CDOoDocuments.StdDocumentDescDocuments.DocumentDescContainers.ViewDescViews.ViewDescStores.StoreDesc"Documents.ModelDescContainers.ModelDescModels.ModelDescStores.ElemDesc! !TextViews.StdViewDescTextViews.ViewDesc!TextModels.StdModelDescTextModels.ModelDescQTextModels.AttributesDesc*: KEVLAR NO SPOOLS LOGNORMAL PRIOR I ########################################################################################## ############### This program represents the collaborative efforts of Avery Ashby, ############### ############### Ramon Leon, and Jayanth Thyagarajan. This is an inclusive odc file ############### ############### containing the model, data, and initial values. March 20, 2002. ############### ########################################################################################## ########################################################################################## ############### MODEL ############### ########################################################################################## model KevlarNoSpoolsLognormalPrior1to2; { ############### Generation of prior values ############### intercept ~ dnorm(0,0.001) # Intecept prior beta.stress ~ dnorm(0,0.001) # Fixed stress effect ############### Creates a lognormal prior for the shape parameter of the Weibull ############### ############### where most certainly r (Beta) is between 1 and 5 ############### anot <- -0.80472 mu <- anot * -1 bnot <- 0.31241 tau <- pow(bnot,-2) # tau = 1/(bnot^2) r ~ dlnorm(mu,tau) # Weibull shape parameter ########################################################################################## ############### This loop reads in the data and calculates Weibull scale parameter ############### for(j in 1:M ) { # M is the number of rows in the data (108) log(eta[j]) <- intercept + beta.stress * log(stress[j]) # This is the function for mu in the Weibull lambda[j] <- pow(eta[j],-r) # Rescale into lambda parameterization } # for use in winBUGS 1.4 ############### End of loop ############### ########################################################################################## ############### This loop gives failure times as exact or censored ############### for(j in 1:M ) { t[j] ~ dweib(r,lambda[j])I(cen[j],) # Failure times are Weibull or censored } ############### End of loop ############### ########################################################################################## ############### Calculates specified failure quantiles for a given spool ############### eta234 <- exp(intercept + beta.stress * log(23.4)) # Eta values at 23.4 MPa stress level quan234 <- eta234 * pow((-log(1 - 0.01)),(1/r)) # 1st percentile at 23.4 MPa stress lambda234 <- pow(eta234,-r) # Rescale into lambda parameterization y.234new ~ dweib(r,lambda234) # Predicted distribution for 23.4 MPa stress probability234 <- 1 - exp(-(pow((1000/eta234),r))) # Prob of failure at 1000 hours for each spool eta225 <- exp(intercept + beta.stress * log(22.5)) # Eta values at 22.5 MPa stress quan225 <- (eta225 * pow((-log(1 - 0.5)),(1/r))) / 1000 # 50th percentile at 22.5 MPa stress (/ 1000) lambda225 <- pow(eta225,-r) # Rescale into lambda parameterization y.225new ~ dweib(r,lambda225) # Predicted distribution for 22.5 MPa stress probability225 <- 1 - exp(-(pow((1000/eta225),r))) # Prob of failure at 1000 hours for each spool ######################################################################################### } ############### End of program model ############### ######################################################################################### ######################################################################################### ############### DATA ############### ######################################################################################### list(M = 108, stress = c(29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7, 29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7, 29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7,29.7, 29.7,29.7,29.7,27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6, 27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6,27.6, 27.6,27.6,27.6,25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5, 25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5,25.5, 25.5,25.5,25.5,23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4, 23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4,23.4), #spool = c(2,7,7,7,7,6,7,5,2,2,2,3,5,7,3,6,3,2,7,2,7,5,8,3,2,6,2,5,4,1,8,8,1,1,1,4, # 4,4,4,3,3,3,2,3,2,2,2,1,2,6,6,2,8,1,2,4,1,6,4,4,1,8,4,6,7,3,2,2,2,2,3,8, # 2,8,2,6,8,8,6,8,8,1,5,4,1,4,1,7,7,6,3,5,2,6,5,6,5,1,1,1,1,4,4,4,4,8,8,8), cen = c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,41000,41000,41000, 41000,41000,41000,41000,41000,41000,41000,41000), t = c(2.2,4,4,4.6,6.1,6.7,7.9,8.3,8.5,9.1,10.2,12.5,13.3,14,14.6,15, 18.7,22.1,45.9,55.4,61.2,87.5,98.2,101,111.4,144,158.7,243.9, 254.1,444.4,590.4,638.2,755.2,952.2,1108.2,1148.5,1569.3, 1750.6,1802.1,19.1,24.3,69.8,71.2,136,199.1,403.7,432.2,453.4, 514.1,514.2,541.6,544.9,554.2,664.5,694.1,876.7,930.4,1254.9, 1275.6,1536.8,1755.5,2046.2,6177.5,225.2,503.6,1087.7,1134.3, 1824.3,1920.1,2383,2442.5,2974.6,3708.9,4908.9,5556,6271.1, 7332,7918.7,7996,9240.3,9973,11487.3,11727.1,13501.3,14032, 29808,31008,4000,5376,7320,8616,9120,14400,16104,20231, 20233,35880,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA)) ############### End of data ############### ######################################################################################## ######################################################################################## ############### INITIAL VALUES ############### ######################################################################################## list(intercept = 84.1, beta.stress = -23.1, r = 1.21) # initial values based on Crowder et al. (1991) list(intercept = 1, beta.stress = -1,r = 1) ############### End of initial values ############### ########################################################################################TextControllers.StdCtrlDescTextControllers.ControllerDescContainers.ControllerDescControllers.ControllerDesc TextRulers.StdRulerDescTextRulers.RulerDescTextRulers.StdStyleDescTextRulers.StyleDescZTextRulers.AttributesDesc$0ZGo * <[ @Documents.ControllerDesc vz pk ~