Weibull slope

[Pravin Kadekodi]

I need a clarification on the weibull slope while doing a acclerated test data analysis.
The general assumption is that the Weibull slope remains constant over the different stress levels of accleration.
I have 2 stress levels with slope of A=2.3 and B=1.3 respectively (when analyzed indepently). I am trying to get the distribution at stress level C, where A>B>C.
While analysis using inverse power law for life-stress distirbution, I get weibull slope = 1.9 for all conditions A,B and the distribution for C is plotted with this slope.

General logic would tell me that since the stress levels are reducing from A to C the slopes should also reduce. Is there a way to do the analysis?

[DrDave]

The models used in ALTA assume that the slope is constant. ALTA to my knowledge does not implement a model that has slope as a function of stress.

Keep in mind that the estimated slopes vary from sample to sample. If the difference between the two estimated slopes is not statistically significant, then do not be alarmed that they are not the same. A method for testing for common slopes is discussed at http://www.weibull.com/AccelTestWeb/common_shape_parameter_likelihood_ration_test.htm

[David]

As DrDave mentioned, ALTA 6 assumes a constant shape parameter across the different stress levels. ALTA does not use an average shape parameter or anything similar, but calculates an overall shape parameter that maximizes the likelihood function given the selected life-stress relationship and life distribution. Another option for checking the assumption of a constant shape parameter can be found at http://www.weibull.com/hotwire/issue16/hottopics16.htm.

I hope this helps.

[Harry]

As discussed above, it is usually assumed that the beta is constant at all the test stresses in ALTA. This assumption also has its physical meaning. For example, if the slope at the low stress is smaller than the slope at the high stress, the probability plots of these two stresses will not be parallel. They will interact at the low tail. This means that for the time before the interaction point, the probability of failure at the lower stress will be higher than the probability of failure at the higher stress. It is not true for most cases in the world.