SKEW NORMAL DISTRIBUTION AND THE DESIGN OF CONTROL CHARTS FOR AVERAGES

2007 ◽  
Vol 14 (01) ◽  
pp. 49-63 ◽  
Author(s):  
TZONG-RU TSAI
Keyword(s):  
Normal Distribution ◽  
Simulation Study ◽  
Control Charts ◽  
Process Capability ◽  
Considerable Improvement ◽  
Quality Characteristic ◽  
Skew Normal Distribution ◽  
Underlying Distribution ◽  
Simulation Results ◽  
Skew Normal

The paper develops two new control charts and process capability ratios based on the skew normal distribution to monitor the process average and evaluate the process capability of non-normal data. Both control charts reduce to Shewhart-type control charts when the underlying distribution of quality characteristic is symmetric. A simulation study is conducted to compare the performances of the proposed control charts with those of existing control charts. Simulation results indicate that considerable improvement over those of existing control charts can be achieved when the proposed control charts are used to monitor the process average of non-normal data. Two examples are presented for illustration.

MAD Control Chart for Autoregressive Models with Skew-Normal Distribution

2020 ◽  
Vol 35 (1) ◽  
pp. 17-23
Author(s):  
Vahideh Gorgin ◽  
Bahram Sadeghpour Gildeh
Keyword(s):  
Normal Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Suitable Model ◽  
Skew Normal Distribution ◽  
Process Mean ◽  
Absolute Deviation ◽  
Nonnormal Distribution ◽  
Autocorrelated Data ◽  
Skew Normal

AbstractThe major problem in analyzing control charts is to work with autocorrelated data. This problem can be solved by fitting a suitable model to the data and using the control chart for the residuals. The problem becomes very important, when the distribution of observation is nonnormal, in addition to being autocorrelated. Much recent research has focused on the development of appropriate statistical process control techniques for the autocorrelated data or nonnormal distribution, but few studies have considered monitoring the process mean of both nonnormal and autocorrelated data. In this paper, a simulation study is conducted to compare the performances of the control chart based on the median absolute deviation method (MAD) with those of existing control charts for the skew normal distribution. Simulation results indicate considerable improvement over existing control charts for nonnormal data can be achieved when the control charts with control limits based on the MAD method are used to monitor the process mean of nonnormal autocorrelated data.

scholarly journals Some properties of the unified skew-normal distribution

2021 ◽  
Author(s):  
Reinaldo B. Arellano-Valle ◽  
Adelchi Azzalini
Keyword(s):  
Normal Distribution ◽  
Fourth Order ◽  
Probability Distributions ◽  
Skew Normal Distribution ◽  
Present Contribution ◽  
The Family ◽  
Multivariate Skewness ◽  
Unified Skew Normal Distribution ◽  
Skewness And Kurtosis ◽  
Skew Normal

AbstractFor the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.

scholarly journals Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 815
Author(s):  
Christopher Adcock
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Degrees Of Freedom ◽  
Special Functions ◽  
Normal Distribution Function ◽  
Skew Normal Distribution ◽  
Marginal Distributions ◽  
Student’S T ◽  
Normal Copula ◽  
Skew Normal

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

The additive logistic skew-normal distribution on the simplex

2005 ◽  
Vol 19 (3) ◽  
pp. 205-214 ◽  
Author(s):  
G. Mateu-Figueras ◽  
V. Pawlowsky-Glahn ◽  
C. Barceló-Vidal
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal
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