parameter estimation in weibull++7

[hustlfm]

i has 14 machine TBF data . the assumption:each time to failure is independent of the last one. therefore,i can do life data analysis of this machines by using weibull++7.
first outcome:
distribution: two-ford Weibull-Mixed (2 parameter)
analysis: MLE
CB : FM
rank: K-M
Beta: 0.8391415208 1.473486147
Eta: 100.1247803 807.3860782
Proportion: 0.5895948018 0.4104051982
LK: -1283.805473
failure\censored: 190 \ 13
second outcome:
distribution: two-ford Weibull-Mixed (2 parameter)
analysis: NLRR
CB: FM
Rank: MED
Beta: 0.707844621 5.185152984
Eta: 224.8120954 1094.05839
Proportion: 0.891178893 0.108821107
LK: -1283.675423
Correlation coefficient: 0.935815397
Failure/censored: 190\ 13

First question: please introduce MLE of mixed weibull model in weibull++7 in detail, because it is difficult than MLE of single weibull distribution.
Second question: please introduce NLRR of mixed weibll model in weibull++7 in detail.
Third question : what method I can choose from two outcome only according to the value of LK? Why the differences of analysis outcome between this two method are so larger, especially the failure plot?

[David]

Information on the Mixed Weibull distribution can be found at http://www.weibull.com/LifeDataWeb/the_mixed_weibull_distribution.htm. NLRR is non-linear rank regression. The basics of this analysis method is presented at the previous link under the Mixed Weibull Parameter Estimation section.

The results are different because the 2-parameter Weibull distribution is different than the 2 subpopulation Mixed Weibull distribution. Keep in mind that you want to use the simplest distribution that represents your data and situation. If your data does not actually have multiple subpopulations then I would not recommend using the Mixed Weibull distribution. The Mixed Weibull distribution is a multi-modal distribution that is used to model data that does not fall on a straight line on a Weibull probability plot. You can use the LK Value to compare distributions when using Maximum Likelihood Estimation (MLE) but it does not make sense to compare the Weibull and Mixed Weibull distributions using this method. These distributions are used to model two different types of data.

I hope this helps.

[hustlfm]

hi ,David,thank you post!
in my example,the fitting model is mixed weibull distribution.I just use different parameter estimation method, one is MLE ,the other is NLRR. If i must choose the result from this two method , how to choose ?Furthmoer, i use the parameter from MLE as the initial value of parameter in MATLAB, and the function is nlinfit , then ,i get a more reasonable fitting curve and value of LK(LK=-12587.2755). I am very confused about this result because in weibull++7 LK=-1283.805473 by using MLE method, which means the result from MATLAB better than weibull++7.
please ,David and everyone, solve this problem!

[David]

The LK Value that is larger (less negative and closer to zero) indicates a better fit. Therefore, if the LK Value found through Matlab is -12587.2755 then this value is much smaller than the LK Value found through Weibull++. -1283.8054 is obviously much larger than -12587.2755 found through Matlab and this indicates that the MLE fit is better in Weibull++. But these values should only be compared if the method used in Matlab is also MLE. You indicated a non-linear fit using Matlab which seems to imply to me more of a non-linear regression method. If so, then the LK Values in this case should not be compared.

In regards to NLRR or MLE, I cannot be specific in regards to your data, but with over 200 data points this certainly is enough data to use MLE. If the suspensions are spread throughout the data, then I would probably recommend MLE even though the suspensions are a small percentage of the data. NLRR may also be applicable. For NLRR you can check the probability plot to see how the model fits the data. The results between NLRR and MLE may not be that much different due to the fairly large sample size. General recommendations regarding MLE and rank regression are presented at http://www.weibull.com/hotwire/issue80/tooltips80.htm under the first tool tip.

I hope this helps.

[hustlfm]

Hi,David,thank you very much!your post helps me get a right understand on LK value.
nlinfit function in MATLAB uses the Levenberg-Marquardt algorithm belongs to non-linear regression method,which is considered as the most effective method to solve the Least-squares problem.
I want to know which algorithm do you used in weibll++7 to solve mixed weibull distribution parameter estimation?how to solve the initial value problem?

[David]

As indicated at http://www.weibull.com/LifeDataWeb/the_mixed_weibull_distribution.htm#parameters, Weibull++ uses a modified Levenberg-Marquardt algorithm to estimate the parameters of the Mixed Weibull distribution when performing regression analysis.

I hope this helps.