1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Exponential distribution Reliability and failure rate (Sec. 3.2-3.3)

2. Exponential distribution  Distribution function:  Density function:

3. Exponential distribution (contd..)  Where to use:  Parameters:

4. Exponential distribution (contd..)  Example:

5. Exponential distribution (contd..)  Memoryless property:

6. Reliability and failure rate  Distribution of time to failure:

7. Reliability and failure rate (contd..)  Probability of survival until time t:

8. Reliability and failure rate (contd..)  Survival probability in the limit:

9. Reliability and failure rate (contd..)  How to estimate survival probability:

10. Reliability and failure rate (contd..)  How to estimate survival probability:

11. Reliability and failure rate (contd..)  Rate of failure of the components:

12. Reliability and failure rate (contd..)  Conditional probability of failure: Example  Conditional probability of failure:

13. Reliability and failure rate (contd..)  Instantaneous failure rate or hazard rate:

14. Reliability and failure rate (contd..)  Hazard rate of the exponential distribution:  Memoryless property:  Example:

15. Distribution types  Increasing hazard rate distribution:  Decreasing hazard rate distribution:  Constant hazard rate distribution:  Increasing/decreasing hazard rate distribution:

16. Inverse bath tub curve  Phase I: Decreasing failure rate  Phase II: Constant failure rate  Phase III: Increasing failure rate