An (m, M) machine repair problem with spares and state dependent rates: A diffusion process approach

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Date
1997
Authors
Jain, Madhu
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Abstract
The diffusion approximation model for (m, M) general machine repair problems with spare part support has been developed. The inter-failure time and repair times are assumed to be generally identically and independently distributed (i.i.d.). The failure rate of operating units in a short system when fewer than M units are operating and all spares are being used, is faster than a normal system. The spare units may also fail with rates different from operating units. The repairmen switch to the faster rate to reduce a backlog of down units in the case of a busy repair facility. By using reflecting boundaries, the approximate formulae for some performance measures, namely, expected number of inoperative/operative units and probability that the system is short/down have been obtained.
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Keywords
approximation model, reflecting boundaries, approximate formulae
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