(m, M) Machining system with two unreliable servers, mixed spares and common-cause failure


1 IIT Roorkee, Roorkee, India

2 Department of Mathematics, St. John’s College, Agra, 282 002, India

3 Department of Mathematics, Institute of Basic Science, Khandari, Agra, 282 002, India


This paper deals with multi-component machine repair model having provision of warm standby units and repair facility consisting of two heterogeneous servers (primary and secondary) to provide repair to the failed units. The failure of operating and standby units may occur individually or due to some common cause. The primary server may fail partially following full failure whereas secondary server faces complete failure only. The life times of servers and operating/standby units and their repair times follow exponential distribution. The successive over relaxation (SOR) technique has been used to obtain the steady state queue size distribution of the number of failed units in the system. To explore the system characteristics, various performance indices such as expected number of failed units in the queue, throughput, etc. have been obtained. Numerical results have been provided to illustrate the computational tractability of the proposed SOR technique. To examine the effect of system descriptors on the performance indices, the sensitivity analysis is also performed.