Estimation of expected number of future failures

[Andrey]

MODEL:
We put into operation a group of identical objects. If any object fail after some operation time, we repair it or replace it with identical object.
After some calendar time T we have:
-records of different operating times for failed objects (few);
-records of different operating times for survived objects - right suspensions (many).

During operation there are presence of all 3 failure modes corresponding to Bathtub Curve - early life, useful life, wearout life, so we should use Mixed-Weibull model.

PROBLEM:
1. For this group of records estimate expected number of future failures in next calendar
time interval from T to T+U for all survivors.
2. Estimate beginning of wear-out.

QUESTION:
What ReliaSoft software is most appropriate for solving this problem?


Regards
Andrey

[tarik]

This type of anlayis is very well handeled using Weibull++. The data you have will consist of times-to-failure data (each failure will have a Failure Mode associated with it) and suspensions (ones that didn't fail), once you enter this data into Weibull++, and chose a distribution (depending on engineering knowledge or what best fits your data) and an analysis method (most likely the MLE method is the most appropriate method, since you have a lot of suspensions), you can obtain a reliability model that you can uses to do other calculations like the expected number of failure for a certain period based on the suspension. Obviously I mentioned many steps here (choosing distribution, analysis method...). I won't go into details about these things now, but if you start this kind of analysis and still need help please let me know.

You can check out these 2 examples that are close to what you are doing

http://weibull.reliasoft.com/w6ex1/index.htm
http://weibull.reliasoft.com/w6ex6/index.htm

[Andrey]

Thanks for answer!

Just another question.

If a group of objects will fail due to more than one failure mode there are 2 approaches:
COMPETING failure mode or MIXING failure mode.

COMPETING - where each failure mode considered as block of the series system,and the resulting reliability for all modes is the product of the reliability for each mode.
MIXING - initial population considered as mix of separate subpopulations,each with a different failure mode, and the resulting reliability for all modes is the sum (with specific weights) of the reliability for each mode.

What approach use if we want to account all 3 life periods of object (corrsponding to 3 failure modes - initial, stable and wearout)?

[Andrey]

My previous question was emerged from next problem.


In book -Reliability-based mechanical desighn,ed. T.A.Cruse, Marcel Deccer, Inc., NY,1997, pp.27-35, are examples of assessing the number of future failures (examples are from real reliability engineering practice).

Described in this book method is the next:
1. Input data - field records of a group N different non-failed operating times (suspensions) and a group of N1 times to failure.
2. Use Weibull model and estimate shape and scale parameters BETA, TETA.
3. Define hazard function h(t, BETA, TETA).
4. For each suspension Ti estimate expected number of future failures NFi according to
NFi= h(Ti, BETA, TETA)*U*Ni, where Ni is a number of objects with suspensed operating time Ti.
5. Sum NFi

The aim of this method is: monitor group of objects from year to year.
So for some year they receive BETA, ETA, next year recive new values BETA, ETA and so on.

The doubt is next: how could they apply the same BETA, TETA for all Ti (in step 4 above)?

Really, for low Ti must be expected initial failure mode, for higher Ti expected stable-life failure mode and for highest Ti expected wear-out mode.
So, probably, h(t) should be necessarily calculated based on Mixed-Weibull (or competitive?). In this case the shape of h(t) will vary with time t according to Buthtub curve.

So I doubt - is it true?

Regards,
Andrey.

[tarik]

When you have data made up of failure times (each failure time was collected and an observation about the cause of failure was recorded), then use the competing failure mode analysis. If you have failure times, but don’t have info about cause of failure, and you suspect that there are different subpopulations in your data, this is usually true if you noticed that the probability plot doesn’t follow a straight line (an s-shape for example), then use the mixed approach (note that you usually need a lot of data for this case).

Here is some reading about the mixed weibull analysis http://www.weibull.com/LifeDataWeb/the_mixed_weibull_distribution.htm and competing failure mode analysis http://www.weibull.com/LifeDataWeb/competing_failure_modes.htm

After reading your last question, I think your problem is simpler, I think the question just wants you to fit a regular 2-parameter weibull distribution to your data (I don’t think the problem suggest doing competing failure mode analysis, unless you were provided with causes of failure). Then get the failure rate equation and calculate returns based on suspensions.

[Andrey]

In common case any object have 3 failure modes. For example: assume that at initial life of object most input is from subpopulation with shape BETA1=0.5, for stable life - most input for subpopulation with BETA2=1,for wear-out life - most input for subpopulation with BETA3=5.

If we process data and fit REGULAR Weibull law (single), we receive, for example,BETA=1.5 .
Now failure rate is h(t, BETA=1.5,TETA), and for prediction number of future failures for ANY suspension time T in this case we use h(T, BETA=1.5,TETA).

But if suspension T1 is low, most input is expected from h(T1, BETA1=0.5,TETA),
for higher T2 most input is from h(T2, BETA2=1,TETA),and for highest T3 - most input is from h(T3, BETA3=5,TETA)(according to their specific weights).

If I anderstand, your advice, based on your experience, is:
use BETA=1.5 for single Weibull law and don't think about possible mixing
failure modes?

Regards,
Andrey

[adam]

Andrey,

I don't think that's what Tarik is suggesting.

Regarding your observation, you are correct. The methodology described it's not very sound. It is prefferable that you use the Mixed Weibull, which will take care of the different phases of the product. Also, what is U in the equation that you provided?

[tarik]

It was brought up to me that Andrey mentioned in the first post that the units could be “repaired”. If the system is replaced then the approach I suggested in the answer is correct but if the system is repaired and not restored to like-new condition then RGA 6 Repairable Systems methods is the appropriate approach. More info about that type of analysis can be found at: http://www.weibull.com/relgrowthwebcontents.htm