Use of Mixed Weibull Form

[Robbie]

I've been trying out the Weibull++ Mixed function. I've taken some operational failure data (mixed modes) and analysed it using the Mixed function (2 subpopulation weibull). With the results I went further and generated using the monte carlo function, two different data set based on the beta and eta values from the mixed weibull function. I combined them in a RBD, however the results were significanlty different from what is obtained using the QCP directly from the mixed mode function results - can anyone eplain why this is? Separating the data, creating two weibull data sets yielding much higher reliability for a given period - presumably this has something related to the mixed mode analysis, however I'm struggling to understand it.

[Arai.M]

Unless I am missing something, it seems like the way you are splitting and combining the data is not correct.

The Mixed Weibull may be used to analyze mixed modes but you have to be really careful on the kind of conclusions you take from that. I often give the example of mortality data when using mixed Weibull. Let say you have mortality data from a city or a country. You have no way of knowing whether the deceased is female or male. You do however know that that those are the two options and that you expect the two populations to fail differently. The data most likely will show two slopes when plotting them in a Weibull probability plot, for example. In this example, the "product" cannot belong to both populations.

Back to failure modes, when analyzing failure data, the failure mode you are seeing is that of the first mode that occurred (or the failure mode that brings the component down). A single component can observe any of the failure modes. Ideally, you want to identify which mode occurred and analyze the different modes separately. Once you do that, you can take the different models and use an analysis such as an RBD to put them "back together". An example of failure mode analysis (specifically for competing failure modes) can be found at http://www.weibull.com/LifeDataWeb/competing_failure_modes.htm (http://www.weibull.com/LifeDataWeb/competing_failure_modes.htm).

What if you have failure data, you know there are two different modes but can't attribute failures to either mode (e.g. no items to inspect, failure analysis of all failed components is not feasible, etc.)? Modeling such data with a single model is still valid, you are basically modeling the time to first failure of the component, regardless of the mode. If you clearly identify different behaviors (e.g. different slopes in a Weibull plot) you might even want to use a mixed Weibull. The resulting parameters though are very likely not the models for the individual failure modes however. If you don't know what failure mode occurred when a component fails, why would a mathematical model know? You are basically fitting a 5 parameter model to your data at that point.

Let me illustrate that last point. I arbitrarily chose 2 distinct distributions for 2 modes, the first distribution was a Weibull distribution with Beta 0.7 and Eta 500. The second distribution was a Weibull distribution with Beta 1.5 and Eta 2000. I then put those 2 modes in series effectively modeling competing failure modes. The component reliability is then Rc = R1 * R2.

I then approximated the reliability of my component with a 2 population mixed Weibull. The results are Beta1 = 0.68, Eta1 = 212, Proportion1 = 0.479, Beta2 = 1.03, Eta2 = 658.2 and Proportion2= 0.521. Note that in this case Rc = R1 * proportion1 + R2 * proportion2.

When I plot both of these components models, the predictions I get for the reliability of my component are virtually identical. However, the individual parameters of the mixed Weibull population are not at all reflective of my individual modes' behaviors.

If all you need is a general idea of what you component's reliability is, a single model, or a mixed model might be good enough. However, if predictions are needed at the mode level, then additional information will have to be gathered.

Hope this helps,
Arai

[Robbie]

Arai,

That has answered my question. I did overlook the "proportion factor" completely.

Many thanks,

Robbie