Analysis with Left Censored Data in Weibull

[Jeff Lischer]

[Originally Posted: 9/19/00--Transferred by ReliaSoft Moderator]

How do you determine if your data is "interval failed" or "left censored"? The ReliaSoft Alternate Rank Method (RRM) seems to use left censored for anything where the initial time of the failure interval is 0, but that is giving me meaningless results. Here's an example where I am testing the number of cycles until a mechanical part fails.

Item Number Failure Type Start End 1 1 Left Censored? 0 25 2 1 Interval 50 75 3 1 Left Censored? 0 100 4 1 Interval 75 100 5 1 Interval 250 350 6 1 Interval 600 700 5 1 Interval 900 1000 8 1 Suspended 600 9 2 Suspended 1400


Using the Weibull++ with RRM for this data I get a MTBF of about 2100. That in itself seems high, but after I add the following new (bad) data:

Item Number Failure Type Start End 10 5 Left Censored? 0 75

the MTBF doubles to 4400!

If I redo the above example replacing all "left censored" data with interval data (with an interval start of 0) I get MTBF of 1000 for the initial data set and 210 for the second set. These numbers make a lot more sense to me. Unfortunately, if you take away Items 1 and 3 from the first data set, then adding Item 10 doesn't give reasonable answers either as Left Censored or as Interval.

What am I doing wrong in the above analyses? Is the definition of left censored more complicated than "if the Start interval is 0, the data is left censored"? Is this data too poorly conditioned for the Weibull distribution?

Thanks for your assistance.

[Anonymous]

[Originally Posted: 9/19/00--Transferred by ReliaSoft Moderator]

Sorry about the formatting above. Here's the data again:

It N FC St End

1 1 LC 0 25 2 1 IF 50 75 3 1 LC 0 100 4 1 IF 75 100 5 1 IF 250 350 6 1 IF 600 700 7 1 IF 900 1000 8 1 RC N/A 600 9 2 RC N/A 1400

and

10 5 LC 0 75

where It = Item Number N = Number in state FC = Failure Code St = Interval start time End = Interval end time IF = Interval Failure LC = Left Censored RC = Right Censored (suspended)

I hope this looks more readable http://63.227.80.170/discus/clipart/happy.gif

[Dr. Dave Olwell]

[Originally Posted: 9/20/00--Transferred by ReliaSoft Moderator]

Jeff,

Thanks for a nice data set.

First, left censored data is a special type of interval data, where the left endpoint on the interval is zero, as you point out.

That is not causing you trouble in this data set. What is producing counter intuitive MTBF times is the heavy infant mortality you are experiencing. For your data set with 12 failures and 3 suspensions, you have 9 units fail before 100 hours. You then have 2 others last longer than 1400 hours. This is classic infant mortality, and is reflected in your low beta estimates.

When you added the five early failures, you exacerbated the infant mortality rate. Paradoxically, that increased the estimated MTBF because the MTBF is very sensitive to low values of beta. The units that don't fail initially are going to last a very long time, and that runs the average up.

I'd probably use MLE on this data set anyway, as there are no exact failure times. RRX really prefers to have some exact failure times to work best, even when you use the RRM method to estimate the points.


Hope this helps. A little plug: we have started a consulting unit at ReliaSoft called Reliasoft Professional Services, which proudly features me as the director. If you ever need in-depth help, please call 1 800 722 7522 and we'll be glad to be of service.


Best wishes,

Dr. Dave