Statistical characteristics for the defect occurrence of raw silk

In order to consider different defects that occur during the computer simulation of raw silk size series, it is necessary to find out the statistical characteristics for the defect occurrence of raw silk. Under the newest International Organization for Standardization standard for electronic testing of raw silk, the defects are classified into small slubs, big slubs, thick places, thin places, and small imperfection elements. By analyzing some probability distributions that happen during the silk reeling process and the formation of the defects, the study proposed that Pólya distribution may fit better than Poisson distribution in describing the number of defects formed in a certain length of silk filament. To verify this theoretical deduction experimentally, the defects for 15 lots of raw silk were tested every 1000 meters using an electronic tester for raw silk; each time 12 skeins were tested together and each test was repeated from 13 to 17 times. A goodness-of-fit test method for Poisson and Pólya distributions was deduced, which was used to analyze the statistical characteristics for the defects except for small imperfection elements. The results showed that when using the capacitive sensor, the defects of big slubs, small slubs, and thick places had a Pólya distribution with a weak spreading characteristic; the thin places were a combination of independent Pólya distributions, and each subclass of thin places took Pólya distribution; when using the optical sensor, all the defects had a Pólya distribution, which was in line with the theoretical deduction.

Some smoothness properties of the Lupaş-Kantorovich type operators based on Pólya distribution

In the present article, we study some smoothness properties of new Lupa?-Kantorovich type operators based on P?lya distribution, as uniform convergence and asymptotic behavior. In order to get the degree of approximation, some quantitative type theorems will be established. The bivariate extension of these operators, with some indispensable results will be also presented.