Quality control and genetic algorithms: Difference between revisions

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The combination of '''quality control and genetic algorithms''' led to novel solutions of complex [[quality control]] design and [[Optimization (mathematics)|optimization]] problems. Quality is the degree to which a set of inherent characteristics of an entity fulfils a need or expectation that is stated, general implied or obligatory.<ref>Hoyle D. ISO 9000 quality systems handbook. Butterworth-Heineman 2001;p.654</ref> [[ISO 9000]] defines [[Quality control|quality control]] as "A part of [[quality management]] focused on fulfilling quality requirements".<ref>ISO 9000:2005, Clause 3.2.10</ref> [[Genetic algorithms]] are search algorithms, based on the mechanics of natural selection and natural genetics.<ref>Goldberg DE. Genetic algorithms in search, optimization and machine learning. Addison-Wesley 1989; p.1.</ref>

==Quality control==

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

:<math>Q_1 ( n_1,\mathbf{ X_1} ) \# Q_2 ( n_2,\mathbf{ X_2} ) \# ... \# Q_q (n_q,\mathbf{ X_q} ) \;</math> (1)

where <math>Q_i ( n_i,\mathbf{ X_i} ) \;</math> denotes a statistical [[decision rule]], {{math|''n_i''}} denotes the size of the sample {{math|'''S'''_''i''}}, that is the number of the samples the rule is applied upon, and {{<math|'''X'''<sub>''i''\mathbf{ X_i}\;</submath>}} denotes the vector of the rule specific parameters, including the decision limits. Each symbol {{math|''#''}} denotes either the [[Boolean operator (Boolean algebra)|Boolean operator]] AND or the operator OR. Obviously, for {{math|''#''}} denoting AND, and for {{math|''n''₁ < ''n''₂ <...< ''n''_''q''}}, that is for {{math|'''S'''₁ ⊂ '''S'''₂ ⊂ .... ⊂ '''S'''_''q''}}, the (1) denotes a {{math|''q''}}-sampling QC procedure.

Each statistical decision rule is evaluated by calculating the respective statistic of the measured quality characteristic of the sample. 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 variable of a sample, the [[range (statistics)|range]], the [[mean]], and the [[standard deviation]] of the values of the variable of the samples, 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.

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==Quality control and genetic algorithms==

In general, we can not use algebraic methods to optimize the [[quality control]] procedures. Usage of [[enumerative]] methods would be very tedious, especially with multi-rule procedures, as the number of the points of the [[parameter space]] to be searched grows exponentially with the number of the parameters to be optimized. [[Optimization (mathematics)|Optimization]] methods based on [[genetic algorithms]] offer an appealing alternative.

Furthermore, the complexity of the design process of novel [[quality control]] procedures is obviously greater than the complexity of the [[Optimization (mathematics)|optimization]] of predefined ones.