Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.     

On Kendall's Autocorrelations

This brief article extends the theory of sample Kendall's autocorrelations by providing their exact variances at lags higher than one under the null hypothesis of randomness, by introducing and investigating their weighted modifications, and by numerical demonstration of these results and their usefulness.     

A Design of s Control Charts with a Combined Double Sampling and Variable Sampling Interval Scheme

In this paper, we propose new estimation techniques in connection with the system of S-distributions. Besides “exact” maximum likelihood (ML), we propose simulated ML and a characteristic function-based procedure. The “exact” and simulated likelihoods can be used to provide numerical, MCMC-based Bayesian inferences.     

Two-Stage Variables Acceptance Sampling Plans Using Process Loss Functions

In this article, a variable two-stage acceptance sampling plan is developed when the quality characteristic is evaluated through a process loss function. The plan parameters of the proposed plan are determined by using the two-point approach and tabulated according to various quality levels. Two cases are discussed when the process mean lies at the target value and when it does not, respectively. Extensive tables are provided for both cases and the results are explained with examples. The advantage of the proposed plan is compared with the existing variable single acceptance sampling plan using the process loss function.     

A New Approach for Testing Periodicity

This article describes testing for periodicity in the presence of FD processes. We propose two approaches for testing the periodicity based on Fisher's test. The first one is performed using the periodogram which has been divided into different parts. The second one is based on the discrete wavelet transform. Properties of the tests are illustrated by means of Monte Carlo simulations.     

A Note on Wald's Type Chi-squared Tests of Fit

The Wald's method for constructing chi-squared tests of fit has been formulated more accurately. It is shown that Wald's type statistics will follow the central chi-squared distribution if and only if the limit covariance matrix of standardized frequencies will not depend on unknown parameters. Several examples that illustrate this important fact are presented. In particular, it is shown that the goodness-of-fit statistic developed by Moore and Stubblebine does not follow the chi-squared limit distribution, and, hence, cannot be used for testing multivariate normality.     

Hayter and Tsui's test with double sampling for the vector mean of multivariate normal population

Abstract

In this paper, we introduce a version of Hayter and Tsui's statistical test with double sampling for the vector mean of a population under multivariate normal assumption. A study showed that this new test was more or as efficient than the well-known Hotelling's T² with double sampling. Some nice features of Hayter and Tsui's test are its simplicity of implementation and its capability of identifying the errant variables when the null hypothesis is rejected. Taking that into consideration, a new control chart called HTDS is also introduced as a tool to monitor multivariate process vector mean when using double sampling.     

An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix

ABSTRACT

We extend Chebyshev's inequality to a random vector with a singular covariance matrix. Then we consider the case of a multivariate normal distribution for this generalization.     

Multiple nonlinear regression of the Markovian arrival process for estimating the daily global solar radiation

Abstract

Solar radiation is a global ecological phenomenon that affects life everywhere. In this study, a new statistical method, called the Quartiles-Moment's method, is proposed to estimate the scale and shape parameters of the exponentiated Gumbel maximum distribution (EGMD). The Kolomogorov–Smirnov test and the percentiles of the dataset are thus used to fit the dataset of the daily global solar radiation and the corresponding daily maximum temperature with EGMD. Thence, multiple nonlinear regression of the daily global solar radiation and the corresponding daily maximum temperature are produced and compared with the real dataset accordingly.