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]] 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>

Alternative quality control (QC) procedures can be applied on a process to test statistically the null hypothesis, that the process 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 for 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 distribution of error in the process. The probability for rejection of a false null hypothesis is called probability for error detection.

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

Q1(n1,X1) # Q2(n2,X2) #...# Qq(nq,Xq) (1)

where Qi(ni,Xi) denotes a statistical decision rule, ni denotes the size of the sample Si, that is the number of the measurements the rule is applied upon, and Xi 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 n1 < n2 <...< nq, that is for S1 subset of S2 subset of ....subset of Sq, 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.

A QC procedure is considered to be optimum when it minimizes (or maximizes) a context specific objective function. The objective function depends on the probabilities for error detection and for false rejection. The probabilities for error detection and for false rejection depend on the parameters of the QC procedure (1) and on the probability density function of the error in the process.

In general, we can not use algebraic methods to optimize the QC 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 methods based on the genetic algorithms (GAs) offer an appealing alternative as they are robust search algorithms, that do not require knowledge of the objective function and search through large spaces quickly. GAs have been derived from the processes of the molecular biology of the gene and the evolution of life. Their operators, cross-over, mutation, and reproduction, are isomorphic with the synonymous biological processes. GAs have been used to solve a variety of complex optimization problems. Furthermore, the complexity of the design process of novel QC procedures is obviously greater than the complexity of the optimization of predefined ones. The classifier systems and the genetic programming paradigm have shown us that GAs can be used for tasks as complex as the program induction.

In fact, since 1993, GAs have been successfully used to optimize and to design novel QC procedures, as it is described in (a), (b) and (c).

==Quality control==

(a) Hatjimihail AT. Genetic algorithms based design and optimization of statistical quality control procedures. Clin Chem 1993;39:1972-8.

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 specifications and consequently 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 forof 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 distributionprobability density function of errora inquality characteristic of the process. The probability forof rejection of a false [[null hypothesis]] isequals calledthe probability for errorof detection. of the nonconformity of the process to the quality specifications.

(b) 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 Kauffman, 1995:551-7.

(c)www.hcsl.com

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 Qi<math>Q_i (ni n_i,Xi)\mathbf{ X_i} )\;</math>denotes a statistical [[decision rule]], ni{{math|''n_i''}} denotes the size of the sample Si{{math|'''S'''_''i''}}, that is the number of the measurementssamples the rule is applied upon, and Xi<math>\mathbf{ X_i}\;</math>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 n1{{math|''n''₁ < n2''n''₂ <...< nq''n''_''q''}}, that is for S1{{math|'''S'''₁ subset⊂ of S2'''S'''₂ subset of⊂ ....subset of⊂ Sq'''S'''_''q''}}, the (1) denotes a {{math|''q''}}-sampling QC procedure.

Each statistical decision rule is evaluated by calculating the respective statistic of the samplemeasured quality characteristic of the measurementssample. 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 of(statistics)|range]], the sample[[mean]], and the mean[[standard deviation]] of the sample,values of the standard deviationvariable of the samplesamples, 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 QC[[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 for errorof detection andof forthe falsenonconformity rejection.of Thethe probabilities for error detectionprocess and forof false rejection. These probabilities depend on the parameters of the QC[[quality control]] procedure (1) and on the probability density functions (see [[probability density function]]) of the errormonitored invariables of the process.

==Genetic algorithms==

In[[Genetic generalalgorithms]]<ref>Holland, weJH. canAdaptation notin usenatural algebraicand methodsartificial tosystems. optimizeThe the QC procedures. UsageUniversity of enumerativeMichigan methodsPress would1975;pp.1-228.</ref><ref>Goldberg beDE. veryGenetic tedious,algorithms especiallyin with multi-rule proceduressearch, asoptimization theand numbermachine oflearning. theAddison-Wesley points1989; ofpp.1-412.</ref><ref>Mitchell theM. parameterAn spaceIntroduction to be searched grows exponentially with the number of the parameters to be optimized. Optimization methods based on the genetic algorithms. (GAs)The offerMIT anPress appealing alternative as they1998;pp.1-221.</ref> are robust search [[algorithms]], that do not require [[knowledge]] of the objective function to be optimized and search through large spaces quickly. GAs[[Genetic algorithms]] have been derived from the processes of the [[molecular biology]] of the [[gene]] and the [[evolution]] of life. Their operators, cross-over, [[mutation]], and [[reproduction]], are [[isomorphic]] with the synonymous biological processes. GAs[[Genetic algorithms]] have been used to solve a variety of complex [[Optimization (mathematics)|optimization]] problems. Furthermore,Additionally the complexity of the design process of novel QC procedures is obviously greater than the complexity of the optimization of predefined ones. The classifier systems and the [[genetic programming]] [[paradigm]] have shown us that GAs[[genetic algorithms]] can be used for tasks as complex as the program induction.

==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.

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 Kaufmann]] 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]]

*[[Optimization (mathematics)]]

==References==

{{reflist}}

==External links==

* [https://asq.org American Society for Quality (ASQ)]

* [https://www.hcsl.com Hellenic Complex Systems Laboratory (HCSL)]

[[Category:Statistical process control]]

[[Category:Genetic algorithms]]