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Abstract Control limits for individual measurements (X) chart are available in the literature using moving range as an estimate of process standard deviation. This paper presents new control limits for X - chart using analysis of means (ANOM) approach. In deriving the control limits, sample standard deviation is used as an estimate of process standard deviation. The expected length of the interval between existing (old) control limits is compared with the expected length of the interval between new control limits for the same confidence coefficient and recommendations are made to the practitioner when to use the new control limits.
Keywords Analysis of means, X-chart, Control limits 1. Introduction For testing the equality of several population means, a graphical procedure, namely, Analysis of Means (ANOM) was introduced by Ott (1967) as an alternative to Analysis of Variance (ANOVA). In Ott's procedure, the results are summarized in an ANOM chart. This chart is similar in appearance to a control chart. Instead of control limits, decision lines are used in ANOM procedure. The main difference between ANOM chart and control chart is that the value of k (number of samples) is usually as large as 20 or more in control charts, whereas k x 2 in an ANOM chart. When there are exactly 2 means the ANOM is simply a graphical form of Student's t - test. In ANOM chart, the sample mean values are compared to the overall grand mean, about which the upper and lower decision lines have been constructed. If a sample mean falls outside these decision lines, it is declared significantly different from the grand mean.
There are several advantages of ANOM plotting, e.g., (i) it provides a comparison of the relative importance and magnitude of the factors as well as their statistical significance, (ii) it provides a pin-pointing of sources of non-randomness, and (iii) it encourages the translation of conclusions into scientific action and for taking managerial decisions. Hence, ANOM plots reveal the statistical significance as well as practical significance of samples being compared.
Several authors extended the ANOM technique for comparing several (i) proportions (ii) counts (iii) treatment effects (iv) interaction effects (v) Linear contrasts (vi) variances (vii) correlation coefficients (viii) Regression coefficients (ix) intercepts (x) autocorrelation coefficients (xi) coefficients of variation....