Probabilistic search techniques

In case of two dimensional APOS, for a given product quality, the upper bound of APOS can be obtained by solving a min-max problem, where the min operator searches over the disturbance space and the max operator maximizes the production as in P3. Similarly, the lower bound of this APOS can be found by solving a set of max-min problem, where the max operator looks for the worst disturbance case and the min operator minimizes the production. A less conservative approach might be possible if the disturbances/uncertain parameters are expressed stochastically, then robust optimization techniques [refer for e.g., 57, and references there in] can be used to establish probabilistic maximum and minimum production. 

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