Sensitivity Analysis of a Cold Standby System with Priority for Preventive Maintenance

INTRODUCTION

In this present paper there are two units one of which is online while other is kept in cold standby mode. Online & cold standby unit are indistinguishable in nature and have just two modes one is full limit and second is totally finished failure. There is single repairman as talked about to upkeep the units in all situations. Online unit just may experience preventive maintenance before failure. A unit is repaired just on its total disappointment need is appointed for preventive maintenance over the repair of a unit preventive upkeep office helps in declines the crumbling rates of online units in various working state. The irregular different related with failure & repair of units, server & preventive support and treatment time of server are measurably free and furthermore have distinct distributions probability. The system is displayed utilizing semi-Markov procedure and RPGT different system reliability parameters. Sensitivity analysis tables & figures for framework parameters are set up for expanding failure and repair rates. Corresponding chart are drawn and analysis of parameters is composed from these tables and graphs in this manner acquired. Gupta, R. 1 the paper discussed about a one unit framework alongside two sorts of repairman & repeat repair policies on failure of unit, this is attempted by any common repairman alongside the way that it may not ready to do a portion of complex repairs. Likewise, there might be a plausibility of harming the units amid repair by him, which can result it to go into increasingly more debased state. Kumar J. & Malik S. C. 2 , Choudhary, A., Neeraj & Kumar, K. 3, Bhardwaj, R. K., Kour, K. & Malik S. C.4 and Liu., R. 5 have also discussed preventive maintenance, reliability modeling analysis of a single unit and its applications. Kumar, R., Poonia, M. & Goel, P.6 have also studied on stochastic and availability analysis of two units with increasing failure/ repair rates. Chaudhary Nidhi, Goel P. 7, Gupta, R., Sharma, S. & Bhardwaj 8 and Tuteja, R. K. & Taneja, G. 9 has studied availability and behavior analysis of two or more units system using RPGT technique. Ms. Rachita and Garg D. 10 and Kumar A., Goel P., Garg D., and Sahu A. 11have also discussed reliability analysis using different technique.

1. A single repair man is accessible 24*7. 2. Repaired framework is as great/good. 3. Failure rate & landing rates are statistically independent. αi:- Constant failure rate. g(t)/f(t) :- repair / preventive maintenance time of unit. w(t):- arrival/leading time of server. AUr : Unit is fizzled & under fix. AWr: Unit is fizzled & waiting for fix. HUt: Server is fizzled & under treatment from past state. HUT: Server is fizzled & continuously under treatment from past state. AUR : Unit is fizzled & under repair from past state. AWR: Unit is fizzled & waiting for repair continuously from past state.

Taking into consideration above assumptions & notations, Transition Diagram of system is given Figure 1.

qi,j(t): Probability compactness function regenerative state ‗i ‘and ‗j‘ pi,j: State transition probability of a regenerative state ‗i‘ to a regenerative state ‗j‘, pi,j = q_(i,j)^* (0);

It can be easily verified that

Ri(t) : Reliability of system at time t, : Mean sojourn time spent in state i,

MTSF (T0): ): The regenerative un-failed states to which the system can transit(initial state ‗0‘), before entering any failed state are: ‗i‘ = 0,1,2,4 taking ‗ξ‘ = ‗0‘.

Availability of the System (A0): The regenerative states at which the system is available are ‗j‘ = 0 to 4 and the regenerative states are ‗i‘ = 0 to 8 taking ‗ξ‘ = ‗0‘ the total fraction of time for which the system is available is given by

Busy Period of the Server: The regenerative states where server j = 1 to 8 & regenerative states are ‗i‘ = 0 to 8, taking ξ = ‗0‘, the total fraction of time for which the server remains busy is Expected Fractional Number of Inspections by the repair man: The regenerative states where the repair man do this job j = 3,5,6,7,8 the regenerative states are i = 0 to 8, Taking ‗ξ‘ = ‗0‘, the number of visit by the repair man is given by

repair rates. Taking αi = 0.10 (1 ≤ i ≤ 2) and varying β1, β2, β3, one by one respectively at 0.80, 0.90, 1.00

Scenario2: Now we consider Sensitivity Analysis scenario 2 with respect to change in failure rates: taking βi = 0.80 (1 ≤ i ≤ 3) and varying α1, α2 one by one respectively at 0.10, 0.20, 0.30.

