Reliability Computation and Bayesian Analysis of System Reliability for Power Function Distribution SHAZIA ZARRIN Department of Statistics & Operations Research Aligarh Muslim University Aligarh, India shaziazarrin@gmail.com SHASHI SAXENA Department of Statistics & Operations Research Aligarh Muslim University Aligarh, India sshashisaxena@gmail.com MUSTAFA KAMAL Department of Statistics & Operations Research Aligarh Muslim University Aligarh, India kamal19252003@gmail.com ARIF-UL-ISLAM Department of Statistics & Operations Research Aligarh Muslim University Aligarh, India arifislam2@yahoo.com Abstract-- This paper presents the reliability computation and Bayesian estimation of system reliability when the applied stress and strength follows the power function distribution. The Power Function Distribution is considered as a simple model to assess component reliability and may exhibit a better fit for failure data and also provide more appropriate information about hazard rate. The results may be applied to semiconductor devices. Maximum likelihood estimator and Bayesian methods are used here. Keywords-- Power Function Distribution; Reliability Computation; Stress-Strength Model; Bayes Estimation; Maximum likelihood Estimator. I. INTRODUCTION In today’s technological world nearly everyone depends upon the continued functioning of a wide array of complex machinery and equipment for our everyday safety, security, mobility and economic welfare. We expect our electric appliances, lights, hospital monitoring control, next-generation aircraft, nuclear power plants, data exchange systems, and aerospace applications, to function whenever we need them. When they fail, the results can be catastrophic, injury or even loss of life. The concept of reliability is used in a variety of business and industrial settings. In general, the concept of reliability is applied where it is important to achieve the same results over and over again. A manufacturing process is said to be reliable when it achieves the same result, within definite limits, each time it occurs. An automobile, or other type of product, is reliable if it performs consistently and up to expectations. Statistical distributions have long been employed in the assessment of semiconductor device and product reliability. The use of the exponential distribution which is frequently preferred over mathematically more complex distribution, such as the Weibull and the lognormal among others, suggest that most engineers favor the application of simpler model to obtain failure rates and reliability figures quickly. It is therefore proposed that the power function distribution be considered as a simpler alternative which, in some circumstances, may exhibit a better fit for failure data and provide more appropriate information about reliability and hazard rates. The power function distribution is also used to appropriate representation of the lower tail of the distribution of random variable having fixed lower bound. In the context of ‘strength-reliability’, the stress-strength model describes the life of a component, which has a random strength Y and is subjected to a random stress X . The component fails at the instant that the stress applied to it exceeds the strength, and the component will function satisfactorily whenever X Y > . Shazia Zarrin et.al / International Journal of Advances in Engineering, Science and Technology (IJAEST) ISSN : 2249-913X Vol. 2 No. 4 Nov 2012-Jan 2013 361