A flange bolt wears out because of fatigue in accordance wit

A flange bolt wears out because of fatigue in accordance with the lognormal distribution with MTTF = 10, 000 hr and s = 2.00. If preventive maintenance consists of periodically replacing the bolt, what is the reliability at 550 hr with and without preventive maintenance? Assume that the bolts are replaced every 100 operating hours.

Solution

solution:

strength of material always follow lognormal distribution means ,its log value has shape like normal distribution curve

1) here failure rate is given by

failure rate=m=1/MTTF=1/10000=10^-4 1/s

2) system reliability at t=550 hr without maintainance is

R1=exp^(-m*t)

R1=exp^(10^-4*550)=.9464=94.64%

3) where when preventive maintainance is carry out for every 100 hr means after every 100 hr new bolt available with 100%,hence till 550 hr 5 replacement and new bolt in operation for 50 hr only ,hence system reliability with maintainance means system reliability at t=50 hr

R2=exp^(m*t)=exp^(10^-4*50)=0.995012=99.50%

4) hwnce system reliability

without maintainance as R1=94.64%

with maintainance a R2=99.501%