Karty kontrolne X i R dla rozkładów skośnych - studium przypadku

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.