Building Cost Function 3D Benchmarks to Improve the Economic Statistical Design of X ¯ Control Charts

Abstract EN

Shewhart or control charts are important Statistical Process Control (SPC) techniquesused for prompt detection of failures in a manufacturing process and minimization of production costs which are modelled with nonlinear functions (cost functions).

Heuristic methods have been used to find the chart’s parameters integrated within the cost function that bestcomply with economic and statistical restrictions.

However heuristic estimation is highlydependent on the size of the search space, the set of initial solutions, and the explorationoperators.

In this paper the 3D analysis of the cost function is presented to more accuratelyidentify the search space associated with each parameter of X ¯ control charts and to improve estimation.

The parameters estimated with this approach were more accurate than thoseestimated with Hooke and Jeeves (HJ) and Genetic Algorithms (GAs) under different failuredistributions.

The results presented in this work can be used as a benchmark to evaluateand improve the performance of other heuristic methods.