How could to model a reliable Weibull distribution that represents x failures plus y nonfailures

[Jose LP]

We are trying to obtain the Weibull distribution for some UPS (Uninterruptible Power Systems) from real field data. Estimated life time for these units is aproximately 10 years (87,600 hrs at 100% Duty Cicle).

We have 550 UPS in the field since May 2000, and up to this moment we have had 12 failures reported that range from 1300 hrs to 24520 hrs. Using the MLE method for calculating B and n parameters, we obtain B=1.1149 and n=10173.61

We would like to estimate the reliability of these units for 4 years 35,040hrs (our warranty period), and we obtain a reliability of 1.89%!!!!! which of course doesn't make sense. We have 538 UPS that have been operating without a failure for more than 3 years!!

We know that this result doesn't represent actual data since 538 units have not failed yet. However, how could we model a "reliable" Weibull distribution that represents these 12 failures plus the 538 non-failures?, of course we cannot wait 7 more years to have 550 failures!

Is the Weibull distribution a good approach for this particular example? If it is, how do we model it?, If it isn't, which other distribution could be useful?

B. Regards,

Jose

[RS Support]

Based on your eta of approximately 10,000 hours and the range of your failure data -- I am fairly sure that you are making the classical mistake of fitting the model based only on the failures and ignoring the suspensions, thus the result you mention. Your data set should also include the non-failed units (also called suspensions or right censored data).

For more information on right censored data see:
http://www.weibull.com/LifeDataWeb/data_classification.htm


For an example doing warranty analysis see:
http://www.weibull.com/LifeDataWeb/lifedataweb.htm


Additional information and examples can also be found at www.weibull.com

[JBersent]

To add to the above point,

Assume that you are interested in determining the life expectancy of human males and you are observing a sample of 20 males. Lets further assume that out of the 20 males under observation one dies at 30 and one at 40, while the others are alive and of various ages. If one only looked at the death ages, without accounting for the ages of the survivors, the life resulting life expectancy (say 35) would be incorrect.

[Jose LP]

JBersent,

You are exactly right. I know that I obtained an incorrect result because I didn't know how to take into account the censored data (UPS that have not failed yet). My question is, how to calculate Beta and eta parameters of the Weibull dist. that consider the 538 censored observations and provide a useful estimation.

RS Support sent a link that explains how to classify data in Weibull++ Software, but what special consideration I have to make to obtain those parameters by myself using MLE or any other method, without the need of the Weibull++ application?

Does anybody have a clue?

Regards,

Jose

[RS Support]

Even though you will find Weibull++ very useful, Weibull.com includes a simple (and free) Weibull parameter estimation tool (built on weibull++ engines) on-line that you can use with censored data. The tool is at http://www.weibull.com/itools/index.htm

Should you want to do the analysis yourself all the needed equations are available in the on-line life data analysis handbook. If you want to use MLE The LK equation (including censored data) is at http://www.weibull.com/LifeDataWeb/likelihood_function.htm. Other pages include more details.