Exercises 11

For this exercise the following parameters are given:

Parameter

Value

Comment

λDU

3E-05

Rate of DU failures

λS

1E-04

Rate of safe failures which requires production shutdown

τ

730

Same proof test interval for all components

MTTR

24 hours

Mean time to repair a safe failure

β

5 %

Common cause failure fraction, standard situation

β-staggered

2 %

Common cause failure fraction when staggered testing is introduced

Problem 1

Consider a 1oo2 configuration
  1. Find PFD, and compare the dependent and independent part
  2. Find the expected number of hours per year where the production system is down due to safe failures

Problem 2

Consider a 2oo3 configuration.
  1. Find PFD with the standard β-factor model
  2. Find PFD with the PDS method
  3. Find the expected number of hours per year where the production system is down due to safe failures, compare with problem 1
  4. What would be the reduction in PFD if you change from a 2oo3 to a 1oo3 voting (assuming) PDS approach, and what is the increase in the yearly number of hours of lost production

Problem 3

Consider again a 1oo2 configuration. Now, assume that the SIS is tested every month, but that every second time component 1 is tested, and every other second time component 2 is tested. The component not being tested is assumed to be left untouched. By staggered testing, the likelihood of introducing common cause failures is reduced, hence the β value is set to 2%. Assume that if a common cause failure is revealed when one component is tested, also the other component is checked for that failure cause.
  1. Find PFD, and compare the dependent and independent part
  2. Compare the result with problem 1

Problem 4

Find the PFH by using the PDS method in case of
  1. You have a 1oo2 system
  2. You have a 2oo3 system