Abstract

The present investigation deals with a machine repair problem consisting of cold and warm standby machines. The machines are subject to breakdown and are repaired by the permanent repairman operating under N-policy. There is provision of one additional removable repairman who is called upon when the work load of failed machines crosses a certain threshold level and is removed as soon as the work load again ceases to that level. Both repairmen recover the failed machines by following the time sharing concept which means that the repairmen share their repair job simultaneously among all the failed machines that have joined the system for repair. Markovian model has been developed by considering the queue dependent rates and solved analytically using the recursive technique. Various performance indices are derived which are further used to obtain the cost function. By taking illustration, numerical simulation and sensitivity analysis have been provided.

Highlights

  • In the present era of modernization, machines have become part and partial of our day to day life

  • We study a Markovian machine repair problem with mixed standbys under the care of a repair facility having one permanent repairman and another additional removable repairman which turn on according to N-policy and threshold policy, J Ind Eng Int (2016) 12:145–157 respectively

  • The noble feature of the present model over other existing models lies in the incorporation of many key realistic factors such as N-policy, time sharing concept, provision of mixed standbys, and facility of additional removable server in case of heavy workload in a combined and collaborated manner for the performance modeling of machine repair system

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Summary

Introduction

In the present era of modernization, machines have become part and partial of our day to day life. The repairman will return to the first machine after rendering its service to each of all other failed machines present in the queue for the fixed (pre-specified) small duration of time This way, the whole cycle will go on by following the round-robin discipline. The noble feature of the present model over other existing models lies in the incorporation of many key realistic factors such as N-policy, time sharing concept, provision of mixed standbys, and facility of additional removable server in case of heavy workload in a combined and collaborated manner for the performance modeling of machine repair system. The secondary additional repairman is called upon as and when the workload of failed machines crosses a critical threshold level Both repairmen work on the time sharing basis which means that both of them repair the failed machines present in the queue by sharing their time with all failed machines accumulated in the system. To summarize the findings and highlight the noble features of the work done, the concluding remarks have been given in the last section on ‘‘Discussion’’

The model
Governing equations
Queue size distribution
KnÀk cðkÞ cðnÞ
Special cases
Ys kY lY
Performance indices
Cost function
Numerical analysis
Discussion
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