Evaluation of Reliability and Availability Characteristics of Two Different Systems Using Linear First Order Differential Equation.
ABSTRACT
This study deals with the reliability and availability characteristics of two different systems, the second system differs from the first system due to the additional feature of preventive maintenance. Reliability and Availability analysis of system having one active unit and one warm stand-by unit with self-reset function and one maintenance facility.
The failure unit is repaired through self-reset or maintenance according to different failure model.( Mean Time to System Failure), Steady- State Availability, Busy Period Analysis and Profit Function are derived for the two systems using linear first order .
Two systems were evaluated theoretically and graphically to observe the effect of preventive maintenance on systems performance. The result finally shows that increase in failure rate leads to decrease in MTSF, Steady-State Availability and Profit Function of figure 4.1, 4.2 and 4.3.
It was also found that increase in repair rate leads to increase in MTSF, Steady- State Availability and Profit Function of figure 4.4, 4.5, and 4.6. Therefore, the result indicated that second system originate better reliability due to the additional feature of preventive maintenance.
INTRODUCTION
The role and importance of reliability have been a core of any engineering industry for the last three decades. Reliability is of importance to both manufacturers and consumers. So, the reliability measure is very important, as the improvement of reliability is achieved through quality.
While this measure of reliability assumes great importance in industry, there are many situations where continuous failure free performance of the system, though desirable may not be absolutely necessary, Yadavalli and Vanwyk (2012). Several authors have studied a two (or more) similar and dissimilar unit standby redundant system.
Haggag (2009a), studied the cost analysis of dissimilar-unit cold-standby system with three state and preventive maintenance using linear first order differential equations. El-sherbeny et al (2009), studied the optimal system for series systems with warm standby components and a repairable service station.
Researchers in reliability have shown a keen interest in the analysis of two (or more) component parallel system owing to their practical utility in modern industrial and technological set ups. Two unit warm standby redundant systems have been investigated extensively in the past.
The most general model is the one in which both the life time and repair time distributions of the units are arbitrary. However the study of standby system with more than two units, though very important, has received much less attention, possibly because of the built in difficulties in analyzing them.
REFERENCES
Agarwal S.C, Sahani, M. and Bansal, S. (2010), Reliability characteristics of cold- Standby redundant system, Applied Mathematics and Computation, 3(2): 193-198
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EL-Said,K.M and Elsherbeny M.S. (2010), Stochastic Analysis of a two-unit cold standby System with two stage repair and waiting time, The Indian Journal of Mathematics, 72(1): 1-10
El-Said,K.M. and El-Hamid, R.A. (2008), Comparison of Reliability characteristics of two systems with preventive maintenance and different modes, Information and Management Sciences, 1(19), 107-118.
El-sherbeny,S.M, Rasheed,A. M and Garieb, D.M. (2009), The optimal system for series systems with warm standby components and a repairable service station,Journal of Statistics and Operation Research, 5(1):290
Hoyland ,A. and Naus,M. (1994), System reliability theory, Models and Statistical Methods, John Willey and Sons, New York.
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