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Lengthy Datasets, how to check for more than 1 distribution.

Folks,

Looking for suggestion...

I have a datasets that shows a bathtub curve like behavior, for example more than 1 distribution type are found in the datasets. I like to be able to partition the datasets numerically to obtained best fit for datasets, iteratively.

For example, (Time not exact, but exact time is use for illustration only)
Dataset consists of 0 to 336 hours.
Between 0 to 70 hours, I have a Infant Mortality Distribution. Weibull Beta < 1.
Between 71 to 250 hours , I have a Exponential Distribution. Weibull Beta =1.
After 250 hours, I have a Wear out. Weibull Beta > 1.

If a best fit distribution, I get a knee jerk distribution..so I want to know is someone have came out with a automatic method to perform data partitioning and perform best fit, and eventually end up with more than 1 distribution being identified.