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JIMO

Statistical process control optimization with variable sampling interval and nonlinear expected loss

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.

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