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Chapter 8 – System Reliability. Motivation. 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?. Learning Objectives. By the end of this chapter, you should:
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Motivation • 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?
Learning Objectives 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.
8.1 Probability Review Definitions • Experiment • Event • Event Space
Axioms of Probability • What is an axiom? • 2 of the 3 axioms
Probability Density Functions • What is a random variable (RV)? • What is a PDF? • Math Definition
Common PDFs Normal Density
Common PDFs Uniform Density
8.2 Reliability Prediction • Reliability (defn) • Failure Rate
Derivations • See the book for derivation of R(t). • If the failure rate is constant, then R(t) = ?
Failure Rate Estimates • What factors influence the failure rate?
Failure rate estimates • Low Frequency FET, Appendix C. • How would you find each of these?
8.3 System Reliability • So far, we have only looked at a single device. • We are interested in collection of devices into a system! • For example
Series Systems • Def’n (Series System) = • We model this as
Parallel Systems Definition: Redundancy Definition: Parallel System
8.4 Summary • 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