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Zusammenfassung:
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Design of control chart for monitoring central tendency of nongaussian
random variables with symmetric or positively skewed distributions is considered.
In the case of nongaussian symmetric distributions, modified X bar control
chart is proposed in this dissertation. For chosen Student, Laplace, logistic and
uniform distributions, theoretical distribution of the standardized sample mean is
calculated and approximated with Pearson type II or Pearson type VII distributions.
Width of control limits and power of X bar control chart are established, for a given
probability of type I error. The results imply that the corresponding Pearson distribution
represents very good approximation of the distribution of the standardized
sample mean. For implementation of X bar control chart in practice, measures of
sample kurtosis are compared and the usage of proposed chart is illustrated on given
data.
In the case of positively skewed distributions, one sided median control chart for
monitoring central tendency of quality characteristics is proposed in this dissertation.
For chosen exponential, gamma and Weibull distributions, theoretical distribution
of sample median is calculated and approximated with Pearson type I or Pearson
type VI distributions. Calculated values of upper control limits and power of median
control chart for theoretical distribution of sample median and corresponding
Pearson distribution are very close. For implementation of median control chart in
practice, measures of sample skewness and sample kurtosis are compared and then
proposed median chart is constructed for given data.
Besides the statistical design of control charts for monitoring central tendency
of nongaussian random variables, their optimal economic statistical design is also
considered. Use of genetic algorithms for constrained minimization of expected loss
function is proposed in this dissertation. Same symmetric distributions as in the case
of statistical design of the X bar control chart and positively skewed distributions
as in the case of statistical design of median control chart are chosen. For all chosen
distributions of quality characteristic, a corresponding Pearson distribution gives
results very close to results based on the theoretical distribution of the standardized
sample mean (sample median). |