Question

A system composes of three components. These components have constant failure rates of 0.0004, 0.0005, 0.0003 failures per hour. The system will stop working, if any one of its components fails. Calculate the following: 1. The reliability of the system at 2500 hour running time? 2. The system hazard rate? 3. Mean time to failure of the system?

Answer 1

soln,

the reliability of a system can be defined as the probability that the product will perform a required function under specified conditions for a certain period of time . in ques the components have constant failure rates therefore the reliability is given by

1)R=e^-(lambeda*t)

failure rates lambeda =.0004,.0005,.0003 failures per hour

operational time =2500 hours

so reliability=e^-(lambeda*2500)=e^-(.0004*2500)

=e^-1=2.71

2)system hazard rate=h(t)=f(t)/R(t) where f(t)=pdfrepresenting a failure distn and R(t)=survival function

=[1/theta e^-1/theta]/e^-1/theta

=1/theta

=lambeda and this is equal to .0004/.271=.0001476failures/cycles

3)mean time to the failure of system

=1/lambeda

1/.0004=2500 hrs.