Application of semi-Markov process and CTMC to evaluation of UPS system availability

In this paper, the authors develop analytical models for the study of the dependability characteristics of systems with uninterruptible power supply (UPS) units. Dependability of systems with UPS cannot be modeled exactly using the prevalent Markov modeling approaches. They develop and solve two approximations to this problem. The first model assumes that battery units will be fully recharged before the next failure occurs. With this assumption, a semi-Markov process (SMP) model is developed and solved to provide formulae to compute availability measures (transient and steady-state), reliability and mean time to failure (MTTF). Another approximation based only on Markov modeling theory is then proposed. The authors show how all the measures can also be computed using the continuous-time Markov chain (CTMC) approach, and also compare some of its results with the equations developed. In practical applications, the closed-form formulae for A(t), A and MTTF are very useful in combination with other system equations in a reliability block diagram or fault-tree. On the other hand, the Erlang approximation is easy to use when one has Markov chain solvers (e.g., the SPNP or SHARPE modeling packages) available for computing dependability measures.