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Analysis of Means Tables Using Mathematical Processors

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Abstract

Introduced by Ellis Ott in the 1960s, the analysis of means (abbreviated ANOM) procedure provides a simple graphical technique for testing for differences between the means of several populations. The ANOM charts are easy to use, similar in appearance and interpretation to control charts, and usually give the same results as the more familiar analysis of variance technique. Unfortunately, the ANOM decision limits depend upon tables of constants that are usually only available in printed form or from specialized software programs. In this article we present new formulas for the ANOM constants and then illustrate how commonly available mathematical processors can be used to calculate the ANOM constants. This approach makes the ANOM constants easily accessible, portable, and unrestricted with regard to the choice of significance level, sample size, and number of populations.

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... Because this paper aims at exploring ANOM using control limits of extreme value statistics we have considered only the control chart aspects. However, a detailed literature about ANOM is available in Rao (2005) [9] and some related works in this direction are Ramig (1983) [8] , Bakir (1994) [1] , Bernard and Wludyka (2001) [2] , Montgomery (2001) [5] , Nelson and Dudewicz (2002) [6] , Rao and Prankumar (2002) [10] , Farnum (2004) [3] , Guirguis and Tobias (2004) [4] . The recently developed ANOM tables or techniques based on various distributions are Srinivasa Rao and Kantam (2012a) [11] , Srinivasa Rao et al. (2012b) [12] , Srinivasa Rao et al. (2012c) [13] and references there in. ...
... Because this paper aims at exploring ANOM using control limits of extreme value statistics we have considered only the control chart aspects. However, a detailed literature about ANOM is available in Rao (2005) [9] and some related works in this direction are Ramig (1983) [8] , Bakir (1994) [1] , Bernard and Wludyka (2001) [2] , Montgomery (2001) [5] , Nelson and Dudewicz (2002) [6] , Rao and Prankumar (2002) [10] , Farnum (2004) [3] , Guirguis and Tobias (2004) [4] . The recently developed ANOM tables or techniques based on various distributions are Srinivasa Rao and Kantam (2012a) [11] , Srinivasa Rao et al. (2012b) [12] , Srinivasa Rao et al. (2012c) [13] and references there in. ...
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... A nonparametric version of the ANOM test was introduced by Bakir [25], and a comparison between ANOM and ANOVA tests using parametric bootstrap was conducted by Chang et al. [26] The exact control limits for the balanced design with equal sample sizes were presented by Nelson [27], Nelson [28], while for the unbalanced design with unequal sample sizes were given by Soong and Hsu [29]. Further, the tables for the ANOM test with equal sample sizes were reported in studies [30][31][32][33] and for unequal sample sizes in studies [34,35]. ...
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In many experiments, our interest lies in testing the significance of means from the grand mean of the study variable. Sometimes, an additional linearly related uncontrollable factor is also observed along with the main study variable, known as a covariate. For example, in Electrical Discharge Machining (EDM) problem, the effect of pulse current on the surface roughness (study variable) is affected by the machining time (covariate). Hence, covariate plays a vital role in testing means, and if ignored, it may lead to false decisions. Therefore, we have proposed a covariate-based approach to analyze the means in this study. This new approach capitalizes on the covariate effect to refine the traditional structure and rectify misleading decisions, especially when covariates are present. Moreover, we have investigated the impact of assumptions on the new approach, including normality, linearity, and homogeneity, by considering equal or unequal sample sizes. This study uses percentage type Ⅰ error and power as our performance indicators. The findings reveal that our proposal outperforms the traditional one and is more useful in reaching correct decisions. Finally, for practical considerations, we have covered two real applications based on experimental data related to the engineering and health sectors and illustrated the implementation of the study proposal.
... In the rest of this article, the same principle is also applied by NWED. We only looked at ANOM control charts [3] in this research since it intends to examine ANOM by employing extreme value statistical control limits. No new ANOM tables or procedures have been examined by us. ...
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It is assumed that the probabilistic model of the quality characteristics follows the new weighted exponential distribution. Control charts based on each subgroup’s extreme values are established. The constants in the control chart are determined by the probability distribution of the extreme value order statistics of the sub-group and the sub-group size. The proposed chart is thus referred to as an extreme values chart. A biased overall mean analysis method (ANOM for truncated population) is used for the new weighted exponential distribution. Examples based on real time data are used to explain the findings.
... Because of this paper aims at exploring ANOM using control limits of extreme value statistics we have considered only the control chart aspects but not any recently developed ANOM tables or techniques. However, a detailed literature about ANOM is available in Rao (2005) and some related works in this direction are Enrick (1976), Schilling (1979), Ohta (1981), Ramig (1983), Mason et al. (1989), Bakir (1994, Bernard and Wludyka (2001), Montgomery (2001, Nelson and Dudewicz and Nelson (2003), Farnum (2004, Guirguis and Tobias (2004) and references therein. The rest of the paper is organized as follows. ...
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... Because this paper aims at exploring ANOM using control limits of extreme value statistics we have considered only the control chart aspects but not any recently developed ANOM tables or techniques. However, a detailed literature about ANOM is available in Rao(2005) [9] and some related works in this direction are Ramig(1983) [?],Bakir(1994) [1], Bernard and Wludyka(2001) [2] , Wludyka et al (2001) [?], Montgomery(2001) [5], Nelson and Dudewicz(2002) [12], Rao and Prankumar(2002) [10], Farnum(2004) [3], Guirguis and Tobias(2004) [4] and references there in. The rest of the paper is organized as follows. ...
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