Accelerated Life Testing of Motorettes

Description

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.

Usage

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)
summary(motor.wei)
# and predict at 130C
unlist(predict(motor.wei, data.frame(temp=130), se.fit = TRUE))

motor.cox <- coxph(Surv(time, cens) ~ temp, motors)
summary(motor.cox)
# 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)) )

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(MASS)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MASS/motors.Rd_%03d_medium.png", width=480, height=480)
> ### Name: motors
> ### Title: Accelerated Life Testing of Motorettes
> ### Aliases: motors
> ### Keywords: datasets
> 
> ### ** 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)
> summary(motor.wei)

Call:
survreg(formula = Surv(time, cens) ~ temp, data = motors)
              Value Std. Error     z         p
(Intercept) 16.3185    0.62296  26.2 3.03e-151
temp        -0.0453    0.00319 -14.2  6.74e-46
Log(scale)  -1.0956    0.21480  -5.1  3.38e-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 

> # 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 = 0.076 )
Rsquare= 0.472   (max possible= 0.936 )
Likelihood ratio test= 25.56  on 1 df,   p=4.299e-07
Wald test            = 11.27  on 1 df,   p=0.0007863
Score (logrank) test = 22.73  on 1 df,   p=1.862e-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
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>