CSE 221: Probabilistic Analysis of Computer SystemsExponential distributionExponential distribution (contd..)Slide 4Slide 5Reliability and failure rateReliability and failure rate (contd..)Reliability and failure rate (contd..)Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Distribution typesInverse bath tub curveCSE 221: Probabilistic Analysis of Computer SystemsTopics covered:Exponential distributionReliability and failure rate(Sec. 3.2-3.3)Exponential distributionDistribution function:Density function:Exponential distribution (contd..)Where to use:Parameters:Exponential distribution (contd..)Example:Exponential distribution (contd..)Memoryless property:Reliability and failure rateDistribution of time to failure:Reliability and failure rate (contd..) Probability of survival until time t:Reliability and failure rate (contd..)Survival probability in the limit:Reliability and failure rate (contd..)How to estimate survival probability:Reliability and failure rate (contd..)How to estimate survival probability:Reliability and failure rate (contd..)Rate of failure of the components:Reliability and failure rate (contd..) Conditional probability of failure: ExampleConditional probability of failure:Reliability and failure rate (contd..)Instantaneous failure rate or hazard rate:Reliability and failure rate (contd..)Hazard rate of the exponential distribution: Memoryless property:Example:Distribution typesIncreasing hazard rate distribution:Decreasing hazard rate distribution:Constant hazard rate distribution: Increasing/decreasing hazard rate distribution:Inverse bath tub curve Phase I: Decreasing failure ratePhase II: Constant failure ratePhase III: Increasing failure
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