case0802: Breakdown Times for Insulating Fluid under different Voltage

In Sleuth3: Data Sets from Ramsey and Schafer's "Statistical Sleuth (3rd Ed)"

Description

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.

Usage

case0802

Format

A data frame with 76 observations on the following 3 variables.

Time

times until breakdown (in minutes)

Voltage

voltage applied (in kV)

Group

factor variable (group number)

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Nelson, W.B., 1970, G.E. Co. Technical Report 71-C-011, Schenectady, N.Y.

Examples

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[2]))   # 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[1] + beta[2]*dummyVoltage  
medianTime <- exp(meanLogTime)  
lines(medianTime ~ dummyVoltage, lwd=2, col="blue")  

detach(case0802)

Example output

'data.frame':	76 obs. of  3 variables:
 $ Time   : num  5.79 1579.52 2323.7 68.85 108.29 ...
 $ Voltage: int  26 26 26 28 28 28 28 28 30 30 ...
 $ Group  : Factor w/ 7 levels "Group1","Group2",..: 1 1 1 2 2 2 2 2 3 3 ...
Analysis of Variance Table

Model 1: logTime ~ Voltage
Model 2: logTime ~ factor(Voltage)
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     74 180.07                           
2     69 173.75  5    6.3259 0.5024 0.7734
Voltage 
 39.792 
           2.5 %   97.5 %
Voltage 46.29848 32.49719

Sleuth3 documentation built on May 2, 2019, 6:41 a.m.