# American Institute of Mathematical Sciences

January  2015, 11(1): 105-133. doi: 10.3934/jimo.2015.11.105

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

 1 Department of Applied Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O.B. 78, Karmiel 2161002, Israel, Israel 2 Department of Industrial Engineering and Management, Ort Braude College of Engineering, 51 Snunit Str., P.O.B. 78, Karmiel 2161002, Israel

Received  April 2013 Revised  December 2013 Published  May 2014

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.
Citation: Valery Y. Glizer, Vladimir Turetsky, Emil Bashkansky. Statistical process control optimization with variable sampling interval and nonlinear expected loss. Journal of Industrial & Management Optimization, 2015, 11 (1) : 105-133. doi: 10.3934/jimo.2015.11.105
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