1 Estimation of variance components

Rao, C. Radhakrishna; Kleffe, J.

doi:10.1016/s0169-7161(80)01003-6

Cited by 42 publications

(45 citation statements)

References 40 publications

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“…This difference makes it difficult to directly apply the regression techniques such as the ordinary least-squares method [23] and robust estimation method for linear models [24], [25] to solve this problem. Equation (6) is actually in the format of a linear mixed model that has been studied in biological and agricultural research [26], [27]. In the terminology of the linear mixed model, U is the fixed effect, [Ũ W ] is the random effect, 0 and [Z (1) Z (2) ] are the design matrices, and V This problem is exactly the root-cause identification problem we are facing.…”

Section: B Formulation Of the Root-cause Identification Problemmentioning

confidence: 99%

“…The typical statistical estimation algorithms are ANOVA, maximum likelihood estimation (MLE), restricted maximum likelihood estimation (REML), and minimum norm quadratic unbiased estimation (MINQUE). Excellent reviews of these methods can be found in [26]. In general, the ANOVA-type estimation method cannot be applied to the complicated general linear mixed model as in (6).…”

Section: Estimation Of the Root Causesmentioning

confidence: 99%

“…The second-step MINQUE uses (1) as the a priori value to obtain 2 i used in (22) and (23). The asymptotic normality of the two-step MINQUE has been thoroughly discussed in [26]. In Section IV, the effectiveness of these two test procedures will be further studied through an experiment.…”

Section: I(u;mentioning

confidence: 99%

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Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes

Zhou

Chen

Shi

2004

IEEE Trans. Automat. Sci. Eng.

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Abstract-Root-cause identification for quality-related problems is a key issue in quality and productivity improvement for a manufacturing process. Unfortunately, root-cause identification is also a very challenging engineering problem, particularly for a multistage manufacturing process. In this paper, root-cause identification is formulated as a problem of estimation and hypothesis testing of a general linear mixed model. First, a linear mixed fault-quality model is built to describe the cause-effect relationship between the process faults and product quality. Then, the estimation algorithms developed for a general linear mixed model are adapted to estimate the process mean and variance. Finally, a hypothesis testing method is developed to determine if process faults exist in terms of statistical significance. A detailed experimental study illustrated the effectiveness of the proposed methodology.Note to Practitioners-Economic globalization brings intense competition among manufacturing enterprises. The key to succeed in this competitive climate is to rapidly respond to fast-changing market demands with high-quality and competitively priced products. To achieve this, we need to quickly identify root causes of quality-related problems in a complicated manufacturing system. However, the current widely adopted quality-control techniques focus more on monitoring than on root-cause identification. These techniques can efficiently detect the changes in the process but the root cause identification is often left to the plant engineers or operators. In this paper, a systematic estimation and testing method is proposed to identify the variational root causes in multistage manufacturing processes. First, a linear model is built based on the design information to describe the cause-effect relationship between the process faults and product quality. Then, an algorithm is developed to estimate the mean and variance of the process faults from the quality measurements of products. Finally, a statistical testing method is developed to determine if process faults (i.e. root causes) exist in terms of statistical significance. A detailed experimental study illustrates the effectiveness of this method. The method presented in this paper is a new quality-control technique and can be used for quality improvement of multistage manufacturing processes.

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Section: B Formulation Of the Root-cause Identification Problemmentioning

confidence: 99%

Section: Estimation Of the Root Causesmentioning

confidence: 99%

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Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes

Zhou

Chen

Shi

2004

IEEE Trans. Automat. Sci. Eng.

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“…For the determination of the variance components, see Rao and Kleffe (1988) and Perović (2005). Here, however, we are concerned with noise determination, and therefore the signal s will not be the subject.…”

Section: Introductionmentioning

confidence: 99%

Estimating the variance in coordinate measuring for binary orbit

Perović¹,

Cvetković

2015

Journal of Geodetic Science

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Abstract:The variance of a purely random error -"pure error" -in measuring the relative coordinates during the calculation of the orbits of binary stars, (its "unbiased estimate"), is necessary for each test used in the orbit calculation for double stars, such as the adequacy test for the orbit model, gross-error tests and the like. Since this variance is unknown, in this paper we present the robust PEROBEPE1 method which provides an unbiased variance estimate for the pure error in the coordinate measurements concerning the orbits of double stars. This estimate is independent of the model adequacy for a double-star orbit and thus can be used in any test concerning double stars.

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“…W vh = Q −1 vh , one can simply obtain the minimum variance estimators. Therefore, LS-VCE is capable of unifying many of the existing VCE methods such as minimum norm quadratic unbiased estimator (MINQUE) (see Rao, 1971, Rao and Kleffe, 1988, Sjöberg, 1983, best invariant quadratic unbiased estimator (BIQUE) (see Caspary, 1987, Koch, 1978, 1999, Schaffrin, 1983, and restricted maximum likelihood (REML) estimator (see Koch, 1986).…”

Section: Unification Of Methodsmentioning

confidence: 99%

Variance Component Estimation by the Method of Least-Squares

Teunissen

Amiri-Simkooei

International Association of Geodesy Symposia

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Abstract. Motivated by the fact that the method of least-squares is one of the leading principles in parameter estimation, we introduce and develop the method of least-squares variance component estimation (LS-VCE). The results are presented both for the model of observation equations and for the model of condition equations. LS-VCE has many attractive features. It provides a unified least-squares framework for estimating the unknown parameters of both the functional and stochastic model. Also, our existing body of knowledge of least-squares theory is directly applicable to LS-VCE. LS-VCE has a similar insightful geometric interpretation as standard least-squares. Properties of the normal equations, estimability, orthogonal projectors, precision of estimators, nonlinearity, and prior information on VCE can be easily established. Also measures of inconsistency, such as the quadratic form of residuals and the w-test statistic can directly be given. This will lead us to apply hypotheses testing to the stochastic model.

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1 Estimation of variance components

Cited by 42 publications

References 40 publications

Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes

Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes

Estimating the variance in coordinate measuring for binary orbit

Variance Component Estimation by the Method of Least-Squares

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