Preventive replacement policies for parallel systems with deviation costs between replacement and failure

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.

[1]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[2]  Ibrahim Yusuf,et al.  Reliability modelling of a parallel system with a supporting device and two types of preventive maintenance , 2016 .

[3]  Anatoly Lisnianski,et al.  Recent Advances in Multi-state Systems Reliability , 2018 .

[4]  Toshio Nakagawa,et al.  NOTE ON MTTF OF A PARALLEL SYSTEM , 2011 .

[5]  Toshio Nakagawa,et al.  Replacement policies with general models , 2019, Ann. Oper. Res..

[6]  Jun Yang,et al.  Reliability analysis and optimal structure of series-parallel phased-mission systems subject to fault-level coverage , 2016 .

[7]  Toshio Nakagawa,et al.  Age replacement models: A summary with new perspectives and methods , 2017, Reliab. Eng. Syst. Saf..

[8]  Shudong Sun,et al.  The Integrated Importance Measure of Multi-State Coherent Systems for Maintenance Processes , 2012, IEEE Transactions on Reliability.

[9]  Toshio Nakagawa.  Random Maintenance Policies , 2014 .

[10]  Hoang Pham.  Reliability of Systems with Multiple Failure Modes , 2003 .

[11]  Jie Mi,et al.  STATISTICAL INFERENCE ABOUT AVAILABILITY OF SYSTEM WITH GAMMA LIFETIME AND REPAIR TIME , 2011 .

[12]  A. Blanc,et al.  Total Productive Maintenance , 1993, International Symposium on Semiconductor Manufacturing.

[13]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[14]  Vijay K. Rohatgi.  Distribution of order statistics with random sample size , 1987 .

[15]  Toshio Nakagawa,et al.  Random number of units for K-out-of-n systems , 2017 .

[16]  Toshio Nakagawa.  Advanced Reliability Models and Maintenance Policies , 2008 .

[17]  Yuan Lin Zhang,et al.  An extended geometric process repair model for a cold standby repairable system with imperfect delayed repair , 2016 .

[18]  Rui Peng,et al.  Defending a parallel system against a strategic attacker with redundancy, protection and disinformation , 2020, Reliab. Eng. Syst. Saf..

[19]  Ali Zeinal Hamadani,et al.  Reliability optimization of series-parallel systems with mixed redundancy strategy in subsystems , 2014, Reliab. Eng. Syst. Saf..

[20]  R. V. Kakubava.  Reliability model for standby system with replacement delays of failed elements , 2013, Automatic Control and Computer Sciences.

[21]  T. Dohi,et al.  Moment-based approach for some age-based replacement problems , 2017 .

[22]  Necip Doganaksoy,et al.  Handbook of Reliability Engineering , 1994 .

[23]  Gokhan Inalhan,et al.  Scheduled Maintenance and Downtime Cost in Aircraft Maintenance Management , 2016 .

[24]  Toshio Nakagawa,et al.  Optimization problems of replacement first or last in reliability theory , 2012, Eur. J. Oper. Res..

[25]  Toshio Nakagawa,et al.  OPTIMAL AGE REPLACEMENT AND INSPECTION POLICIES WITH RANDOM FAILURE AND REPLACEMENT TIMES , 2011 .

[26]  Toshio Nakagawa,et al.  Optimization Problems of a Parallel System With a Random Number of Units , 2012, IEEE Transactions on Reliability.

[27]  Ferenc Szidarovszky,et al.  New one cycle criteria for optimizing preventive replacement policies , 2016, Reliab. Eng. Syst. Saf..