Statistical process control optimization with variable sampling interval and nonlinear expected loss
Valery Y. Glizer Vladimir Turetsky Emil Bashkansky
Journal of Industrial & Management Optimization 2015, 11(1): 105-133 doi: 10.3934/jimo.2015.11.105
The optimization of a statistical process control with a variable sampling interval is studied, aiming in minimization of the expected loss. This loss is caused by delay in detecting process change and depends nonlinearly on the sampling interval. An approximate solution of this optimization problem is obtained by its decomposition into two simpler subproblems: linear and quadratic. Two approaches to the solution of the quadratic subproblem are proposed. The first approach is based on the Pontryagin's Maximum Principle, leading to an exact analytical solution. The second approach is based on a discretization of the problem and using proper mathematical programming tools, providing an approximate numerical solution. Composite solution of the original problem is constructed. Illustrative examples are presented.
keywords: variable sampling interval nonlinear loss optimal control approximation quadratic programming. Statistical process control optimization

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