.Level Il methods are reliability methods that use twovaluestodescribeeachuncertainvariable.ie..itsmeanand variance,supplementedwithameasureofcorrelationbetweenthevariables,usuallythecovariance. Reliability index methods, such as thefirst-order second-moment method, are examples ofLevellmethods·Reliability indices determined as safety measures byLevelll methods have a geometric interpretationas adistance measuredin unitsof standarddeviationfromthe mean value to the design point. (Level ll methodsarenot,generally,consideredappropriateforstructuralreliability analysis performed in accordancewiththisClassificationNote.They arereferredtohereforthesakeofcompleteness.)16
• Level II methods are reliability methods that use two values to describe each uncertain variable, ie., its mean and variance, supplemented with a measure of correlation between the variables, usually the covariance. Reliability index methods, such as the first-order second-moment method, are examples of Level II methods. • Reliability indices determined as safety measures by Level II methods have a geometric interpretation as a distance measured in units of standard deviation from the mean value to the design point. (Level II methods are not, generally, considered appropriate for structural reliability analysis performed in accordance with this Classification Note. They are referred to here for the sake of completeness.) 16
Levelill methodsarereliability methods which usethe jointprobability distribution of all the uncertain variables to describethesevariables.Thesemethodsapplytheprobabilityoffailureasthe basic reliability measure.The probabilityoffailure maybetransformedintoageneralisedreliabilityindex.Level lllmethodsincludenumericalintegration,approximativeanalytical methods, such as first-and second-order reliabilitymethods,andsimulationmethods.Simulationmethods.suchasMonte Carlo simulation and directional sampling, are alsoapproximative,butconvergetowardsexactsolutions..This Classification Note is concerned with structural reliabilityanalysesundertakenusingLevel lllmethods.17
• Level III methods are reliability methods which use the joint probability distribution of all the uncertain variables to describe these variables. These methods apply the probability of failure as the basic reliability measure. The probability of failure may be transformed into a generalised reliability index. • Level III methods include numerical integration, approximative analytical methods, such as first- and second-order reliability methods, and simulation methods. Simulation methods, such as Monte Carlo simulation and directional sampling, are also approximative, but converge towards exact solutions. • This Classification Note is concerned with structural reliability analyses undertaken using Level III methods. 17
·Level IV methods are reliability methods that comparea structural prospect with a reference prospectaccording to the principles of engineering economicanalysis under uncertainty. Such a decision analysisconsiderscostsandbenefitsof constructionmaintenance, repair and consequences offailure.?Level Iv methods can be used to assess targetreliabilities to be used as acceptance criteria forreliabilityanalyses basedon Level lllmethods.18
• Level IV methods are reliability methods that compare a structural prospect with a reference prospect according to the principles of engineering economic analysis under uncertainty. Such a decision analysis considers costs and benefits of construction maintenance, repair and consequences of failure. • Level IV methods can be used to assess target reliabilities to be used as acceptance criteria for reliability analyses based on Level III methods. 18
Failure criteria for significant structural failure modesare to beformulated in accordance with the current state-of-the-art withinthe particular technical field. Suggested references within thepublicationsofDetNorskeVeritasareDNVRules,ClassificationNotes,andRecommendedPractices..Uncertainties in load, strength and other governing properties areusuallytobeestimatedfromdatafrommeasurementsorfromtestdata banks.Targetreliability values to be usedas acceptancecriteriaforcalculatedreliabilitiesdependonvariousconditions,includingtheconsequenceoffailure,modeluncertainty,redundancy,possibilityofwarningoffailureetc19
• Failure criteria for significant structural failure modes are to be formulated in accordance with the current state-of-the-art within the particular technical field. Suggested references within the publications of Det Norske Veritas are DNV Rules, Classification Notes, and Recommended Practices. • Uncertainties in load, strength and other governing properties are usually to be estimated from data from measurements or from test data banks. • Target reliability values to be used as acceptance criteria for calculated reliabilities depend on various conditions, including the consequence of failure, model uncertainty, redundancy, possibility of warning of failure etc. 19
FreqResistancedLoad<)=F (x)f(x)dxOORR-QB:Stress & LoadR0B0tlndicationonlyNot a measure!Z=R-QP = Φ(-β)P, = p[z<0]= F(0)=20
20