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ClassNotes04

# ClassNotes04 - Reliability Engineering OEM 2009 ESI 6321...

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Reliability Engineering OEM 2009 ESI 6321 –Applied Probability Methods in Engineering 2 Reliability Engineering Reliability is the probability that a system will perform properly for a specified period of time. Reliability depends on Definition of “performing properly” (or “failure”) Operating conditions Time (age of system) Reliability as a function of time is important system characteristic.

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3 Failure rate Informally, we will define the failure rate of a system as the rate at which the system will fail if the system has not yet failed for t time units. We will formalize this later. How do we expect this rate to vary over time? Increasing? Decreasing? Constant? Mixed? 4 Failure rate Nature of failures: “Infant mortality” failure Random failures “Age-related” failures A common assumption is therefore that the failure rate follows a bathtub curve .
5 Time to failure We will define reliability as it relates to time through the following random variable: Let F denote the cumulative distribution function (cdf) of this random variable: T = time to failure F ( t ) = Pr( T ! t ) = probability that failure takes place no later than time t 6 Reliability We then define reliability as a function of time as It is easy to see that r (0) = 1 r ( t ) ! Pr( T > t ) = 1 " F ( t ) = probability that system operates without failure for at least t time units lim t !" r ( t ) = 0

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