1 Vijay Goyal, Dr. Pardeep Goel International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 4, Special Issue May 2015 Behavioral Analysis of Two Unit System with Preventive Maintenance and Degradation Post Repair With Standby to One Unit Using RPGT *Vijay Goyal, Research Scholar , J.J.T. University, Jhunjhnu (Rajasthan) **Dr. Pardeep Goel, Associate Professor M.M. (P.G.) College, Fatehabad (Haryana) Keywords: - Availability, Reliability, Primary Circuits, Tertiary Circuits, Preventive Maintenance Degraded state, Base-State, Regenerative Point Graphical Technique (RPGT), MTSF, Busy period of the Server, Expected No. of Server’s Visits, Fuzzy Logic, Steady State. ABSTRACT: In this paper Behavioral Analysis of two units system with preventive maintenance and degradation in one unit Post Failure and the other unit with perfect repair using Regenerative Point Graphical Technique (RPGT) is discussed. Initially, the two units A & B are working at full capacity in which unit A may have two types of failures one is direct and second one is through partial failure mode, but unit B can fail directly. Unit C is Standby to Unit B and capacity of doing work of Unit C is less than Unit B. There are two servers (repairmen), First is for unit A and second for Unit B .On partial failure (before complete failure) server repairs the unit and on complete failure the unit A cannot be restored to its original capacity i.e. it is in degraded state. But Unit B can be restored to original form. When Unit B fails then Unit C is connected with the help of A Perfect Switch. Fuzzy logic is used to determine failure/working state of a unit. If the server report, that unit A is not repairable, then it is replaced by a new one. Taking failure rates exponential, repair rates general and taking into consideration various probabilities, a transition diagram of the system is developed to determine Primary circuits, Secondary circuits & Tertiary circuits and Base state. Problem is formulated and solved using RPGT. Repair and Failure are statistically independent. Expressions for system parameters i.e. mean time to system failure, availability, number of server visits and busy period of the server are evaluated to study the behavior of the system for steady state. Particular cases are taken to study the effect of failure and repair rates on mean time to system failure, availability, expected number of server visits and busy period of the server. Profit optimization is also discussed. System behavior is discussed with the help of graphs and tables. Introduction: - Various industries and processing systems are assembly of a number of units. Here we have discussed the behavior of a two units system prevalent in various process industries. Considering the importance of individual units in system Kumar, J. & Malik, S. C. [1] have discussed the concept of preventive maintenance for a single unit system. Gupta,P., Sharma, S.K., Goel, A. & Modgal, V. [2], Malik, S. C. [3] have discussed reliability analysis of a one unit system with un-repairable spare units and its applications. Gupta, P., Lal, A. K., Sharma, R. K. and Singh, J. [4] Goel, P. & Singh J. [5], Sharma S. & Goel, P. [6],Goyal V.& Goel P.[7] and Satpal & Goel P.[8]. have discussed behavior of systems with imperfect switch using RPGT. We have discussed the behavioral analysis of two unit system in which unit A have parallel sub units so it can work in reduced capacity as well as in full capacity. The system can fail from normal mode to complete failure directly or via partial failure. Most of the systems consists a number of units and one of these units may be important for working of system, hence need more care over other units. Further, there are units which may not be repaired to their original capacity after complete failure. Since the capability of unit after repair depends on the repair mechanism adopted and unit may have increased