Reliability Block Diagram confusing results

[mciemian]

We are having trouble duplcating the Windchill Quality Solutions RBD calculations. We have tried a simple problem and the tool calculation is different then the hand calculations.

We have a 2 of 3 parallel operating block with an individual MTBF of 1000 for each of the items placed in seires with a block with an mtbf of 500.

Goal was to verify effective system MTBF.

Hand methods show answer as 312.5, but RBD results are at 350. We've looked at all the setups and parameters and can't determine why it is different.

Anyone else experieinced similar results not matchiing hand calculations like this ?

[gmongiardino]

I have the same problem with a different but equally simple configuration.

Furthermore, I tried your configuration and I obtained the same (wrong) result.

[ptc-2749313]

Hello all,

This is a common request of our technical support. The summary of my response is that our calculations are correct, and the handbook calculations you are referencing are approximations and are incorrect.

Here are the details:

- The reported MTBF value of 350 is nothing but the MTTF value in RBD. We calculate effective MTBF directly and also calculate equivalent failure rate (see below).

- So, what is effective MTBF?

If we use preventive maintenance, we can eliminate the failures or reduce failure rate by renewing the system before it fails. So, the mean time to failure will increase with PM. So, the effective MTBF is always greater than the MTTF (when failure rate is an increasing function). If there is no preventive maintenance (or its interval is too long), then it is equal to the MTTF (sometime it is called MTBF as well). So, there is no software bug in the RBD and it works as expected.

Why the difference?

The handbook calculation of MTBF as the reciprocal of failure rate, which is an approximation.

If you want to use this method, you can use equivalent failure rate in RBD and calculate MTBF as the reciprocal of equivalent failure rate. The equivalent failure rate at 1000 is 3182.72 E-6. So, the MTBF is 314.27. However, you may not like this approach because the equivalent failure rate is a function of time. You may not know what time to use in the calculation.

What is the 312.5 value?

1. It is based some approximations. You assume that FR = 1/MTBF and MTBF = 1/FR for all cases.
2. They calculate failure rate of each block as the reciprocal of MTTF. There are two blocks in the system: (1) 2/3 with component MTBF of 1000, and (2) single block with MTBF of 500. The respective MTTF values are: (1) 5/6 * 1000, and 500.
3. MTTF of 2/3 redundancy: 1/(3FR) + 1/(2FR) = 5/(6FR) – can be derived either from Markov chains or integration of reliability function
4. Then calculate failure rate as the reciprocal of MTTF. Hence, after applying FRM of 1E6, we get: (1) 6/5 * 1000, and (2) 2000.
5. This is an approximation. It is not exact, because 2/3 block’s failure rate is not constant even though each component within the block follows exponential distribution
6. Because the blocks are in series, find the system failure rate as the sum of the failure rates of the blocks. Hence, FR = 16/5 * 1000.
7. Then find the MTBF as the reciprocal of FR. Hence, MTBF = 5/16 * 1000 = 312.5
8. This step is also an approximation, because the system failure time distribution is not exponential.

[gmongiardino]

Thanks a lot Daniel!

I was wrong because I forgot that the failure rate of a parallel is not constant although the individual failure rates are constant.

[Raymond_Yuen]

Can you please tell me how I can display the Failure rate (unit) instead of the failure rate (predicted) in the RBD? We attach the RBD diagrams for different system configuration in the same report. Showing different predicted failures on each diagram for the same assembly is confusing for the reader. 

[LightningTumble]

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@My Wegmans Connect wrote:

Can you please tell me how I can display the Failure rate (unit) instead of the failure rate (predicted) in the RBD? We attach the RBD diagrams for different system configuration in the same report. Showing different predicted failures on each diagram for the same assembly is confusing for the reader. 

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Not familiar with the topic.