COMPARATIVE-ANALYSIS FOR THE M/E(K)/1 MACHINE REPAIR PROBLEM WITH SPARES

This paper deals with the M/E(k)/1 machine repair problem with spares under steady-state conditions. Spares are considered to be either cold standby, warm standby, or hot standby. We present exact formulas for the probability mass functions of the number of failed machines in the system. Approximate formulas for the probability density function of the number of failed machines in the system are obtained through diffusion approximation. A study of the derived exact results, compared to the approximate results, shows that the diffusion approximation approach is sufficiently accurate for practical use.