Abstract We consider the problem of time-sampling optimization for a Statistical Process Control. The aim of this optimization is to minimize the expected loss, caused by a delay in the detection of an undesirable process change. We study the case where the criterion of the optimization is a quadratic polynomial of this delay. The optimization problem is modeled by a calculus of variations problem where the functional is minimized by a proper choice of the time-sampling interval. This functional also depends on a numerical parameter, characterising a magnitude of the process change. The problem is solved in two cases of the information on this parameter: (i) the value of the parameter is known; (ii) the value of the parameter is unknown, while we know the interval where this parameter varies. Examples and numerical simulation, illustrating the theoretical results, are presented.
Optimal Time-Sampling in a Statistical Process Control with a Polynomial Expected Loss
2019-10-26
25 pages
Article/Chapter (Book)
Electronic Resource
English
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