Machine repair problem with an unreliable server and controlled arrival of failed machines

OPSEARCH ◽  
2013 ◽  
Vol 51 (3) ◽  
pp. 416-433 ◽  
Author(s):  
Madhu Jain ◽  
Chandra Shekhar ◽  
Shalini Shukla
Keyword(s):  
Machine Repair ◽  
Unreliable Server

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

scholarly journals A time-shared machine repair problem with mixed spares under N-policy

2016 ◽  
Vol 12 (2) ◽  
pp. 145-157 ◽  
Author(s):  
Madhu Jain ◽  
Chandra Shekhar ◽  
Shalini Shukla
Keyword(s):  
Machine Repair
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