Laplace Transformation Techniques vs. Extended Semi-Markov Processes Method

We consider a continuously monitored one-unit system supported by an identical spare unit, and perfectly repaired by an in-house regular repairer within a predetermined fixed patience time, or by a visiting expert repairer who arrives when the system fails or when the patience time is over, and who repairs all failed units. We demonstrate the difficulties and the shortcomings of the Laplace transformation technique, and how these are overcome by the extended semi-Markov process method. MSC: primary 90B25; secondary 60K20

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