Improvement of the Real Capacity of the Process (Cpk), for Processes with Restrictions, Through the Method of Simultaneous Perturbation of Stochastic Approximations

The Real Process Capability Index (Cpk) measures the percentage of production that meets the specifications established for the good or service generated by the process. Stochastic Approximation Algorithms (SAA) correspond to iterative methods that generate a sequence of random vectors that converge to the root of a real function or converge to the optimal value of a real function. In this article, the second type of these EAAs is developed, with an orthogonal projection on the set of independent variables of the process, to determine the operating conditions of the process, in which it reaches its maximum Cpk. The convergence of this algorithm to a Karush-Kuhn-Tucker point is tested. In addition, the Monte Carlo simulation results in the application of this algorithm are presented graphically, where an increasing trend is observed in the succession of the Cpk values generated in this simulation process.