Duane Model

[grel041]

I am currently in a reliability class and we are studying the Duane Model. I have a homework question in which you are needing to find the two parameters K and Alpha by using a table of cumulative time and cumulative MTBF.

What I am looking for is some guidance and not just an answer. Any help would be greatly appreciated. My first though is using method of least squares to estimate the parameters, but the math doesn't work out.

Thank you,

Lee

[Pantelis]

See our online textbook for what you are asking ... specifically

http://www.weibull.com/relgrowthwebcontents.htm#Duane

[grel041]

Excellent! Thank you for the help. I only have one question left.

My question states: If at the end of 10000 hours of testing the results are as follows.

Time Cumulative MTBFcum
40 42
130 55
340 120
1100 150
2500 300

Would using the least squares method be the best way to answer the question? As a double check I used eqn. 4 from the online textbook with the values of a-hat and b-hat that I calculated and the data was close to the MTBF values above, but not exact. The values that I calculated are a-hat = 0.469164 and b-hat = 6.74155.

Thank you.

[Pantelis]

Traditionally the Duane model is computed using least squares. The MLE solution can also be used but this is identical to the Crow-AMSAA model or NHPP. So if you want to be a purist use LS for the Duane and MLE for the NHPP.

[grel041]

Great news. Thank you very much for your help.