A construction worker is considering the possibility of machinery having a life

Question

A construction worker is considering the possibility of machinery having a life time that follows the Weibull CDF F_x(x) = 1 - e^-(x/theta)^beta, for x > 0. To test this, he observed the following simple random sample of X: 3.1 15.3 23.6 7 12.4 2.2 1. Plot de data in the PP plot corresponding to the Weibull CDF. Write a table providing the abscissas and coordinates of the plotted points 2. Plot the straight line that you think is the best fit to the points in the PP plot of the previous question. Estimate theta and beta using the fitted line 3. Test the null hypothesis H_0: X ~ Weibull(theta = 10, beta = 2) using the Kolmogorov-Smirnov test with a type I error probability 0.05. Would you reject H_0?

Explanation / Answer

Problem 1

#Creating the data set

X<-c(3.1,15.3,23.6,7,12.4,2.2)

#load package Renext

#generating pp plot

Y<-weibplot(X,shape=1.416677,scale=11.671509,mono=FALSE)
Y

Problem 2

# fiting straight line to estimate the parameters
fit<-fitdistr(X, densfun="weibull", lower = 0)
fit

# load package reliaR
#generating qq plot
A<-qq.weibull.ext(X, alpha.est= 11.671509,beta.est=1.416677, line.qt = FALSE)
A

Problem 3

# Load package Sim.DiffProc
# KS test
test_ks_dweibull(X,shape=1.416677,scale=11.671509)

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