Quality control and genetic algorithms: Difference between revisions

Revision as of 22:44, 20 May 2009

Revision as of 05:22, 22 May 2009

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The QC procedure to be designed or optimized can be formulated as:

''Q''₁(''n''₁,'''''X''₁''''')# ''Q''₂(''n''₂,'','''X''₂''') ''#...# ''Q''_''q''(''n''_''q'','''''X''_''q''''''')'' (1)

where ''Q''_''i''(''n''_''i'','''''X''_''i''''')'')'' denotes a statistical decision rule, ''n_i'' denotes the size of the sample '''S'''_''i''''', that is the number of the measurements the rule is applied upon, and '''X'''_''i''''' denotes the vector of the rule specific parameters, including the decision limits. Each symbol ''#'' denotes either the [[Boolean]] operator AND or the operator OR. Obviously, for ''#'' denoting AND, and for ''n''₁ < ''n''₂ <...< ''n''_''q'''', that is for '''S'''₁''' <math>\subset</math> '''S'''₂''' <math>\subset</math> ....<math>\subset</math> '''S'''_''q''''', the (1) denotes a ''q''-sampling QC procedure.

Each statistical decision rule is evaluated by calculating the respective statistic of the sample of the measurements. Then, if the statistic is out of the interval between the decision limits, the decision rule is considered to be true. Many statistics can be used, including the following: a single value of the sample, the [[range]] of the sample, the [[mean]] of the sample, the [[standard deviation]] of the sample, the cumulative sum, the smoothed mean, and the smoothed standard deviation. Finally, the QC procedure is evaluated as a [[Boolean]] proposition. If it is true, then the [[null hypothesis]] is considered to be false, the process is considered to be out of control, and the run is rejected.