ModellingconsequencesfromfailureandmaterialpropertiesbydistributionmixturesOriginalResearchArticle

Themainresultofthispaperisthefindingthatthemaximumvarianceofanydistributionmixtureisattainedfromsamplingoneoratmosttwoindividualdistributionscomposingthemixture.Anupperboundforthevarianceofthepropertiesfromsamplinginhomogeneousmicrostructureisderivedwhichdoesnotdependontheprobabilitieswithwhichtheindividualmicrostructuralzonesaresampled. Apowerfulanalogyexistsbetweenthedistributionofthemechanicalpropertiesfromsamplinginhomogeneousmicrostructureandthedistributionofconsequencesgivenfailure.Theconsequencesfromfailurearemodelledbyadistributionmixturecomposedoftheindividualdistributionsoftheconsequencesfromfailurecharacterisingmutuallyexclusivefailuremodes.Similarly,anefficientalgorithmisdevelopedwhichdeterminestheupperboundofthevarianceoftheconsequencesfromfailureirrespectiveoftheprobabilitiesoftriggeringtheseparatefailuremodes.Theconcept‘potentiallossesfromfailure’isintroduced.Itisdemonstratedthatthepotentiallossesfromfailureisadistributionmixtureanditsexpectedvalueequalstheriskoffailure.Anexpressionforthevarianceofthepotentiallossesfromfailureisalsoderived. Usingthemodeloftheconsequencesfromfailureasadistributionmixture,amethodisdevelopedforsettingreliabilityrequirementsbasedonminimumfailure-freeoperatingperiods(MFFOP).TheMFFOPreliabilityrequirementslimittheriskofprematurefailurebelowamaximumacceptablelevel.