A Discussion About Drenick’s Theorem
Abstract
FredĀ and Philip Sage discussing the possible source of the widespread use of MTBF.
Key Points
Join Fred and Philip as they discuss Drenick’s theorem and it uses and misuses. Plus they discuss a wide range of other topics concerning reliability engineering.
Topics include:
- Philip’s response to Fred’s article on Drenick’s Theorem
- How paying attention to what is useful actually works
- The when, how, and why MTBF is not a useful measure.
Enjoy an episode of Speaking of Reliability. Where you can join friends as they discuss reliability topics. Join us as we discuss topics ranging from design for reliability techniques to field data analysis approaches.
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Show Notes
Article on Drenick’s Theorem on the NoMTBF.com blog
I loved the podcast, thanks Fred and Phil. I have many comments which I’ll leave later. I wrote a paper using Drenick’s Theorm in 1996 ( “Use of a Simulation Model to Select Preventive Maintenance Times,” David Coit, Communications in Reliability, Maintainability & Supportability, vol. 3, no. 1, January 1996). This an short-lived SAE journal that is now defunct. This based on work I was doing earlier for IITRI. I had actually never heard of Drenick or his theorem But I arrived on the same result on my own. I was somewhat disappointed when I found our someone else had done this 30 years earlier š
Thanks as always for listening and commenting David.
I’ll have to see if I can find a copy of the paper. Thanks for the reference.
Although if your paper supports the use of MTBF, I will be disappointed. š
cheers,
Fred
Here is the longer version of my comments. Maybe of these were already stating by Fred or Phil, so just adding emphasis
1. Drenick’s Theorem is mathematically provable, so it shouldn’t be criticized. If someone applies it where it does not belong or makes an incorrect assumption using this theorem as his rationale, don’t blame poor Drenick.
2. Even when Drenick’s Theorem does apply, it should NEVER be used as justification for an exponential failure time distribution for components or lower-level assemblies.
3. For most consumer products with a mixture of components, Drenick’s Theorem will NEVER apply within the useful life of the system, because we will never reach steady state, which requires many multiples of the mean life of the components.
4. Even if the system is complex, if it dominated a one or several failure mechanisms, again Drenick’s Theorem doesn’t apply (Fred mentioned this).
5. So when does Drenick’s Theorem apply? actually many places, machines in machine shops or heavy industry, mechanical systems in trains and subways, the railroad tracks themselves (a system of smaller track segments), systems of nozzles in coal burning plant, many systems in many energy plants, etc., so if applied correctly, it can be useful and can help decision-making!
6. If some or all components are replaced preventatively instead of at failure, Drenick’s theorem may still apply, as long as the replacement is done at the time that the on-condition state is reaches. However, in this case, the steady state rate of occurrence of failures will be lower.
That’s enough for now, although I have more. Keep up the good work !
A bit of a novice at this, and the higher concepts are beyond my current level of understanding, but… Could the theorem be applied for example to a large water distribution or collection network to justify increased redundancy of equipment at node points (pumping stations and chemical dosing – duty standby arrangements) and the implementation of a ārun to failā maintenance strategy?
Hi Michael, no not really…. set up your maintenance strategy based on the failure mechanisms you are experiencing. If wear out or corrosion is an issue, then monitor and plan maintenance to avoid the eventual failures.
Run to failure may be appropriate for some elements of your system, and very expensive for most of it.
Drenick’s theorem is not a justification for a run to failure approach. You have to consider the cost of unscheduled downtime, damage tot he system by running worn out or faulty equipment, etc.
Cheers,
Fred
Can I also have a copy of your paper? Thanks for the comment!