ENMA 420-520 Lecture 11 Slides

# ENMA 420-520 Lecture 11 Slides - Click to edit Master...

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Unformatted text preview: Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #11 Product and System Reliability 11 10/17/09 Definitions Reliability: the probability that the product will meet a set of specifications for a given time Failure time: a random variable that represents the length of time T a product performs to specifications. The density function of T is called the failure time distribution f(t). 22 10/17/09 Reliability and Failure Time The probability that a product will fail before time t0 is the cumulative distribution function F(t0): Then reliability can be defined as: 33 lll = l ==== l ======= & = lll l = 1 === l 10/17/09 Hazard Rates Define events A and B: A: Item fails in the interval (t, t + &t) B: Item survives until time t then P(A|B) = P(A[B) / P(B). However, if the item fails in the interval (t, t + & t) then it must have survived until time t so P(A|B) = P(A) / P(B). For sufficiently small &t this is approximated by: 44 lll ll = ==== l 1 = (= ) = ==== l l (= ) l (= )= ==== = (= ) 10/17/09 Hazard Rates (Contd) A constant hazard rate implies that the item never gets fatigued (also called a memoryless distribution). Example: exponential distribution has a hazard rate of 1/ Often appropriate for maintained systems systems whose parts are replaced on an ongoing basis so the overall hazard rate remains constant 55 10/17/09 Hazard Rates (Contd)...
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## This note was uploaded on 10/17/2009 for the course MET 387 taught by Professor Dean during the Spring '09 term at Old Dominion.

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ENMA 420-520 Lecture 11 Slides - Click to edit Master...

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