16ImprovementpotentialTheimprovementpotentialofcomponentiattimetisdefinedas:1lP(ilt) = h(1i,p(t)) -h(p(t))jlP(ilt)is hencethe differencebetween the system reliability witha perfect componentiand the system reliabilitywiththeactual component i.It tells ushow much it is possibletoimprove the current system reliability if we could replace the current component i with aperfectcomponent.NTNU-TrondheimNorwegian University ofScience and Technologywww.ntnu.edu
16 Improvement potential The improvement potential of component ݅ at time ݐ is defined as: ܫூ ݅ݐ ൌ݄ 1, ݐ െ ݄ሺሺݐሻሻ ܫூ ݅ ݐ is hence the difference between the system reliability with a perfect component ݅, and the system reliability with the actual component ݅. It tells us how much it is possible to improve the current system reliability if we could replace the current component ݅ with a perfect component
17ImprovementpotentialConsider a series structure of two independent components,1 and 2,with componentreliabilities pi and p2,respectively.Assumethat p>p2,i.e., component1 is themostreliable of the two.The reliability of the series system is h(p(t)) = PiP2:1. Improvement Potential of component 1 is IIP(1) = P2 - piP22. Improvement Potential of component 2 is IIP(2) = P1 - PiP2Thismeans thatJlP(2)>lP(1)and we can concludethat when using the ImprovementPotential measure,the most important component in a series structure is the one with thelowest reliability.To improve a series structure,we shouldthereforeimprove the"weakest"component,i.e..the component withthelowest reliability.NTNU-TrondheimNorwegian University ofScienceandTechnologywww.ntnu.edu
17 Consider a series structure of two independent components, 1 and 2, with component reliabilities ଵ and ଶ, respectively. Assume that ଵ ଶ, i.e., component 1 is the most reliable of the two. The reliability of the series system is ݄ ݐ ൌଵଶ. 1. Improvement Potential of component 1 is ܫூ 1 ൌଶ െ ଵଶ 2. Improvement Potential of component 2 is ܫூ 2 ൌଵ െ ଵଶ This means that ܫூ 2 ܫூ 1 and we can conclude that when using the Improvement Potential measure, the most important component in a series structure is the one with the lowest reliability. To improve a series structure, we should therefore improve the “weakest” component, i.e., the component with the lowest reliability. Improvement potential
18ImprovementpotentialConsider a parallel structure of two independent components, 1 and 2, with componentreliabilitiesp1 andp2,respectively.Assume that pi>p2,i.e.,component1isthe mostreliableofthetwo.Thereliabilityoftheseriessystemish(p(t))=pi+p2-pip2.1. mprovement Potential of component 1 is I'P(1) = 1 -[pi + p2 -Pip2]2. Improvement Potential of component 2 is IIP(2) = 1 -[P1 + P2 - Pip2]This means that jiP(2)>JiP(1)and we can conclude that when using the ImprovementPotential measure,allthecomponentsinaparallel structureareequallyimportant.NTNU-TrondheimNorwegian University ofScience and Technologywww.ntnu.edu
18 Consider a parallel structure of two independent components, 1 and 2, with component reliabilities ଵ and ଶ, respectively. Assume that ଵ ଶ, i.e., component 1 is the most reliable of the two. The reliability of the series system is ݄ ݐ ൌଵ ଶ െ ଵଶ. 1. Improvement Potential of component 1 is ܫூ 1 ൌ 1 െ ሾଵ ଶ െ ଵଶሿ 2. Improvement Potential of component 2 is ܫூ 2 ൌ 1 െ ሾଵ ଶ െ ଵଶሿ This means that ܫூ 2 ܫூ 1 and we can conclude that when using the Improvement Potential measure, all the components in a parallel structure are equally important. Improvement potential
19ImprovementpotentialAsimplegeometricalcomparisonoftrianglesyieldsIP(ilt)[B(ilt)11 -pi(t)andtheimprovementpotentialcanthereforebeexpressedasrIP(ilt) = IB(ilt) - (1 -pi(t))or,byusingthefaulttreenotation[IP(ilt) =[B(ilt) -qi(t)NTNU-Trondheim莎Norwegian University ofScience and Technologywww.ntnu.edu
19 A simple geometrical comparison of triangles yields ݐ|݅ ܫ 1 ൌ ݐ|݅ ூܫ 1െሺݐሻ and the improvement potential can therefore be expressed as ሻሻݐሺ െ ሺ1 · ݐ|݅ ܫ ൌ ݐ|݅ ூܫ or, by using the fault tree notation ሻሻݐሺݍ · ݐ|݅ ܫ ൌ ݐ|݅ ூܫ Improvement potential
20ImprovementpotentialIn practice, it is not possible to improvethe reliabilityp;(t)of component i to 1o0%reliability.Letusassumethatitispossibletoimprovepi(t)tonewvalue p(")(t) representing,for example,the state of the art for this type of components.:Wemaythencalculatetherealisticorcredibleimprovementpotential(Cip)of componentiat timet, defined by[CIP(ilt) = h (p(n (t)i,p(t)) - h(p(t)where h (p("(t)i,p(t) denotes the system reliability when component iis replaced by anewcomponentwithreliability p(r (t).NTNU-TrondheimNorwegian University ofScienceandTechnologywww.ntnu.edu
20 Improvement potential In practice, it is not possible to improve the reliability ݐ of component ݅ to 100% reliability. Let us assume that it is possible to improve ݐ to new value ሺሻሺݐሻ representing, for example, the state of the art for this type of components. We may then calculate the realistic or credible improvement potential (CIP) of component i at time t, defined by ܫூ ݅ݐ ൌ݄ ሺሻሺݐሻ, ݐ െ ݄ሺሺݐሻሻ where ݄ ሺሻሺݐሻ, ݐ denotes the system reliability when component ݅ is replaced by a new component with reliability ሺሻሺݐሻ