CONCLUSION:-

From the above table 3 & figure 2, it is concluded that T0 is constant for corresponding repair rates. From the above table 4 we see that A0 increase more quickly with the expansion in repair rates of units. However, the rate of increase in greatest when β rate of server increase on contrasting the impact of β rates it is quicker with the expansion in repair rate of units. From table 5, we see that B0 increase in repair rates, yet its rate of diminishing increasingly over the other repair rates if there should arise an occurrence of online units repair rates. From the table 6 it is seen that estimation of V0 is same for same estimation of repair rates of units. Be that as it & server as we produced using top to bottom, while contrasting the tabular qualities in columns, we see that T0 increment quick with the expansion in failure rate of online unit. From table 8 & figure 7, we see that Ao decrease all the more quickly with the expansion, in restoration rate of preventive support, subsequently to keep estimation of Ao. From table 7 & figure 8 that it is concluded that value of B0 Increases in all columns as failure rates increment. Be that as it may, it increment at quicker rate with increment in failure rate of online units. From table 10, we see that value of V0 increment with the expansion in failure rates which is practical too.

1. Gupta, R. (2017). ―Stochastic Analysis of a Repairable Model for One Unit System with Three Types of Repair Policy‖, International Journal of Statistics and Applied Mathematics, Vol. 2 (6), ISSN 2456-1452, pp. 126-130. 2. Kumar J., Kadyan M. S., Malik S. C. & Jindal C. (2014). ―Reliability Measures of a Single-Unit System Under Preventive Maintenance and Degradation With Arbitrary Distributions of Random Variables‖, Journals of Reliability and Statistical Studies:, ISSN 0974-8024, Vol. 7, pp. 77–88. 3. Choudhary, A., Neeraj & Kumar, K. (2010). ―Profit Analysis of a Complex System with Correlation in Time to Preventive Maintenance and Time Taken in Preventive Maintenance‖, Journal of Reliability and Statistical Studies, Vol. 3 (1), ISSN 0974-8024, pp. 95-103. 4. Bhardwaj, R. K., Kour, K. & Malik S. C. (2015). ―Stochastic Modeling of a System with Maintenance and Replacement of Standby Subject to Inspection‖, Americal Journal of Theoretical and Applied Statistics, Vol. 4 (5), ISSN 2326-9006, pp. 339-346. 5. Liu. R. and Liu, Z. (2011). ―Reliability Analysis of a One-Unit System with Finite Vacations‖, Management Science Industrial Engineering (MSIE) International Conference, pp. 248-252. 6. Kumar, R., Poonia, M. & Goel, P. (2016). ―Availability Analysis of Two Unit System with Warm Standby having Imperfect Switch over System using RPGT‖, 7. Chaudhary Nidhi, Goel P., Kumar Surender (2013). ―Developing the reliability model for availability and behavior analysis of a distillery using Regenerative Point Graphical Technique‖, IJIFR, ISSN: 2347-1697, Vol. 1 (4) pp. 26-40. 8. Gupta, R., Sharma, S. & Bhardwaj, P. (2016). Cost Benefit Analysis of a Urea Fertilizer Manufacturing System Model, Journal of Statistics an Application & Probability Letters An International Journal, Vol. 3, pp. 119-132. 9. Tuteja, R. K. & Taneja, G. (1993). Profit Analysis of a One Server One Unit System with Partial Failure Subject to Random Inspection, Micro Electronic Reliability, Vol. 33 (3), ISBN 0026-2714 (93)-90019-U, pp. 319-322. 10. Ms. Rachita and Garg, D. (2016). ―Transient analysis of markovian queue model with multi stage service‖, Redset, pp. 264-272. 11. Kumar A., Goel P., Garg D. and Sahu A. (2017). ―System Behavior Analysis in the urea fertilizer industry‖, Book: Data and Analysis, Redset 2017.

Research Scholar, G. D. Goenka University, Gurugram, Haryana rnkumar535@gmail.com