A paper presented recently at Discovery Summit addressed this very problem. The author of the paper was Dr. David Trindade, and he spoke on analyzing Defective Subpopulations (DS).
A DS can occur when a manufacturing process introduces a defect into a small portion of the total parts produced. For example, perhaps a motor manufacturer buys electrical brushes from several vendors. Unknowingly at the time of assembly, one of the vendors (supplying perhaps 15% of the brushes for this particular motor model) provided brushes that would ultimately fail early in the life of the motors. Brushes from the remaining vendors were all OK. So there is a small fixed portion of the population of motors that will fail early in life.
We could analyze the reliability of the motor using JMP's Life Distribution platform, and assume that there are two "causes" of failure by perhaps fitting two Weibull curves to the data. One of the curves would fit the early failure data, while the second would take care of the rest of the motors.
But this isn't exactly correct. The Weibull distributions would assume that the entire population was susceptible to either type of failure for the entire lifespan of the product, when in fact only a few motors would experience the early failures. Once the motors in this subpopulation have all failed, no more motors would fail due to this "bad brush" cause.
That is where Defective Subpopulation distributions come in. Here, we assume that only a portion of the products have this initial, early life failure defect. The result is a better model of the reliability of the product or system.
If you are interested in seeing more on this subject, I encourage you to read Dr. Trindade's excellent paper. Enjoy!
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