Probabilistic Analysis of a System of Two Non-identical Parallel Units with Priority to Repair Subject to Inspection

Two reliability models for a system of non-identical units – one is original and the other is a substandard unit (called duplicate unit) are analyzed probabilistically in detail by using regenerative point technique. There is a single server who comes immediately to do inspection and repair whenever needed. On the failure of original unit, server inspects the operative duplicate unit to see whether the unit is capable of performing the desired function well or not. If duplicate unit is not capable to do so, the operation of the system is stopped and server starts repair of the original unit immediately. However, no inspection is done at the failure of the duplicate unit as the original unit alone is capable of performing the given task well. In model 1, priority to repair the original unit is given in case system fails completely and duplicate unit is already under repair whereas in model II there is no such priority. The failure and repair times of each unit are assumed to be independent and uncorrelated random variables. The distributions of failure time of the units are taken as negative exponential while that of repair and inspection times are general. Graphs are plotted to compare some econo-reliability measures of the models such as MTSF, availability and profit for a particular case.