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

x=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)
> length(x)
[1] 25
> sum(x)
[1] 981
> lam=25/981;lam
[1] 0.0254842
> F_bar=c()
> for(i in 1:length(x))
+ {
+ F_bar[i]=exp(-lam*x[i])
+ }
> plot(F_bar,main="plot of reliability function",type="l")

> F=1-F_bar
> pdf=c()
> pdf[1]=F[i]
> for(i in 2:25)
+ {
+ pdf[i]=F[i]-F[i-1]
+ }
> x1=x[-1];pdf1=pdf[-1]
> plot(x1,pdf1,type="l",main="plot of pdf")
> hist(pdf1,main="plot of histogram of pdf")

> hz=pdf/F_bar ##hazard function
> plot(hz,type="l",main="plot of hazard function")

> data.frame(failure_time=x,reliability_fun=F_bar,pdf,hazard_fun=hz)
failure_time reliability_fun pdf hazard_fun
1 5 0.8803630 0.813990436 0.92460777
2 6 0.8582111 0.022151885 0.02581170
3 8 0.8155655 0.042645624 0.05228964
4 10 0.7750389 0.040526507 0.05228964
5 11 0.7555372 0.019501699 0.02581170
6 12 0.7365263 0.019010993 0.02581170
7 15 0.6823156 0.054210671 0.07945102
8 20 0.6006854 0.081630215 0.13589513
9 24 0.5424709 0.058214446 0.10731349
10 29 0.4775713 0.064899614 0.13589513
11 33 0.4312883 0.046283047 0.10731349
12 40 0.3608229 0.070465350 0.19529068
13 43 0.3342652 0.026557712 0.07945102
14 50 0.2796518 0.054613391 0.19529068
15 54 0.2525498 0.027102000 0.10731349
16 58 0.2280744 0.024475454 0.10731349
17 60 0.2167410 0.011333311 0.05228964
18 60 0.2167410 0.000000000 0.00000000
19 61 0.2112874 0.005453685 0.02581170
20 62 0.2059709 0.005316459 0.02581170
21 62 0.2059709 0.000000000 0.00000000
22 63 0.2007882 0.005182685 0.02581170
23 64 0.1957359 0.005052277 0.02581170
24 65 0.1908108 0.004925150 0.02581170
25 66 0.1860096 0.004801223 0.02581170
>