Machine repair system with threshold recovery policy, unreliable servers and phase repairs

ABSTRACT

This study aims to discuss queueing modeling of machine repair problems under threshold recovery policy (Q), server unreliability and k-type phase repairs. When one or more machines in the system fails/fail, the service facility (or all $\mathit{R}$-servers) is activated and repairs the failed machine according to the first come, first served (FCFS) discipline. The service facility may experience a partial or complete breakdown while providing service and needs to be repaired in required phases under the threshold recovery policy (Q). The matrix geometric approach is applied to solve the system governing equations, and a sensitivity analysis is presented to understand the effect of various parameters on system performance metrics. The greedy selection method and the golden section method are used to compute optimal rates of $\left(R^{\ast },{\mu }^{\ast }\right)$ of service facility in order to minimize the cost function of the system.

KEYWORDS:

• Machine Repair System
• Threshold recovery policy (Q)
• Mixed standbys
• Matrix geometric method
• Unreliable servers
• Phase repairs

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Kamlesh Kumar

Kamlesh Kumar: Presently, Kamlesh Kumar is working as an Assistant Professor in the Department of Mathematics, Central University of Jammu, India since December, 2013. He has acquired his Ph.D. degree from the Department of Mathematics, Indian Institute of Technology, Roorkee India under the supervision of Dr. Madhu Jain. He has qualified CSIR-NET and GATE. He has guided one Ph.D. student. His area of interest in research is queueing modeling of machine repair problems.

Madhu Jain

Madhu Jain: Madhu Jain is a faculty member in the Department of Mathematics, Indian Institute of Technology, Roorkee (India). She has been a gold medalist of Agra University, India at M. Phil. level. There are more than 350 research publications in refereed International/National journals and more than 20 books to her credit in addition to two reference books. Her current research interest includes Performance Modeling, Soft Computing, Bio-informatics, Reliability Engineering and Queueing Theory. She has visited various reputed Universities/Institutes in USA, Canada, UK, Germany, France, Holland and Belgium.

Chandra Shekhar

Chandra Shekhar: Chandra Shekhar is working as Professor in the Department of Mathematics, BITS Pilani, Rajasthan (India) since September 2004 earned his Doctoral degree from H.N.B. Garhwal University, Srinagar, Uttarakhand (India) on topic “Some queueing models for prediction and evaluation of performance of computer systems”. Presently he is actively involved in teaching and research in the area of Engineering Mathematics, Operations Research, Optimization, Probability & Statistics and Differential Equation and having much research interest in Queueing theory, Computer and communication system, Machine repair problem, Reliability & maintainability and Stochastic process.