Accelerated Life Testing of Motorettes

The motors data frame has 40 rows and 3 columns. It describes an accelerated life test at each of four temperatures of 10 motorettes, and has rather discrete times.

motors

Format

This data frame contains the following columns:

temp

the temperature (degrees C) of the test.

time

the time in hours to failure or censoring at 8064 hours (= 336 days).

cens

an indicator variable for death.

Source

Kalbfleisch, J. D. and Prentice, R. L. (1980) The Statistical Analysis of Failure Time Data. New York: Wiley.

taken from

Nelson, W. D. and Hahn, G. J. (1972) Linear regression of a regression relationship from censored data. Part 1 – simple methods and their application. Technometrics, 14, 247–276.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(survival)
plot(survfit(Surv(time, cens) ~ factor(temp), motors), conf.int = FALSE)

# fit Weibull model
motor.wei <- survreg(Surv(time, cens) ~ temp, motors)
## IGNORE_RDIFF_BEGIN
summary(motor.wei)
#> 
#> Call:
#> survreg(formula = Surv(time, cens) ~ temp, data = motors)
#>                Value Std. Error     z       p
#> (Intercept) 16.31852    0.62296  26.2 < 2e-16
#> temp        -0.04531    0.00319 -14.2 < 2e-16
#> Log(scale)  -1.09564    0.21480  -5.1 3.4e-07
#> 
#> Scale= 0.334 
#> 
#> Weibull distribution
#> Loglik(model)= -147.4   Loglik(intercept only)= -169.5
#> 	Chisq= 44.32 on 1 degrees of freedom, p= 2.8e-11 
#> Number of Newton-Raphson Iterations: 7 
#> n= 40 
#> 
## IGNORE_RDIFF_END
# and predict at 130C
unlist(predict(motor.wei, data.frame(temp=130), se.fit = TRUE))
#>    fit.1 se.fit.1 
#> 33813.06  7506.36 

motor.cox <- coxph(Surv(time, cens) ~ temp, motors)
summary(motor.cox)
#> Call:
#> coxph(formula = Surv(time, cens) ~ temp, data = motors)
#> 
#>   n= 40, number of events= 17 
#> 
#>         coef exp(coef) se(coef)     z Pr(>|z|)    
#> temp 0.09185   1.09620  0.02736 3.358 0.000786 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#>      exp(coef) exp(-coef) lower .95 upper .95
#> temp     1.096     0.9122     1.039     1.157
#> 
#> Concordance= 0.84  (se = 0.035 )
#> Likelihood ratio test= 25.56  on 1 df,   p=4e-07
#> Wald test            = 11.27  on 1 df,   p=8e-04
#> Score (logrank) test = 22.73  on 1 df,   p=2e-06
#> 
# predict at temperature 200
plot(survfit(motor.cox, newdata = data.frame(temp=200),
     conf.type = "log-log"))

summary( survfit(motor.cox, newdata = data.frame(temp=130)) )
#> Call: survfit(formula = motor.cox, newdata = data.frame(temp = 130))
#> 
#>  time n.risk n.event survival  std.err lower 95% CI upper 95% CI
#>   408     40       4    1.000 0.000254        0.999            1
#>   504     36       3    1.000 0.000498        0.999            1
#>  1344     28       2    0.999 0.001910        0.995            1
#>  1440     26       1    0.998 0.002697        0.993            1
#>  1764     20       1    0.996 0.005325        0.986            1
#>  2772     19       1    0.994 0.007920        0.978            1
#>  3444     18       1    0.991 0.010673        0.971            1
#>  3542     17       1    0.988 0.013667        0.962            1
#>  3780     16       1    0.985 0.016976        0.952            1
#>  4860     15       1    0.981 0.020692        0.941            1
#>  5196     14       1    0.977 0.024941        0.929            1