Inverse Power Law, Multiple Stresses, ALTA

[canadaboy]

I noticed that ALTA Standard does NOT allow analysis of 2 stress types when using Inverse Power Law model. I called Reliasofts technical support and was told that this was due to the math.

Is this true?. . . or is it simply a choice in the software programming for ALTA 7 that may be implemented at a later date?

I have a hard time believing that the math won't support a dual-stress type analysis. Can't the GLL model reduce to the Inverse Power Model?

[David]

The Inverse Power Law (IPL) is defined as a single stress model. The model is given by:

L(V) = 1/(K*V^n)

where L = characteristic life, V = stress and K and n are parameters to be estimated. Information on the Inverse Power Law can be found at http://www.weibull.com/AccelTestWeb/inverse_power_law_ipl_relationship.htm and also in Wayne Nelson's book Accelerated Testing: Statistical Models, Test Plans and Data Analyses, 1990.

Keep in mind that there is a difference between the number of stresses being applied (number of stress columns in ALTA) and the stress levels. The stress levels are the individual levels for the applied stress. For example, you may be conducting an accelerated test with voltage using 10, 20 and 30 V. In this case there are 3 stress levels and only 1 stress (voltage). Multiple stress levels are required for all models since this helps to determine the relationship between life and stress.

Yes, the General Log-Linear (GLL) model can reduce to the Inverse Power Law. It can reduce to the IPL when you have a single stress and the Power life-stress relationship is chosen as the stress transformation. Information on the GLL model can be found at http://www.weibull.com/AccelTestWeb/general_log_linear_model.htm.

Now, if you are looking for a model which can handle multiple stresses, there are different options within ALTA. For two stresses, the Temperature-Humidity, Temperature-NonThermal or Generalized Eyring models can be used. For more than 2 stresses, the Proportional Hazards or GLL models can handle data with up to 8 stresses. Information regarding all of these models can be found in the Accelerated Life Testing Reference at http://www.weibull.com/acceltestwebcontents.htm. If you have two non-thermal type stresses, then I would recommend using the GLL model and select the Power life-stress transformation. This will emulate a two stress IPL, but these same results cannot be duplicated by selecting Inverse Power Law since it is a one stress model.

Sorry to be a bit lengthy, but just wanted to try and clarify as much as possible.

I hope this helps.

[canadaboy]

David -
Thank you for your reply. The lengthy reply is appreciated since you didn't know my full history or thought process. More good information is valuable.

I have a situation where we have 2 non-thermal stresses relating to loosening of threaded joints.

The 2 main points you made that helped were:
(1) The IPL is defined as a single stress model (I see and accept this).
My confusion was interpreting comments in The Accelerated Testing (402) course materials (slide 99), "The previous principles can be expanded for use in situations where more than one stimulus is present". I assumed this could be done for the Inverse Power Law. And this must be true because of Point (2) below.

(2) GLL with a power-life transformation can "emulate" IPL with 2 stresses. This is the key piece of information.

I fear that ALTA Standard (which we have) can only handle the single non-thermal stress situation (ie. IPL). We could can analyze multiple stresses, but I assume this can only be done individually, 1 at a time, without seeing interactions of the 2 stresses.

Is it correct, then, to assume we need ALTA PRO (GLL, Power-Life Trans) to simultaneously analyze 2 non-thermal stresses???

[David]

That's proabably a point I should have clarified in my previous post. The GLL, Proportional Hazards and Generalized Eyring (all which I previously mentioned) are all in ALTA PRO and not in the Standard version. If you would like to analyze data with two nonthermal stresses then the PRO version is recommended. The Standard version of ALTA can handle up to two stresses with the Temperature-Humidity and Temperature-NonThermal models. These models were not specifically setup for two nonthermal stresses. But you could theoretically try and see how they model your data. Your best bet would be to use the GLL model.

In regards to the statement from the course materials, this is simply a precursor to the following section which discusses the combination models (Temperature-Humidity and Temperature-NonThermal). This section shows, for example, how the Temperature-Humidity is a double Eyring model. Unfortunately, we do not have a similar model for two nonthermal stresses (double IPL). But as I have mentioned you can get around this using the GLL model.

I hope this helps.

[Pantelis]

Canadaboy

You are correct on what you assumed/stated...