Karty kontrolne X i R dla rozkładów skośnych - studium przypadku

• Autorzy: Czabak-Górska I. D.

Warianty tytułu

EN

X and R control chart for skewed distribution - case of study

• Języki publikacji: PL

Abstrakty

EN

To meet the requirements, the products generally should be produced by a process that is stable and repetitive. It is however impossible to produce a certain type of product, in the same company and under the same conditions in such way to produce the get perfect parameters of this product, due to the occurrence of assignable causes. To analyze the stability of the production process (in order to detect assignable causes and statistical process control) used to Shewhart control charts, which are based on the assumption that the distribution of the quality characteristic (so called process distribution) is normal distributed or approximately normal distributed. However, the review of the literature has shown that in practice, the assumption of normality of many quality characteristics this condition doesn't hold, which in turn affects the improper assessment of the process stability. The most common distributions of measurement data, (beyond the normal) is skewed. For skewed population Type I Risk probabilities grow larger as the skewness increases. In this case four approach are plausible: increase the sample size up to a thousand, ignore skewness and use the classic Shewhart control charts, assume that the population distribution of the population is known and take a charts in accordance with the distribution or assume that the distribution of the population is not known and the use of heuristic methods. However, the use of one of the first three methods may prove to be uneconomical (e.g. due to the need to incur additional costs) and even result in incorrect assessment of the stability of the process. „Golden middle” in this situation can be heuristic methods, i.e. method of analysis percentiles distribution, variance weighted method or the method of correction of asymmetry, that were briefly described in this paper. The analysis of heuristic methods allowed for the choice of the least complicated due to the applicability in manufacturing companies. Additionally the studies carried out by the Cahn and Cui, showed that the Type I Risk probabilities of CS method is closer to the standard value of 0.27% than the other presented methods and, therefore, the effectiveness of this approach is much better, so in case study the author used CS method. The main aim of the paper is determine the control limits for the X and R charts based on the skewness correction (SC) method, including the risks associated with incorrect choice of method for determining the control limits. For this purpose, measurement data from a company producing automotive seat frames was analyze. All calculations were made in Statistica and Excel environment.

Słowa kluczowe

PL

rozkład skośny; karty kontrolne; karty kontrolne Shewharta; metoda korekcji asymetrii; metoda CS

EN

skewed distribution; control chart; Shewhart control chart; skewed correction method; CS method

• Wydawca: Polskie Towarzystwo Zarządzania Produkcją
• Czasopismo: Zarządzanie Przedsiębiorstwem
• Rocznik: 2016
• Tom: Vol. 19, nr 4
• Strony: 10--17
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Czabak-Górska I. D.

• Politechnika Opolska, Wydział Inżynierii Produkcji i Logistyki, Instytut Innowacyjności Procesów i Produktów, Katedra Inżynierii Jakości Produkcji i Usług

Bibliografia

• [1] Bai D.S., Choi LS., X and R Control charts for skewed populations. „Journal of Quality Technology”, 27, 1995, pp. 120-131.
• [2] Betül K., Yazici B., Individuals control chart in case of non-normality. „Journal of Modern Applied Statistical Method”, vol. 5, iss. 2, article 28, 2006, pp. 542-550.
• [3] Buthmann A., Dealing with non-normal data: Strategies and Tools, dostępny: http://www.isixsigma.com/ tools-templates/normality/dealing-non-normal-data-strategies-and-tools/ [dostęp: 10.11.2014].
• [4] Chan L.K., Cui, H.J., Skewness correction X and R charts for skewed distributions. „Naval Research Logistics”, 50, pp. 1-19.
• [5] Chang Y.S., Bai S., Control charts for positively-skewed populations with Weighted Standard Deviation. „Quality anf Reliability Engineering International”, 17, 2001, pp. 397-406.
• [6] Choobineh F., Ballard J. L., Control-Limits of QC Charts for Skewed Distributions Using Weighted-Va-riance. „IEEE transactions on reliability”, vol. R-36, no. 4, 1987, pp. 473-477.
• [7] Greber T., Statystyczne sterowanie procesami - doskonalenie jakości z pakietem STATISTICA. Wydaw-nictwo StatSoft, Kraków 2000.
• [8] Hamrol A., Strategie i praktyki sprawnego działania. Wydawnictwo Naukowe PWN, Warszawa 2015.
• [9] Karagöz D., Hamurkaroglu C, Control Charts for Skewed Distributions: Weibull, Gamma, and Lognormal. „Metodolovski zvezki”, vol. 9, no. 2, 2012, pp. 95-106.
• [10] Montgomery D.C., Introduction to Statistical Quality Control. John Wiley & Sons, Inc., 6th Edition, New York 2009.
• [11] PN-ISO 8258+AC1: Karty kontrolne Shewharta. Polski Komitet Normalizacyjny, Warszawa 1996.
• [12] Rao S.B., Durgamamba A.N., Rao S.R., Variable control Charts Based on Percentiles Of Size Biased Lo-max Distribution. ProbStat Forum, vol. 7, 2014, pp. 55-64.
• [13] Rao S.B., Kantam R.R.L., Mean andränge charts for skewed distributions - a comparision based on half logistic distribution. „Pakistan Journal of Statistics”, vol. 28(4), 2012, pp. 437-444.
• [14] Rewilak J., Metoda doboru środków pomiarowych w Statystycznym Sterowaniu Procesem. Rozprawa doktorska, Kraków 2002.
• [15] Samanta B., Bhattacherjee A., Problem of non-normality in statistical quality control: a case study in a surface mine. „The Journal of The South African Institute of Mining and Metallurgy”, vol. 104/ 2004, pp. 257-264.
• [16] Schoonhoven M., Does R. J. M. M., The X Control Chart under Non-Normality. „Quality and Reliability Engineering International”, vol. 26, 2010, pp. 167-176.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).