 How do you know how long your design is going to last?  Is there any way we can predict how long it will work?  Why do Reliability Engineers get paid so much? 2

By the end of this chapter, you should:  Have a familiarity with the basic principles of probability and understand how they apply to reliability theory.  Understand the mathematical definition and meaning of failure rate, reliability, and mean time to failure.  Understand how to determine the reliability of a component.  Understand how to derate the power of electronic components for use under different operating temperatures.  Understand how to determine the reliability of different system configurations. 3

Definitions  Experiment  Event  Event Space 4

 What is an axiom?  2 of the 3 axioms 5

 What is a random variable (RV)?  What is a PDF?  Math Definition 6

Normal Density 7

Uniform Density 8

 Reliability (defn)  Failure Rate 9

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 See the book for derivation of R(t).  If the failure rate is constant, then R(t) = ? 11

 What factors influence the failure rate? 12

 Low Frequency FET, Appendix C.  How would you find each of these? 13

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 So far, we have only looked at a single device.  We are interested in collection of devices into a system!  For example 20

 Def’n (Series System) =  We model this as 21

Definition: Redundancy Definition: Parallel System 22

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 Probability Review ◦ Random Variables ◦ PDFs and CDFs ◦ Mean and Variance  Reliability Estimation ◦ Failure rate and the bathtub curve ◦ Reliability & MTTF ◦ Application to single components (MIL-SPEC)  System Reliability ◦ Series systems ◦ Parallel systems ◦ Combination systems 25