Chain-Pooling ANOVA for Two-Level Factorial Replication-Free Experiments

Holms, A. G.; Berrettoni, J. N.

doi:10.1080/00401706.1969.10490734

Cited by 14 publications

(3 citation statements)

References 5 publications

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“…The H statistical values were presented and adopted in the three-level unreplicated saturated factorial design method by Holms et al [31,35], and can be expressed as:…”

Section: H Statistical Valuementioning

confidence: 99%

Parameters Studies on Surface Initiated Rolling Contact Fatigue of Turnout Rails by Three-Level Unreplicated Saturated Factorial Design

Wang

et al. 2018

Applied Sciences

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Surface initiated rolling contact fatigue (RCF), mainly characterized by cracks and material stripping, is a common type of damage to turnout rails, which can not only shorten service life of turnout but also lead to poor running safety of vehicle. The rail surface initiated RCF of turnouts is caused by a long-term accumulation, the size and distribution of which are related to the dynamic parameters of the complicated vehicle-turnout system. In order to simulate the accumulation of rail damage, some random samples of dynamic parameters significantly influencing it should be input. Based on the three-level unreplicated saturated factorial design, according to the evaluation methods of H, P and B statistic values, six dynamic parameters that influence the rail surface initiated RCF in turnouts, namely running speed of vehicle, axle load, wheel-rail profiles, integral vertical track stiffness and wheel-rail friction coefficient, are obtained by selecting 13 dynamic parameters significantly influencing the dynamic vehicle-turnout interaction as the analysis factors, considering four dynamic response results, i.e., the normal wheel-rail contact force, longitudinal creep force, lateral creep force and wheel-rail contact patch area as the observed parameters. In addition, the rail surface initiated RCF behavior in turnouts under different wheel-rail creep conditions is analyzed, considering the relative motion of stock/switch rails. The results show that the rail surface initiated RCF is mainly caused by the tangential stress being high under small creep conditions, the normal and tangential stresses being high under large creep conditions, and the normal stress being high under pure spin creep conditions.

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“…The H statistical values were presented and adopted in the three-level unreplicated saturated factorial design method by Holms et al [31,35], and can be expressed as:…”

Section: H Statistical Valuementioning

confidence: 99%

Parameters Studies on Surface Initiated Rolling Contact Fatigue of Turnout Rails by Three-Level Unreplicated Saturated Factorial Design

Wang

et al. 2018

Applied Sciences

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“…Inference in incomplete block designs is considered in (463). A program for non-orthogonal ANOVA and ANOCOV (the Analysis of Covariance) is found in (104)• Chain-pooling ANOVA for replicationfree experiments is discussed in (238).…”

Section: Measurement Processmentioning

confidence: 99%

Statistical and mathematical methods in analytical chemistry

Currie¹,

Filliben²,

DeVoe³

1972

Anal. Chem.

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“…With the purpose of eliminating the subjectivity of the graphical methods for detecting significant contrasts, a large number of formal procedures have been proposed: Birnbaum (1959Birnbaum ( , 1961, Holms and Berrettoni (1969), Zahn (1975b), Seheult and Tukey (1982), Box and Meyer (1986), Johnson and Tukey (1987), Voss (1988), Benski (1989), Lenth (1989), Bissell (1989Bissell ( , 1992, Le and Zamar (1992), Juan and Pena (1992), Loh (1992), Dong (1993), Schneider et al (1993), Venter and Steel (1996), Loughin and Noble (1997), Hamada and Balakrishnan (1998), Lawson et al (1998), Al-Shiha and Yang (1999), Voss and Wang (1999), Schoen and Kaul (2000), Ye et al (2001), etc.…”

Section: Introductionmentioning

confidence: 99%

A New Quantitative Method for Analysing Unreplicated Factorial Designs

Chen¹,

Kunert

2004

Biometrical J

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SummaryThe paper proposes a new method for the analysis of unreplicated factorial designs. The new method does not use an estimate of the error variance and has the potential to identify up to m À 1 active contrasts, where m is the number of contrasts in the study. It can be shown that the proposed test statistic, called MaxU r , is a function of the generalized likelihood ratio test statistic under normality, which was also used by Al-Shiha and Yang (1999). Our strategy to identify active contrasts using MaxU r , however, is different from the multistage procedure proposed by Al-Shiha and Yang (1999). Additionally, our simulation study seems to show that the new method is superior to Al-Shiha and Yang's (1999) method.In order to test the performance of the new method, we did an extensive simulation study based on 10,000 samples to compare the new method with 12 other methods from the literature. To reasonably compare these methods, some of the 12 existing methods had to be slightly modified, such that the probability of falsely rejecting the global null hypothesis of no active factors was 0.05 for all methods. Two types of evaluation standard were used, the empirical power and the loss of decision. The results show that the new method performs very well, especially for large number of active contrasts (say more than 3 out of 15).A second purpose of the simulation study was to compare the performance of two well-known estimates for the variance. One is the PSE introduced by Lenth (1989), the other the ASE introduced by Dong (1993). The simulation study confirmed the approximations of Kunert (1997) which indicate that Dong's (1993) estimate should perform better for small numbers of active factors.

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Chain-Pooling ANOVA for Two-Level Factorial Replication-Free Experiments

Cited by 14 publications

References 5 publications

Parameters Studies on Surface Initiated Rolling Contact Fatigue of Turnout Rails by Three-Level Unreplicated Saturated Factorial Design

Parameters Studies on Surface Initiated Rolling Contact Fatigue of Turnout Rails by Three-Level Unreplicated Saturated Factorial Design

Statistical and mathematical methods in analytical chemistry

A New Quantitative Method for Analysing Unreplicated Factorial Designs

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