Reliability prediction of imperfect switching systems subject to Weibull failures

Reliability prediction plays a very important role in system design and evaluation. In order to accurately predict the system reliability, one should consider the system configuration and the failure distribution of its components. This paper discusses the imperfect switching system with one component in an active state and n spares in a standby state. When the operating component breaks down, the switch detects the failure via the sensor and the defective component is replaced with a functional spare, so the system can resume operation. The Weibull distribution is one of the most flexible failure distributions which is widely used because it can adequately describe the reliability behavior during the lifetime of present day components/systems. This paper assumes the operating components follow Weibull failures, but the spares, sensor and switch failures follow an exponential distribution. In addition, three assumptions are made with regard to its switch failures: (i) under the energized condition, (ii) under the failing-open condition, and (iii) under the failing-closed condition. Due to the intractability of the Weibull distribution in imperfect switching models, it is difficult to solve the multiple integration involved analytically. Therefore, a numerical integration method using Simpson's rule was selected as a tool to address the problem of multiple integration for the Weibull distribution. A recursive algorithm is developed for the reliability prediction of a series system with m imperfect switching sub-systems subject to Weibull failures. Finally, a sensitivity analysis is performed on the two parameters of the Weibull distribution, on the effect of spare addition, as well as different failing conditions (switch and sensor) on system reliability. A numerical example is also given to explain and demonstrate the practical application of the developed reliability prediction models.