A robust analysis for unreplicated factorial experiments

Aboukalam, M. A. F.; Al-Shiha, Abdullah

doi:10.1016/s0167-9473(00)00027-x

Cited by 15 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Several of the aforementioned methods have this assumption deeply rooted in their hypothesis testing. Recent nonsubjective rules for the unreplicated orthogonal design analysis have been considered by Aboukalam and Al-Shiha (2001) and Al-Shiha and Yang (2000). The need for posterior adjustment of probabilities in multifactorial testing was explained by Stephenson et al (1989).…”

Section: Introductionmentioning

confidence: 99%

Order Statistics for a Two-Level, Eight-Run Saturated-Unreplicated Fractional-Factorial Screening

Besseris

2009

Quality Engineering

View full text Add to dashboard Cite

Saturated-unreplicated fractional factorial designs remain popular in factor screening investigations. Among the most commonly used schemes is the classical two-level, eight-run orthogonal design. A brute force method is employed to compute a reference cumulative population frequency and cumulative distribution function by permuting directly ranked observations. The technique is simple and nongraphical. It is based on Wilcoxon-Mann-Whitney rank-sum test appropriately adapted for fractionalfactorial composite inference. Contrary to most popular methods, this new approach does not rely to the effect-sparsity assumption. The method is illustrated in three unreplicated-saturated case studies. We discuss the performance of this test with other mainstream competing schemes.

show abstract

Section: Introductionmentioning

confidence: 99%

Order Statistics for a Two-Level, Eight-Run Saturated-Unreplicated Fractional-Factorial Screening

Besseris

2009

Quality Engineering

View full text Add to dashboard Cite

show abstract

“…Several other simulation studies comparing some of the available methods have been published by, e.g., Zahn (1975b), Voss (1988), Berk and Picard (1991), Loh (1992), Dong (1993), Benski and Cabau (1995), Haaland and O'Connell (1995), Loughin and Noble (1997), Hamada and Balakrishnan (1998), Lawson et al (1998), Al-Shiha and Yang (1999), Aboukalam and Al-Shiha (2001), Ye et al (2001), etc. The study by Hamada and Balakrishnan (1998) is one of the most detailed.…”

Section: Simulation Study For Comparison Of Methodsmentioning

confidence: 99%

“…In the comment on the paper by Hamada & Balakrishnan (1998), Lenth suggested the "decent-chance detection capability" (DCDC), which is the effect size that can be detected with 50% power when the size of the test is a. Aboukalam and Al-Shiha (2001) suggested using the probability that an effect is considered inactive given that it is really an inactive effect ( pow II ) as a criterion, which is in fact nothing than the compliment (1-IER) that was used by Hamada & Balakrishnan (1998), etc.…”

Section: Evaluation Standardsmentioning

confidence: 99%

A New Quantitative Method for Analysing Unreplicated Factorial Designs

Chen¹,

Kunert

2004

Biometrical J

View full text Add to dashboard Cite

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.

show abstract

“…Nestes casos, pode-se assumir que os erros experimentais nos valores dos efeitos são as interações de altas ordens (k≥3) ao se supor que estas interações não são significativas (TEÓFILO & FERREIRA, 2006). Outros métodos podem ser utilizados para estimar os erros dos efeitos, tais como o método de Lenth, a análise de gráficos de probabilidade normal e half-normal, entre outros (ABOUKALAM & AL-SHIHA, 2001), (LENTH, R. V., 1989), (LENTH, 2006) e (LI, SUDARSANAM, & FREY, 2006).…”

Section: Explorando Uma Superfície De Respostaunclassified

Planejamento De Experimentos Para Otimização De Critérios De Aceitação Da Calibração De Instrumentos De Medição

GUERRA¹

View full text Add to dashboard Cite

show abstract

A robust analysis for unreplicated factorial experiments

Cited by 15 publications

References 8 publications

Order Statistics for a Two-Level, Eight-Run Saturated-Unreplicated Fractional-Factorial Screening

Order Statistics for a Two-Level, Eight-Run Saturated-Unreplicated Fractional-Factorial Screening

A New Quantitative Method for Analysing Unreplicated Factorial Designs

Planejamento De Experimentos Para Otimização De Critérios De Aceitação Da Calibração De Instrumentos De Medição

Contact Info

Product

Resources

About