Methods of increase of efficiency of the multidimensional statistical control
- 1 д.т.н., профессор, кафедра «Прикладная математика и информатика», Ульяновский государственный технический университет
- 2,3 аспирант, Ульяновский государственный технический университет
Abstract
The statistical control of process in which the object condition is defined by the several correlated parametres is considered. The basic tool of the control on one of parametres is Shewhart-s chart; as a rule, double cards - for the control of stability of an average level of process and its dispersion are used. For the multidimensional statistical control of process various tools can be used, most widespread of them is Hotelling-s chart.
Efficiency of the control is defined by sensitivity of a card to possible infringements of process. The special characteristic - average length of series is used: quantity samples from the moment of infringement of process till the moment of detection of this infringement. For increase of sensitivity of Hotelling-s chart use of warning border is offered.
In modified Hotelling-s chart it is entered, except control border in addition warning border; thus the area of possible values of controllable statistics breaks into three not crossed subsets: 1) area in which process is statistically operated, 2) area in which process is in a \"transitive\" condition ¬(how position of warning border is defined,¬ the finding of several points in this area can testify to process infringement), 3) the area in which occurs process infringement.
Position of control and warning borders is found numerically by the decision of an optimising problem; results of calculation are presented in the form of the table.
Hotelling-s chart is focused on the control of an average level of multiple parametre process. For the control of multidimensional dispersion the card of the generalised dispersion is considered. The basic parities for map development are resulted, research of its efficiency on the basis of average length of series is carried out. It is noticed, that efficiency of this card can be raised by analogy to Hotelling-s chart by use of warning border.
The example of the control of stability of a thickness of metallization is resulted at printed-circuit board manufacturing: are constructed Hotelling-s chart with warning border and a card of the generalised dispersion.
How to cite
Клячкин В.Н., Кравцов Ю.А., Святова Т.И. Методы повышения эффективности многомерного статистического контроля // Наукоемкие технологии. 2013. № 5. С. 53–58.
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