Some important details on technical system: Matrix representation, odds ratio, embedding subsystems

Abstract

The system signature calculated independently from the distribution of the lifetime of the units in the analysis of technical systems enables us to have important information about the reliability of the system. System signature is a probability vector obtained from possible sequences of units according to the moments of deterioration. The reliability of the system can be easily obtained if the distribution of the lifetime of the units is known and if the distributions can be listed as open among themselves. However, when the distributions cannot be listed as open among themselves, it is a very important finding that the system reliability is calculated with the help of system signature by generating the order statistics. It is also possible to calculate the odds ratios of the units when the lifetime of the units is certain. In this study, odds ratio could be calculated by calculating the probability of fail the system of each unit by considering the possible situations of the system, as in the system signature, regardless of the distribution of lifetime of the units. In addition, the technical system is represented by a matrix by establishing a relation between the system fail probabilities of the units obtained in the study and the system signature. However, examples of some technical systems given in the study.