<jupyter_start><jupyter_text>Nonrepairable parallel structuresFailure rate function for a parallel structure of two independent and identical components that are Weibull distributed with $\alpha=1.8$ and $\theta=1$<jupyter_code>t<-seq(0, 3, length=300) # time axis
a<-1.8
# the Weibull shape parameter
th<-1                # the Weibull scale parameter
th1<-2^(-1/a)*th     # the transformed scale parameter
m<-(2*th-th1)*gamma(1+1/a) # the MTTF
x<-2*dweibull(t, a, th, log=FALSE) -
dweibull(t, a, th1, log=FALSE)
y<-1+pweibull(t, a, th1, log=FALSE) -
2*pweibull(t, a, th, log=FALSE)
z<-x/y
plot(t, z, type="l")
segments(m, 0, m, 2.1)
text(m, 2.6, expression(MTTF[S]))<jupyter_output><empty_output>
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