Question

For the following data set, tabulate and plot the nonparametric the a) reliability function, b) probability density function, and c) hazard function. There are 25 systems on test with the following times to failure.

5, 6, 8, 10, 11, 12, 15, 20, 24, 29, 33, 40, 43, 50, 54, 58, 60, 60, 61, 62, 62, 63, 64, 65, 66

What observations would you make based on your analysis?

Answer 1

## The above example soved using R :

## The Data is given
##

sample=c(5, 6, 8, 10, 11, 12, 15, 20, 24, 29, 33, 40, 43, 50, 54, 58, 60, 60, 61, 62, 62, 63, 64, 65, 66) sample

lam <- 25

dens <- dexp(sample, rate=lam)

cdf <- pexp(sample, rate=lam) reli <- 1 - cdf hazd <- dens/reli

par(mfrow=c(2, 2)) plot(sample, dens, type="l",main="Density plot") plot(sample, cdf, type="l",main="cdf plot") plot(sample, reli, type="l",main="reliability plot") plot(sample, hazd, ylim=c(0, 4), type="l",main="hazard plot")