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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 de nitions 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 speci cations 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 di erent 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.
i
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. |
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