Konstrukcija i osobine kontrolnih kartica za stacionarne i nekorelisane podatke
Design and performances of control chartsfor stationary and uncorrelated data
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UniversityУниверзитет у Београду
FacultyУниверзитет у Београду, Математички факултет
Tema ove doktorske disertacije pripada oblasti kontrole kvaliteta, koja predstavlja praktično korišćenje statistike prilikom praćenja i poboljšavanja proizvodnog procesa. 1930. godine Volter Šuhart je počeo da proučava kontrolu kvaliteta, baziranu na kontrolnim karticama, koristeći statističke principe. Kasnije, posle Drugog svetskog rata, Edvard Deming odneo je ovu disciplinu u Japan, gde je ona doživela procvat. Konstrukcija i osobine kontrolnih karti su najvažnija pitanja u ovoj oblasti. Cilj izučavanja osobina kontrolnih karti u ovoj tezi je da se uporede postojeće i predložene kontrolne karte.
The subject of this thesis belongs the area of quality control, which represents the practical usage of statistics in following and improving the production process. In 1930 Walter Shewhart started studying quality control, based on control charts, and using statistical principles. Later on, after World War II, Edward Deming took this discipline to Japan, where it ourished. The design and the performance of control charts are the most important problems in this area. The purpose of studying the characteristics of control charts in this thesis is to compare the existing and the suggested control charts. The thesis is divided into four chapters. The rst chapter is introductory and contains motivation and basic denitions related to this subject. In this study it is always assumed that the data are normally distributed, and that the in-control process data are stationary and uncorrelated. Shewhart control charts and the corresponding limits are constructed in order to meet the given specications for the quality characteristic that we investigate. Quality control that is applied to a production process always has costs related to the control. The important parameters connected to the cost of quality control are: width of control limits k, the sample size n and the interval between the samples h. In Chapter 2 a new loss function is given, which is connected to the production process and to X−bar quality control chart. Using Matlab program for optimization, values of ^k; ^n and ^h are found, which minimize the loss function for given costs. For given values of cost, a non-linear regression model is built using a package Sigma plot and the obtained values are compared to those obtained by numerical optimization. In Chapter 3, the time series model Yi = Xi + (1 − )Yi−1 is investigated, where 0 < B 1 is a constant, Xi are N(; 2) distributed. Exponentially Weighted Moving Average (EWMA) control charts for this model are presented, and type I and type II errors are calculated in the case when i is large. For dierent sample sizes, the new comparison between the optimal design of the X-bar and EWMA control charts for Normally distributed quality characteristic is given, comparing the corresponding cost-loss functions, power functions and average run lengths.The process of calibration is one of the methods in statistical process control, introduced for improving the quality of the products and for reducing the production costs. In Chapter 4, two new models of non-symmetrical loss function are introduced. Here, the loss function is connected to one product under control (not to the whole sample). Using our program, written in statistical software R, the value which minimizes the expected loss for Shewhart X control chart is found. This value is used as the new central target value of the quality characteristic, that is, the production process is calibrated with this new value. The thesis ends with Conclusions, where the results of the thesis are summarized, and with some open problems to be investigated.