HOW TO ESTIMATE LIFE WITH ONE POINT DATA FOR MECHANICAL COMPONENTS

[AJIT]

[Originally Posted: 8/31/00--Transferred by ReliaSoft Moderator]

I would like to know how can I estimate life (basically MTTF) for a mechanical component subjected to life test. And oen specific situation is that the component doesn't fail during the test time. The testing is stopped after a specified time due to cost.

[Dr. Dave Olwell]

[Originally Posted: 9/5/00--Transferred by ReliaSoft Moderator]

Hi, Ajit!

First let me say that I wouldn't recommend estimating anything based on one suspended data point, generally. There is an exception, which I'll discuss below.

To use your one suspended point, you are going to have to assume a distributional model. The most common choice is the exponential (Weibull with beta = 1) , but we can use any Weibull shape parameter. We are going to obtain a best guess and a conservative guess for the MTTF using that shape parameter. Here's how.

Let's say I have one suspended data point at 100 hours. I enter the point into Weibull++ and try to fit a model. When I try to fit a Weibull model, I am prompted to enter a shape parameter and a confidence level. I enter 1 for the shape parameter (that is the exponential model) and 50% for the confidence. Weibull++ returns an estimate of 144 for the scale paramter, which for the exponential distribution is the estimated mean life. This is my best guess. To get a lower confidence bound (say at the 90% level) I repeat the process, but this time I put 90% confidence. I get 43 back as my estimate. So I interpret this to say my best guess for the average life is 144, but there is a 10% chance it could be as low as 43 units. Note that the best guess is more than three times the conservative guess -- quite a spread!

If I am willing to assume a different shape parameter (say beta = 2, corresponding to linear wearout), I can do the same thing. My best guess with beta = 2 is that the MTTF is 106, and there is a 10% chance it could be as low as 58.4 (note I have to use the QCP to find the MTTF because the scale parameter is the MTTF only when beta is exactly equal to one).

I mentioned that there was one circumstance where this might be okay. If I am sure that I have wearout, assuming the exponential distribution will give me a conservative lower confidence bound estimate of the MTTF. (This is like the previous post on sample sizes.) If my goal is to show that I am 90% confident my MTTF is greater than, say, 10, I am home free with my one point, becasue my reliablity so clearly exceeds the requirement. If I had to show a MTTF with 90% confidence that was greater than, say, 75 hours, I'd need more data to make the case.

Hope this short answer has helped. If you have additional questions, you can always contact me at ReliaSoft Professional Services (1 800 722 7522) and get some of our world class reliability consulting services!

Best wishes,

Dave Olwell RSPS

[S. Nath]

[Originally Posted: 9/6/00--Transferred by ReliaSoft Moderator]

DR. Dave: I think, in the weibull analysis, as beta increases from 1 to 2 the MTTF should decrease and not increase as you have written in your reply. Best regards.

[Dr. Dave Olwell]

[Originally Posted: 9/6/00--Transferred by ReliaSoft Moderator]

Hi. I agree with you that as beta goes up the point estimate for MTTF goes down, but that is not what I said.

I said the * lower confidence bound * for the MTTF increased, not the point estimate, as beta increases.

See the example I provided in the post, which makes the point, and try a few of your own. Let me know if you disagree.

Thanks for your feedback. It is nice to know someone reads these critically.

Dr. Dave

RSPS

[Sekhar]

[Originally Posted: 9/7/00--Transferred by ReliaSoft Moderator]

Dr. Dave Olwell; I am a bit confused at this point as these values make more sense than the ones in your reply to Ajit.

Table of Weibull ++ computed values for the problem with one suspension with 100 hours.

Beta 50%lowerbound ETAhours 90%lowerboundMTTF 1 144 43 2 12 5.84

Please note that I did not want to be critical and have always enjoyed reading your replies.

Sekhar

[Dr. Dave Olwell]

[Originally Posted: 9/8/00--Transferred by ReliaSoft Moderator]

Thanks for your comments. When I said I was glad someone reads these critically, I meant with a critical eye (or carefully) not that you were being personally critical.

Looking at the numbers in your post, I get the same as you for beta = 1, but for beta = 2 I still get the ones in my original post which are different from the ones you provided. Can you send me an email (David.Olwell@reliasoft.com ) saying how you got your numbers? Then we can work this out off forum until we agree, and one of us can post the agreed numbers.

Best wishes,

Dr. Dave