© 2018 JETIR August 2018, Volume 5, Issue 8 www.jetir.org (ISSN-2349-5162) JETIRC006397 Journal of Emerging Technologies and Innovative Research (JETIR) www.jetir.org 471 SYSTEM RELIABILITY WITH IMPERFECT FAULT COVERAGE A. Merceline Anita 1 , F. Almas Firdose 2 1,2- Department of Mathematics, Sacred Heart College, Tirupattur Email id: 1 mercelineanita@gmail.com Abstract In this Paper, we deal with the Reliability Analysis of a System which comprises two subsystems connected in series. Each subsystem has an active and a spare unit with constant failure rates. Reliability of the subsystems with covered and uncovered faults has been calculated with known coverage parameter and failure rates for a particular time period. The mean time to failure and hazard rate function of the System has been calculated. Numerical illustration is also provided by graphical representation of Reliability analysis. Keywords Imperfect Fault Coverage, Standby Redundancy, MTTF and hazard rate function. 1. INTRODUCTION Reliability of a System is defined as the probability that it performs its purpose within tolerance for the period of time planned under the given operating conditions. The concept of Reliability stresses four elements namely probability, tolerance, time and operating conditions. It tells how much reliable a system is. [3] It is a key concern of the System engineer in any repairable system. Complex systems like computer and telecommunication networks, electric appliances and many more are real life examples. Designing the systems and determining their reliability are very important task for the system managers and analyst. In many practical situations, the production may be disturbed due to the sudden failure of the machines which brings unwanted loss of income as well as goodwill in the market. Such situation can be controlled up to some extent using the support of standby units and repairs. With the help of standbys, the system remains active and continues to perform its job in case of failure. The standby concept has attracted many researchers working in the field of Reliability theory. Reliability analysis has also been done for Machine repair problem with standbys. Reliability modeling with imperfect coverage has been examined by many authors time to time. Due to imperfect coverage, the Reliability of Repairable systems cannot be improved with the increase of redundancy. [2] In this paper, we discuss the analysis of Reliability in Repairable system with imperfect fault coverage. The perfect detection and recovery of an active unit is done with probability c which is known as coverage parameter and imperfect detection and recovery has been done with the probability 1-c. We formulate the model involved in our study and analyze its System Reliability using fault coverage parameter and failure rates of active and spare units in the subsystems. In section 1, we give the introduction, in section 2, basic concepts have been given and in section 3 we have dealt with Reliability of a System with Imperfect fault coverage. In section 4, we analyze the System Reliability of the model involved in our study. In section 5, we present numerical illustration with graphical representation. Finally in section 6, we draw the conclusion.