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Any population of components produced might be composed of two sub-populations: weak components are less reliable, and deteriorate faster whereas strong components are more reliable, and deteriorate slower. When selecting an approach to classifying the two sub-populations, one could build a criterion aiming to minimize the expected mis-classification cost due to mis-classifying weak (strong) components as strong (weak). However, in practice, the unit mis-classification cost, such as the cost of mis-classifying a strong component as weak, cannot be estimated precisely. Minimizing the expected mis-classification cost becomes more difficult. This problem is considered in this paper by using ROC (Receiver Operating Characteristic) analysis, which is widely used in the medical decision making community to evaluate the performance of diagnostic tests, and in machine learning to select among categorical models. The paper also uses ROC analysis to determine the optimal time for burn-in to remove the weak population. The presented approaches can be used for the scenarios when the following information cannot be estimated precisely: 1) life distributions of the sub-populations, 2) mis-classification cost, and 3) proportions of sub-populations in the entire population.