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

Abstract

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.

Survey on queueing models with standbys support

“…They used a threshold policy to turn on the removable additional repairman by using a product type technique to derive formulae for the steady-state probabilities and other performance measures. Jain et al [52] used the SOR method for obtaining the steady state queue size distribution of the average number of failed units for multi-component machining system with common cause failure and mixed standbys.…”

Fault tolerant system with imperfect coverage, reboot and server vacation

“…The queue size distribution has been established by Kumar and Jain (2013) for both F-policy and N-policy by employing the recursive method. Recently, Jain et al (2015) developed multi-component machine repair model with two heterogeneous servers and having the facility of warm standby units along with on-line units. They derived the steady state queue size distributions and other measures of performance with the implementation of successive over relaxation technique.…”