The combination of quality control and genetic algorithms led to novel solutions of complex

quality control Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as "a part of quality management focused on fulfilling quality requirements". This approach places ...

design and 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. ISO 9000 defines

as "A part of quality management focused on fulfilling quality requirements". Genetic algorithms are search algorithms, based on the mechanics of natural selection and natural genetics.

Quality control

Alternative

(QC) procedures can be applied to a process to

test Test(s), testing, or TEST may refer to: * Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities Arts and entertainment * ''Test'' (2013 film), an American film * ''Test'' (2014 film), ...

statistically the

null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...

, 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

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

equals the probability of detection of the nonconformity of the process to the quality specifications. The QC procedure to be designed or optimized can be formulated as: :

Q_1 ( n_1,\mathbf ) \# Q_2 ( n_2,\mathbf ) \# ... \# Q_q (n_q,\mathbf )\;

(1) where

Q_i ( n_i,\mathbf )\;

denotes a statistical decision rule, denotes the size of the sample , that is the number of the samples the rule is applied upon, and

\mathbf\;

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 , that is for , the (1) denotes a -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 Range may refer to: Geography * Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra) ** Mountain range, a group of mountains bordered by lowlands * Range, a term used to i ...

, the

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...

, and the

standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...

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

is considered to be false, the process is considered to be out of control, and the run is rejected. A

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

procedure (1) and on the probability density functions (see

probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...

) of the monitored variables of the process.

Genetic algorithms

Genetic algorithms are robust search

algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing c ...

, that do not require

knowledge Knowledge can be defined as awareness of facts or as practical skills, and may also refer to familiarity with objects or situations. Knowledge of facts, also called propositional knowledge, is often defined as true belief that is distinc ...

of the objective function to be optimized and search through large spaces quickly. Genetic algorithms have been derived from the processes of the

molecular biology Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and physi ...

of the

gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...

and the

evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

of life. Their operators, cross-over,

mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mi ...

, and

reproduction Reproduction (or procreation or breeding) is the biological process by which new individual organisms – "offspring" – are produced from their "parent" or parents. Reproduction is a fundamental feature of all known life; each individual or ...

, are

isomorphic In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word is ...

with the synonymous biological processes. Genetic algorithms have been used to solve a variety of complex optimization problems. Additionally the classifier systems and the genetic programming

paradigm In science and philosophy, a paradigm () is a distinct set of concepts or thought patterns, including theories, research methods, postulates, and standards for what constitute legitimate contributions to a field. Etymology ''Paradigm'' comes f ...

have shown us that 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

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 genetic algorithms offer an appealing alternative. Furthermore, the complexity of the design process of novel

procedures is obviously greater than the complexity of the optimization of predefined ones. In fact, since 1993, genetic algorithms have been used successfully to optimize and to design novel

procedures.He D, Grigoryan A. Joint statistical design of double sampling x and s charts. European Journal of Operational Research 2006;168:122-142.

References

{{reflist

External links

American Society for Quality (ASQ)

Hellenic Complex Systems Laboratory (HCSL)
Statistical process control Genetic algorithms

Quality control

Genetic algorithms

Quality control and genetic algorithms

See also

References

External links