Six Sigma Continuous Data Tools

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Continuous Data Tools


With Six Sigma there are two types of problems that occur within a process: problems with variation and problems with centering. The goal of Six Sigma is to have a process which is centered on a target with minimum variation.

Six Sigma continuous data tools are used to describe the nature and extent of these two types of problems when studying a continuous CT characteristic.

  • With variation problems, we make inferences about the standard deviation or the variance of the population based upon sample data.
  • With centering problems, we make inferences about the mean or the median of the population based upon sample data.

Confidence Interval

Confidence Intervals allow us to estimate population parameters (mean, standard deviation, etc.) within a range of values set at a pre-assigned probability called "confidence level".

A confidence interval is a range of values that is used to estimate the true population parameter , based on observations of a sample. The confidence interval represents an acceptance region. If a sample average or sample standard deviation falls within this region, the null hypothesis is accepted.

t-Test, Z-Test, ANOVA

Many Six Sigma continuous data tools exist for the mean. The One Sample t-Test and Z-Test are used to compare the population mean with a value such as the target. The t-Test is normally used for small sample size (<30) and the Z-Test for larger samples (> 30). However, as the sample size increases, the results of the t-Test approach the Z -Test.

When using a limited sample ( n < 30 ), a one sample t-Test can be used to establish if the population of the mean of a CT characteristic can be statistically proven to be located on a given target. We can also determine the confidence interval that will contain the true population mean within a set probability level.

When we want to determine the influence of factors such as procedures, material type, assembly sequence, temperature, etc. on our process, we can use the Two- Sample t-Test to determine if the mean of a CT characteristic significantly changes under two different conditions. For 2 or more conditions, we can use the One-Way ANOVA Test (analysis of variance).

The Two-Way ANOVA allows us to analyse the effect of two factors on a CT characteristic. An interaction effect between the two factors means that they have a combined effect on the CT characteristic.

Homogeneity of Variance Tests

The homogeneity of variance tests is used to determine if the variances of a CT characteristic significantly changes under two or more different conditions introduced by one factor.

Correlation Coefficient

The correlation coefficient is used to calculate the strength of the linear relationship between a continuous dependent variable (Y) and a continuous independent variable (X).

When the relationship is strong, an equation that describes this relationship can be obtained through linear regression analysis. A fitted line plot allows us to visualize the equation with prediction bands.

Non-parametric Continuous Data Tools


Most of the Six Sigma continuous data tools assume that the data comes from a normal distribution. When it is impossible to characterize the population distribution, or when the distribution is not normal, nonparametric tests can be used.

With these tests, instead of studying the mean, the median is used because it is a more appropriate measure of central tendency for data coming from non-symmetrical distributions.

One -Sample Wilcoxon Test

The One -Sample Wilcoxon Test is usually used to determine if the median of a CT characteristic is on target.

Mann-Whitney, Kruskal-Wallis and Mood's Median Tests

The Two -Sample Mann-Whitney Test is used to determine if the median of a CT characteristic significantly changes under two different conditions.

To determine the influence of one factor, we can use the Kruskal Wallis Test or the Mood's Median Test to determine if the median significantly changes under two or more different conditions. Compared to the Kruskal Wallis, the Mood's Median Test is more robust to the presence of outliers in the data, but it is a less efficient test.

From Continuous Data Tools to Six Sigma Tools.

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