Determining overall reliability by RGA

[Arvind]

Hi,

I have tested 8 units to 75000 cycles as part of developmental testing, i have the times to failure for each

like Unit 1 - 3 failures by 35k
5 failures by 45k etc .. these are recoverable / repairable failures & the units are put back into the test after they are set right.

I would like to determine the overall reliability at 75000 cycles for the product. I tried using the RGA for multiple systems but realised it is not suitable for multiple failures @ a given time.

Can you pl suggest me how to go about this.

Regards
Arvind

[David]

Hi Arvind,

Do you actually have 3 failures at 35K for unit 1 or did 3 failures occur between 0 and 35K? The reason I ask is because in your post you indicate "3 failures by 35K", using the word "by". This made me think that the events did not all occur at 35K.

If the failures did actually occur at 35K, you can simply have multiple rows for the failures occuring at 35K. In this case, you would have 3 rows, one row for each failure at 35K. If the failures did not all occur at 35K but at some time between 0 and 35K then I would recommend using grouped data. You can group the data for all of the units based on an interval that you choose. For example, you could group the failures for every 10K. So, you would then count the number of failures among all units between 0 and 10K, 10K and 20K and so forth. You would want to pick an interval so that you have enough granularity within your data. You can see what makes the most sense based on your data.

I hope this helps.

[Arvind]

Hi david,

Thanks for your inputs.

I was able to group the failures @ specific stages

Beta - 1.46
Lambda - 0.1615

however the result shows chi sq - failed ???? does that mean the curve fitting & hence the results would not be accurate.

Also i would like to know how do i estimate the reliability @ specified time.Since it is not available in QCP.

Regards
Arvind.

[David]

If the Chi-Square goodness-of-fit (GOF) test failed then this indicates that the Crow-AMSAA model does not adequately fit the data. However, I would not use the result of this test as the sole indicator of whether or not the model fits. How does the Cumulative Number of Failures vs. Time plot look? Does it appear that the model tracks the data? If so, then the Crow-AMSAA model may sufficiently track the data. There is no absolute answer either way. You have to try and interpret the results that are given. It is helpful to look at multiple references so that you get a better idea of the situation. The other thing to keep in mind is that the Chi-Square GOF may indicate that it failed, but it does not say by how much. You can view the statistical results by right-clicking in the Results Area (where the parameters are displayed) and selecting Statistical Tests. The Upper value is Dcrit and the Test Value is the test statistic.

One thing I did notice is that your value of Beta is greater than one. This obviously indicates that you do not have growth, but in fact are getting worse (wear-out). Do the confidence bounds on Beta include one (this can be checked via the QCP)? I am guessing that they do not. Given that Beta is greater than one, this is most likely having an affect on the GOF test as well. I would try adjusting the interval length if you can. Maybe try to make it smaller, but this also depends on how your data is collected. If you only checked the units every 35K cycles then obviously you cannot use an interval less than this.

Assuming that at 75K cycles you have fixed the design, you can assume the exponential distribution (constant failure rate) to estimate the reliability. Given that:

R(t) = exp(-lambda*t) = exp[-(1/MTBF)*t]

You can use the MTBF at 75K cycles to estimate the reliability. Keep in mind that this reliability is the probability that you will not see any failures by time t.

If you would like you can also email your RGA file to ReliaSoft Support at Support@ReliaSoft.com and we can take a closer look.

[Arvind]

Hi David.

Thanks alot for your inputs.I shall mail the file to the ID given by you.

cheers
Arvind