DOC PREVIEW
UI CS 448 - PRA & PSA

This preview shows page 1-2-3-4 out of 13 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 13 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 13 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 13 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 13 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 13 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

CS448/548 Sequence 25PRA & PSA!Probability Risk Assessment–PRA!Probability Safety Assessment–PSA!Fault Tree Analysis–FTA!Event Tree Analysis–ETA1CS448/548 Sequence 25PRA & PSA!Probability Risk/Safety Assessment–general term for risk assessments that use probability models to represent the likelihood of different risk levels–reliability assessment methods used to analyze systems which are considered critical–PSA normally deals with issues of safety–PRA may deal with non-safety issues2CS448/548 Sequence 25Definitions!Variability–true heterogeneity or diversity–example: drinking water»for different people the risk from consuming the water may vary»could be caused by different body weight, exposure duration & frequency3CS448/548 Sequence 25Definitions!Uncertainty–caused by lack of knowledge–example: drinking water»risk assessor is certain that different people consume different amounts of water»BUT may be uncertain about how much variability there is4CS448/548 Sequence 25Definitions!Random Variable X–a function that assigns a real number X(s) to each sample point s in sample space S–e.g. coin toss, number of heads in a sequence of 3 tosses– – s hhh hht hth htt thh tht tth ttt X(s) 3 2 2 1 2 1 1 0 –X is a random variable taking on values in the set 5CS448/548 Sequence 25Definitions!Cumulative Distribution Function (cdf)–The cdf of a random variable X is defined as the probability of the event6CS448/548 Sequence 25Definitions!Probability Density Function (pdf)–The pdf of a random variable is the derivation of – Since is a non-decreasing function,–The pdf represents the “density” of probability at point x7CS448/548 Sequence 25Definitions!cdf vs. pdf–adult body weight (males and females combined) –Arithmetic mean 71.7kg, std = 15.9kg–Source: Finley et.al. 19948CS448/548 Sequence 25Definitions!Expectation of a random variable–in order to completely describe the behavior of a random variable, an entire function, namely the cdf or pdf, must be given–however, sometime we are just interested in parameters that summarize informationi.e. mean time to failure = expected lifetime of the system9CS448/548 Sequence 25PRA & PSA!Fault Tree Analysis–most widely used method in system reliability analysis–this is a top down approach–typical components are AND and OR10CS448/548 Sequence 25–example: (source Relax Software Corp.)11CS448/548 Sequence 25PRA & PSA!Event Tree Analysis–visual representation of all events which can occur in a system–example: (source Relax Software Corp.)12CS448/548 Sequence 25Reliability of Series System!Any one component failure causes system failure!Reliability Block Diagram (RBD)...1 2 n13CS448/548 Sequence 25Reliability of Series SystemthusMean time to failure of series system:Thus the MTTF of the series system is much smaller thanthe MTTF of its componentssystem is weakerthan weakestcomponent14CS448/548 Sequence 25Reliability of Parallel System!All components must fail to cause system failure!Reliability Block Diagram (RBD) –assume mutual independence...12n15CS448/548 Sequence 25 X is lifetime of the systemn componentsAssuming all components have exponential distributionwith parameter !16CS448/548 Sequence 25 from previous pageProduct law of unreliability17CS448/548 Sequence 25Stand-by Redundancy!When primary component fails, standby component is started up.!Stand-by spares are cold spares => unpowered!Switching equipment assumed failure free Let denote the lifetime of the i-th component from the time it is put into operation until its failure.System lifetime: 18CS448/548 Sequence 25Stand-by Redundancy!MTTF –gain is linear as a function of the number of components, unlike the case of parallel redundancy–added complexity of detection and switching mechanism19CS448/548 Sequence 25M-of-N SystemStarting with N components, we need any M components operable for the system to be operable.Example: TMRWhere is the reliability of the i-th component20CS448/548 Sequence 25M-of-N SystemThe probability that exactly j components are not operating isthen21CS448/548 Sequence 25Reliability Block Diagram!Series Parallel Graph–a graph that is recursively composed of series and parallel structures. –therefore it can be “collapsed” by applying series and/or parallel reduction–Let Ci denote the condition that component i is operable»1 = up, 0 = down–Let S denote the condition that the system is operable»1 = up, 0 = down–S is a logic function of C’s22CS448/548 Sequence 25Reliability Block Diagram–Example:C1C3C2 C5C4C6C7 C8+ => parallel (1 of N). => series (N of N)23CS448/548 Sequence 25K of N system!Example 2-of-3 systemmay abbreviatedraw as parallel C1C3C22-of-324CS448/548 Sequence 25Fault Trees!Fault Trees–dual of Reliability Block Diagram–logic failure diagram–think in terms of logic where»0 = operating, 1 = failed!AND Gate–all inputs must fail for the gate to fail!OR Gate–any input failure causes the gate to fail!k-of-n Gate–k or more input failures cause gate to


View Full Document

UI CS 448 - PRA & PSA

Download PRA & PSA
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view PRA & PSA and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view PRA & PSA 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?