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Quality control and genetic algorithms

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Quality control is a set of activities intended to ensure that quality requirements are actually being met. Quality is the degree to which a set of inherent characteristics fulfils a need or expectation that is stated, general implied or obligatory[1]. Genetic algorithms are search algorithms, based on the mechanics of natural selection and natural genetics[2]. The fruitful connection between quality control and genetic algorithms led to novel solutions of complex quality control design and optimization problems.

Quality control

Alternative quality control[3] (QC) procedures can be applied on a process to test statistically the null hypothesis, that the process conforms to the quality requirements, therefore 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 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 process. The probability of rejection of a false null hypothesis equals the probability of detection of the nonconformity of the process to the quality requirements.

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 samples 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 S2 .... Sq, the (1) denotes a q-sampling QC procedure.

Each statistical decision rule is evaluated by calculating the respective statistic of a monitored variable of samples taken from the process. 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, 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 QC 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 QC procedure (1) and on the probability density functions (see probability density function) of the monitored variables of the process.

Genetic algorithms

The genetic algorithms[4][5][6] (GAs) 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. Moreover the classifier systems and the genetic programming paradigm have shown us that GAs can be used for tasks as complex as the program induction.

See also

References

  1. ^ Hoyle D. ISO 9000 quality systems handbook. Butterworth-Heineman 2001;p.654
  2. ^ Goldberg DE. Genetic algorithms in search, optimization and machine learning. Addison-Wesley 1989; p.1.
  3. ^ Duncan AJ. Quality control and industrial statistics. Irwin 1986;pp.1-1123.
  4. ^ Holland, JH. Adaptation in natural and artificial systems. The University of Michigan Press 1975;pp.1-228.
  5. ^ Goldberg DE. Genetic algorithms in search, optimization and machine learning. Addison-Wesley 1989; pp.1-412.
  6. ^ Mitchell M. An Introduction to genetic algorithms. The MIT Press 1998;pp.1-221.
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