Efficiency analysis of series machines under operation-dependent-failures

Series machines, i.e., machines connected in series with no buffering, are pervasive in production systems. In the analysis, design, and optimization of the series-machine system, the efficiency analysis is one of the most fundamental issues. There are not a lot of researches analyzing the efficiency of the series-machine system under the assumption of Operation-Dependent-Failures (ODF) mechanism and almost all of them assumed that machines break down in terms of ODF-I (i.e., the breakdown of a machine could make all other series machines forced down) rather than under ODF-II (i.e., the breakdown of a machine does not make any other series machines forced down). The reason that ODF-I is usually assumed in the literature is that the analysis of the series-machine system under ODF-II is much more complex than under ODF-I, although ODF-II might be more common in practice. To systematically analyze the efficiency of the series-machine system, in this paper, we propose an analytical method to investigate the efficiency under both ODF-I and ODF-II failure mechanisms. Different from under ODF-I, analytical expressions of the efficiency of series-machine systems under ODF-II are hard to obtain and thus, limit bounds of the efficiency are derived and an algorithm is developed to calculate its exact value. Results show that the series-machine system under ODF-II is more efficient than under ODF-I, which, intuitively making sense, is the reason that ODF-II are more common in the industry.