ABSTRACT
The constant failure rate, λ(t) is defined as:
λ λt t years( ) = = …0 10 (1) Here λ is overall failure rate of the system and
it is constant over time because an exponential distribution is assumed for failures. The overall failure rate comprises of safe failures, λS and the dangerous failures, λD. The safe failures further divided into safe undetected failures, λSU and safe detected failures, λSD. The dangerous failures are further divided into dangerous undetected failures, λDU, dangerous detected failures, λDD and dangerous
1 INTRODUCTION
These days, there is a huge explosion of the new technologies and Industrial applications in the market and most of them rely on sensors, actuators and logical processing units for their safety operation without a failure, due to this phenomenon, the calculation of the probability of failure on demand average, PFDavg, is important for all the safety related systems in order to prevent the downtime of the device. Periodic maintenance is necessary for any safety related system and interval between these periodic proof tests or maintenance is called proof test interval, T1 that depends on the demand i.e., the frequency of operation of the system. A safety level called safety integrity level, SIL, can be assigned to a system based on its defined acceptable failure range. According to IEC 61508, a safety system can be categorized into the different safety levels, SIL, based on two criteria’s. The first is probability of a dangerous failure, i.e., for low demands of a safety function a failure occurs in the system and the proof test interval, T1 for this system is two years or ten years. In the second criteria, the probability of dangerous failure is calculated in such a way that a failure exists while a continuous or high demand occurs and the proof test interval, T1, for this system can be one month or three months or six
non-detectable failures, λND. The overall failure rate is described in the figures below (Börcsök 2003).
