Test Time Vs Distribution Assumed

[Abhay]

While running the DRT in weibull, I have seen that test time is less with assumed weibull distribution (say beta = 2.5) as compared to exponential distribution when test is planned to demonstrate reliability requirements with certain CL attached.

When the test is planned to demonstrate MTBF with CL attached, the exponential distribution yields less test time as compared to weibull.

Why is SO. what is the math and logic behind.

Thanks in advance.

[Pantelis]

When you assume a distribution and a Weibull beta, you are in fact assuming (specifying) a failure rate behavior. You are then designing a demonstration test based on that assumed failure rate behavior.

As an example when assuming a constant failure rate, and the truth is an increasing failure rate, you will underestimate the reliability at earlier ages and overestimate it at later ages. So if you now know the truth to be an increasing failure rate (you specify it with a beta) you will reach that reliability (high value) sooner than when assuming a constant failure rate.

An interesting article regarding the use of the exponential distribution can be found at http://www.reliasoft.com/newsletter/4q2001/exponential.htm (http://www.reliasoft.com/newsletter/4q2001/exponential.htm)

Now with respect to the underlying math see: http://www.weibull.com/LifeDataWeb/test_design.htm#demonstration (http://www.weibull.com/LifeDataWeb/test_design.htm#demonstration)


Hope this helps

[Abhay]

Thanks for the reply and apologies to get back to u late.

I accept the fact of difference netween exponential and weibull distribution what you explained, But still, I feel my question is unanswered.

I have seen that expontial test plan takes more time to demonstrate than the weibull assumption. I accept that but when it comes to plan test to demonstrate MTBF, the exponential distribution yields less test time as compared to weibull.

Why is SO. what is the math and logic behind.

Thanks in advance again,
http://reliability-discussion.com/images/misc/progress.gif

[Pantelis]

With respect to the math. Did you see my last link... it is there. Folllow the derivations and repeat them with R for both the exponential and Weibull.