Breakdown Times for Insulating Fluid under different Voltage
In an industrial laboratory, under uniform conditions, batches of electrical insulating fluid were subjected to constant voltages until the insulating property of the fluids broke down. Seven different voltage levels were studied and the measured reponses were the times until breakdown.
A data frame with 76 observations on the following 3 variables.
times until breakdown (in minutes)
voltage applied (in kV)
factor variable (group number)
Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.
Nelson, W.B., 1970, G.E. Co. Technical Report 71-C-011, Schenectady, N.Y.
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str(case0802) attach(case0802) ## EXPLORATION plot(Time ~ Voltage) myLm <- lm(Time ~ Voltage) plot(myLm, which=1) # Residual plot logTime <- log(Time) plot(logTime ~ Voltage) myLm <- lm(logTime ~ Voltage) abline(myLm) plot(myLm,which=1) # Residual plot myOneWay <- lm(logTime ~ factor(Voltage)) anova(myLm, myOneWay) # Lack of fit test for simple regression (seems okay) ## INFERENCE AND INTERPREATION beta <- myLm$coef 100*(1 - exp(beta)) # Back-transform estimated slope 100*(1 - exp(confint(myLm,"Voltage"))) # Interpretation: Associated with each 1 kV increase in voltage is a 39.8% # decrease in median breakdown time (95% CI: 32.5% decrease to 46.3% decrease). ## DISPLAY FOR PRESENTATION options(scipen=50) # Do this to avoid scientific notation on y-axis plot(Time ~ Voltage, log="y", xlab="Voltage (kV)", ylab="Breakdown Time (min.); Log Scale", main="Breakdown Time of Insulating Fluid as a Function of Voltage Applied", pch=21, lwd=2, bg="green", cex=1.75 ) dummyVoltage <- c(min(Voltage),max(Voltage)) meanLogTime <- beta + beta*dummyVoltage medianTime <- exp(meanLogTime) lines(medianTime ~ dummyVoltage, lwd=2, col="blue") detach(case0802)
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