Week 12: Asset Criticality & Reliability Flashcards
How does a series system behave?
Like an OR gate.
How does a parallel system behave?
Like an AND gate.
What is reliability?
The probability that a component/ system will function properly.
What is the formula for a series system?
Rs = Ps^s1 * Ps^s2 etc
What is the formula for a parallel system?
Ps^f = (1-Ps^s1) * (1-Ps^s2) etc
Rs = 1 - Ps^f
To maximise the improvement in network reliability …
One should improve the link with the highest reliability importance (RIa) where:
RI_a = dR/dr_a
How would you calculate reliability for a simple network with 2 links in series? And its reliability importance (RI_a)?
what happens when link 1 is more reliable than link 2?
R = (probability that link 1 survives) * (probability that link 2 survives)
= r1 * r2
RI1 = r2 RI2 = r1
If link 1 is more reliable than link 2 (r1 > r2), then RI1 < RI2. Hence, you should improve link 2 as you should improve the less reliable link.
How would you calculate reliability for a simple network with 2 links in parallel? And its reliability importance (RIa)?
1 - R = (probability that link 1 fails) * (probability that link 2 fails)
= (1-r1) * (1-r2)
R = 1 - (1-R)
RI1 = 1 - r2 RI2 = 1- r1
If link 1 is more reliable, this is a counter-intuitive result.
What do you do if you have a counterintuitive result (Birnbaum)?
You must perform time-consuming tasks to find adequate estimates for input parameters.
Start with rough estimates, calculate Birnbaum’s measure of importance for various components/parameter sensitivities and spend most of the time finding high quality data for the most important components.
Lowest value of Birnbaum’s measure will have negligible effect on reliability. Extra efforts to find high quality data for components is a waste of time!
Explain redundancy.
Level of redundancy = (n-k)
k = minimum number of properly functioning components for system to function.
If more than (n-k) functions fail, system fails.
