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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 control]] is a process by which entities review the quality of all factors involved in production. 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]] 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==
Alternative [[quality control]]<ref>Duncan AJ. Quality control and industrial statistics. Irwin 1986;pp.1-1123.</ref> (QC) procedures can be applied onto a process to [[Statistical hypothesis testing|test]] statistically the [[null hypothesis]], that the process conforms to the quality requirements,specifications thereforeand that the processconsequently is in control, against the alternative, that the process is out of control. When a true [[null hypothesis]] is rejected, a statistical type I error is committed. We have then a false rejection of a run of the process. The probability of a type I error is called probability of false rejection. When a false null hypothesis is accepted, a statistical type II error is committed. We fail then to detect a significant change in the probability density function of a quality characteristic of the process. The probability of rejection of a false [[null hypothesis]] equals the probability of detection of the nonconformity of the process to the quality requirementsspecifications.
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)
''Q''<sub>1</sub>(''n''<sub>1</sub>,'''''X''<sub>1</sub>''')# ''Q''<sub>2</sub>(''n''<sub>2</sub>,'''''X''<sub>2</sub>''') #...# ''Q''<sub>''q''</sub>(''n''<sub>''q''</sub>,'''''X''<sub>''q''</sub>''') (1)
where ''Q''<sub>''i''</submath>Q_i (''n''<sub>''i''</sub> n_i,'''''X''<sub>''i''\mathbf{ X_i} )\;</submath>''') denotes a statistical [[decision rule]], {{math|''n<sub>i</sub>''}} denotes the size of the sample {{math|'''S'''<sub>''i''</sub>}}, that is the number of the samples the rule is applied upon, and '''X'''<submath>''i''\mathbf{ X_i}\;</submath> denotes the vector of the rule specific parameters, including the decision limits. Each symbol {{math|''#''}} denotes either the [[Boolean logicoperator (Boolean algebra)|Boolean operator]] operator AND or the operator OR. Obviously, for {{math|''#''}} denoting AND, and for {{math|''n''<sub>1</sub> < ''n''<sub>2</sub> <...< ''n''<sub>''q''</sub>}}, that is for {{math|'''S'''<sub>1</sub> <math>\subset</math>⊂ '''S'''<sub>2</sub> <math>\subset</math>⊂ ....<math>\subset</math> ⊂ '''S'''<sub>''q''</sub>}}, the (1) denotes a {{math|''q''}}-sampling QC procedure.
Each statistical decision rule is evaluated by calculating the respective statistic of athe monitoredmeasured variablequality characteristic of samples taken from the processsample. 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.
A [[quality control]] procedure is considered to be optimum when it minimizes (or maximizes) a context specific objective function. The objective function depends on the probabilities of detection of the nonconformity of the process and of false rejection. These probabilities depend on the parameters of the [[quality control]] procedure (1) and on the probability density functions (see [[probability density function]]) of the monitored variables of the process.
==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 the [[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.
In fact, since 1993, [[genetic algorithms]] have been used successfully to optimize and to design novel [[quality control]] procedures.<ref> Hatjimihail AT. Genetic algorithms based design and [[Optimization (mathematics)|optimization]] of statistical quality control procedures. [[Clin Chem]] 1993;39:1972-8. [http://www.clinchem.org/cgi/reprint/39/9/1972]</ref><ref>Hatjimihail AT, Hatjimihail TT. Design of statistical quality control procedures using genetic algorithms. In LJ Eshelman (ed): Proceedings of the Sixth International Conference on Genetic Algorithms. [[San Francisco]]: [[Morgan KauffmanKaufmann]] 1995;551-7.</ref><ref>He D, Grigoryan A. Joint statistical design of double sampling x and s charts. European Journal of Operational Research 2006;168:122-142.</ref>
==See also==
*[[Quality control]]
*[[Genetic algorithm]]
*[[Genetic algorithm scheduling]]
*[[Optimization (mathematics)]]
==External links==
* [httphttps://www.asq.org/index.html American Society for Quality (ASQ)]
* [httphttps://www.illigalhcsl.uiuc.edu/web/com IllinoisHellenic GeneticComplex AlgorithmsSystems Laboratory (IlliGALHCSL)]
* [http://www.hcsl.com Hellenic Complex Systems Laboratory (HCSL)]
[[Category:QualityStatistical process control]]
[[Category:Genetic algorithms]]
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