with high reliability can be achieved through redundancy and maintenance (Barlow and Proschan 1965). It was shown that a system would be survival
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Xufeng Zhao [email protected] Satoshi Mizutani [email protected] Mingchih Chen [email protected] Toshio Nakagawa [email protected]
1
Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2
Aichi Institute of Technology, Toyota 470-0392, Japan
3
Fu Jen Catholic University, New Taipei City 24205, Taiwan
123
Annals of Operations Research
for a specified time span by either planning preventive maintenance policies or changing the number of units (Nakagawa 2008; Shen et al. 2020; Yang et al. 2020). The qualitative relations between system reliability and unit reliability, and the reliability of many redundant systems were summarized (Ushakov 1994). A parallel system which consists of n identical units in parallel is a typical redundant model and it has been widely used in applications (Ardakan and Hamadani 2014; Lisnianski et al. 2018; Pham 2003; Peng et al. 2016, 2020; Nakagawa and Yun 2011). Preventive maintenance policies have been studied extensively for the parallel structured systems (Nakagawa 2008). More recently, Si et al. (2012) discussed an integrated importance measure of component states for maintenance processes in both series systems and parallel systems. Yusuf (2016) developed a two unit active parallel system with two types of online and offline preventive maintenance policies with an external supporting device. Fallahnezhad and Najafian (2017) described an application of statistical analysis for determining the best preventive maintenance strategy for a parallel system, to trade-off bet
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