Transcription of Probabilistic Fundamentals Workshop Course Materials ...
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01. Develop an expression for the reliability of the following system. Calculate the system reliability if all the components have a reliability of probability and Reliability Concepts1234655555 RedundantRedundant3/5 system1 basic probability and Reliability Concepts RS [R1(R2R3 R4 R2R3R4) R6 R1R6(R2R3 R4 R2R3R4)] [R55 5R54Q5 10R53Q52] R RS [ ( ) ( )][ ] [ ][ ] (a) Calculate the availability of the following system if each component has a failure rate of 5 f/yr and an average repair time of hours.(b) Estimate the system availability using minimal cut probability and Reliability Concepts12346 InputOutput53 basic probability and Reliability ConceptsRs=Rs(4 is good)R4 + Rs(4 is bad)Q4Rs=Rs(3 is good)R3 + Rs(3 is bad)Q3=(R1 + R5 -R1R5) R3 + (R5R6) Q3 Given 4 is goodRs=R1R2R3 + R5R6 -R1R2R3R5R6 Given 4 is badRs=R4[(R1 + R5 -R1R5) R3 + (R5R6) Q3]+Q4[R1R2R3 + R5R6 -R1R2R3R5R6]Substituting4 basic probability and Reliability ConceptsComponent Unavailability = Q = 55 95 availability = ( )[ ] + ( )[ ]= Unavailability = CutsProbability1, , , , 4, , 4, , 4, Unavailability Availability probability and Reliability Concepts01.
1 Basic Probability and Reliability Concepts R S [ R 1 ( R 2 R 3 R 4 R 2 R 3 R 4) R 6 R 1 R 6 ( R 2 R 3 R 4 R 2 R 3 R 4)] u [ R 5 5 5 R 5 4 Q 5 10R 5 3Q 5 2] R 0.8 R S [0.8 (0.928 ) 0.8 0.64( 0.928 )][ 0.942080 ] [0.948480 ][ 0.94208 ] 0.893544
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