The Reliability and Availability Analysis of a Single-Unit System under the Influence of Random Shocks and the Variation in Demand from Production with Erlang Distribution

This study evaluates the reliability measures for a system consisting of a single unit that is subject to random shocks at random times with mismatches between demand and production. The system may sometimes be subject to random shocks leading to a system failure with probability p. The system may also fail completely for various reasons other than shocks. The unit is serviced by a technician if it is affected by a shock. However, the system may fail during operation for various other reasons, such as a programming error, human error, operational continuity and stress, and weather conditions. A single technician immediately repairs or maintains the failed unit. The system is in an operational state when there is demand or in an idle state when there is no demand. The distributions of all times in this system follow a negative exponential, while the time to repair follows a two-stage Erlang distribution. The expressions for the reliability metrics are obtained as functions of time using the Laplace transform and the supplementary variables technique. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, the efficiency of the system is illustrated using numerical examples.