Probabilistic Descriptions of Irregular System Downtime

Mathematical expressions are presented for the probability distributions and related statistical parameters, such as mean value and standard deviation, of system downtime and resulting loss of production caused by irregular equipment failure and repair. The expressions have been derived assuming exponential failure and repair distributions for the different pieces of equipment, with a mean-time-to-failure which is much larger than the mean-time-for-repair. The descriptions can be applied to a variety of system configurations of varying degrees of complexity, i.e. single units, units with standbys, units in parallel, any of these configurations in series and networks of series configurations.