RELIABILITY PREDICTION OF IMPERFECT SWITCHING SYSTEMS SUBJECT TO WEIBULL FAILURES

ÐReliability prediction plays a very important role in system design and evaluation. In order to accurately predict the system reliability, one should consider the system con®guration 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 ̄exible 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 dicult 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 eect of spare addition, as well as dierent 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. # 1998 Elsevier Science Ltd. All rights reserved. INTRODUCTION AND LITERATURE REVIEW In predicting the reliability of a given system, it is necessary to specify the equipment components, the system con®guration which describes how the components are connected, and the rules of operation. The equipment failure process is described by probability laws governing failures. Reliability engineers have used several distributions to describe the characteristics of failures. Some of these distributions are the exponential, gamma, lognormal, truncated normal, and Weibull distributions. The exponential distribution has been widely used to model electronic components and large systems during the useful life period [1±5]. However, in many cases, it is used because it is easy to apply rather than the choice being based on thorough understanding of the fundamentals [4]. Recently the Weibull distribution has assumed a position of importance because it is very ̄exible in data ®tting and it can adequately describe the reliability behavior during the life-time of an operating component system [6, 7]. On the other hand, the switching system is widely used in the industry. For example, electronic components, aerospace parts, power supply units can all be considered as active/redundant components in the switching system. This system consists of k redundant components/ spares. When the operating components break down, the switch detects the failure using the sensor and the defective component is replaced with a working one, so the system can keep on running. The installation of the sensor is mainly for detecting component failure. When failures occur, the sensor will instruct the switch to provide a replacement. Chow [1] has done studies on an imperfect switching system, which contains two identical components. When the sensor or the switch fails, system reliability is aected. Considering the component, sensor and switch follow exponential failures, the reliability model can be directly obtained through solving a simple integration. Chow [2] also derives the mean time between failures and the system reliability for some redundant systems with consideration for repair. Nakagawa and Osaki [8] investigate two Computers ind. Engng Vol. 34, No. 2, pp. 481±492, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0360-8352/98 $19.00+0.00 PII: S0360-8352(97)00143-5