可能性概率probability-展示頁(yè)
2025-05-25 18:13本頁(yè)面
【正文】 ils ? Success / Failure ? ? Probability of Complementary Events ? P(A*) = 1 – P(A) ? Probability of successful operation for the next year is . ? What is the probability of failure the next year ? (0,2) 169。 ABB Page 8 Functional safety Event Types ? Independent – ? Events that do not affect each other ? Coin Tosses ? Dice Throws ? Complimentary – ? When one oute does not occur, the other will always occur ? Coin ? Mutually Exclusive – ? When one event occur the other can not happen ? Dice 169。 ABB Page 6 Functional safety Probability Assignment ? Probability assigned by two methods: ? Physical property determination ? Geometry, physical shape ? Experimental oute determination ? Number of occurrences/Number of Trials ? Probability is a number : (0 P 1) 169。 ABB Page 4 E x t e n d e d A u t o m a t i o n S y s t e m 8 0 0 x A Functional safety Engineering Probability 169。 ABB Page 2 Functional safety Probability multiplication PFD= P(A ∩ B)+P(B ∩ C) +P(A ∩ C) A1 A2 B1 B2 診斷覆蓋率 DC 診斷覆蓋率 DC 未診斷率 1DC 169。169。 ABB Page 1 Functional safety Probability multiplication PFD=PD(A∩B) = PD (A) * PD (B) A B PDU PDU PDD PDD 共因系數(shù) b 診斷覆蓋率 DC A B PSU PSU PSD PSD 共因系數(shù) b 診斷覆蓋率 DC PFD=PD(A∩B) = PD (A) + PD (B) – PD (A ∩ B) PFS=PS(A∪ B) = PS (A) + PS (B) PD (A) * PD (B) 169。 ABB Page 3 Functional safety 169。 ABB Page 5 Functional safety Probability ? Rules of Probability ? Types of Event ? Probability multiplication ? Probability addition ? Fault Trees 169。 ABB Page 7 Functional safety Probability ? P(Gold) = ? P(Mable) = 169。 ABB Page 9 Functional safety Independent Events ? Events that do not effect each other ? Tossing of two coins ? Throwing a pair of dice ? Failure of one ponent in a system ? ? Normally considered independent 169。 ABB Page 11 Functional safety Mutually Exclusive Events ? Mutually Exclusive ? When one event occur the other can not happen ? Toss of one die ? Oute of 1,2,3,4,5,6 are mutually exclusive 169。 ABB Page 13 Functional safety Probability multiplication ? For Independent events ? P ( A AND B ) = P (A) * P (B) Limit Switch Solenoid Valve ? In the next year, the probability of successful operation for a limit switch is and the probability of successful operation for a solenoid valve is . ? What is the probability of success for the system consisting of both elements ? ? Limit switch AND solenoide ? P(A)*P(B)= * = 169。 ABB Page 15 Functional safety Probability Addition ? Mutually Exclusive Events ? P(A or B) = P(A) + P(B) ? Roll 1 die. ? What is the probability of getting a 4 or a 6 ? ? Probability of getting 4 1/6 ? Probability of getting 6 1/6 ? The probability of rolling 4 OR 6 ? P(A) + P(B) = 1/6 + 1/6 = 2/6 169。 ABB Page 17 Functional safety Probability Addition ? Independent Events ? P(A or B) = P(A) + P(B) – P(A AND B) ? A bag contains 100 objects. ? All are either round marbles or square blocks ? All are either red or gold ? 75 % of objects are marbles ? 80 % of the objects are gold ? If an object is randomly selected what is the
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