Processing Times Modeled by Reliability Systems with a Random Number of Spare Units

A processing job with high reliability of final results is requested. It is performed as a multi-stage process. The facility at each stage may work correctly or malfunction. To enter any subsequent stage a secure result from the previous stage is required. This leads to the necessity of duplication of jobs at each stage many (random number of) times to provide two coinciding results, and a successful and reliable end. Then the total processing time, the quality of total processing of the job and related characteristics are modeled like those in a reliability system with random redundancy. Some analogies with the conventional results in reliability theory apply. Optimization problems are formulated and examples from information traffic are shown.