61 Lean Six Sigma Graphs and Statistics

LEAN-SIX-SIGMA-GRAPHS-AND-STATISTICS

This Lean Six Sigma Graphs and Statistics reference guide contains a short explanation for when to use each graph or statistical test and where to find it in Minitab.

This article on Lean Six Sigma Graphs and Statistics has been in the making since we first started on our Lean Six Sigma path back in 2002. Yes, we had Minitab back then already, LOL.

Achieving process excellence very much depends on appropriately and correctly employing the tools and techniques contained within Lean Six Sigma. Many factors can lead to poor improvement results, and most often a direct link back to the incorrect use or interpretation of graphical or statistical tests is found.

The embedded guide additionally offers images of the Lean Six Sigma graphs or statistical test referred to in the text below.

Lean-Six-Sigma-Graphs-Reference

Lean Six Sigma Graphs and Statistics used in the Define and Measure Phases

NameUsed ForWhere In Minitab
Simple Dotplots – Descriptive GraphsUse to assess and compare distributions by plotting the values along a number line. Dotplots are especially useful for comparing distributions.Graph > Dotplot
Individual Value Plot – Descriptive GraphsUse to assess and compare sample distributions by plotting individual values for each variable or group in a vertical column, making it easy to spot outliers and see the distribution.Graph > Individual Value Plot
Pie Chart- Descriptive GraphsUse to display the proportion of each data category relative to the whole data set.Graph > Pie Chart
Histogram Distribution – Descriptive GraphsUse to examine the shape and spread of sample data. Histograms divide sample values into many intervals called bins. Bars represent the number of observations falling within each bin (frequency).Graph > Bar Chart
Probability Distribution Plot – Descriptive GraphsUse probability distribution plots to view and compare the shape of distribution curves and to view areas under distribution curves corresponding to either probabilities or data values.Graph > Probability Distribution Plot
Run Charts – Time SeriesUse to evaluate patterns in data over time. Minitab can generate calendar values, clock values, or index values for the time scale, or you can use your own column of stampGraph > Time Series Plot   Stat > Time Series > Time Series Plot
Boxplots – Descriptive GraphsUse boxplots (also called box-and-whisker plots) to assess and compare sample distributions.Graph > Boxplot Stat > EDA > Boxplot
Interval Plot – Descriptive GraphsUse to plot means and either confidence intervals or error bars for one or more variables. An interval plot illustrates both a measure of central tendency and variability of the data.Graph > Interval Plot   Stat > ANOVA > Interval Plot
Pareto DiagramsA Pareto chart can help you determine which of the defects comprise the “vital few” and which are the “trivial many.”Stat > Quality Tools > Pareto Chart
Scatter Plots – Relational PlotsUse to illustrate the relationship between two variables by plotting one against the other.Graph > Scatterplot
Matrix Plots ( X-Y Matrix)- Relational PlotsAssess the relationships between many pairs of variables at once by creating an array of scatterplots. There are two types of matrix plots.Graph > Matrix Plot
Marginal Plots plus Histogram – Relational PlotsUse to assess the relationship between two variables and examine their distributions. Scatterplot with Histograms.Graph > Marginal Plot > choose With Histograms > OK
Marginal Plots plus Boxplot Relational PlotsUse to assess the relationship between two variables and examine their distributions. Scatterplot with Boxplots.Graph > Marginal Plot > choose With Boxplots > OK
Marginal Plots plus Dotplot Relational PlotsUse to assess the relationship between two variables and examine their distributions. Scatterplot with DotplotsGraph > Marginal Plot > choose With Dotplots > OK
Graphical Descriptical StatisticsUse to produce a graphical summary for each column or each level of a By variable.Stat > Basic Statistics > Graphical Summary
 Individuals Chart -Time SeriesAn individual chart is a control chart of individual observations. You can use individual charts to track the process level and detect the presence of special causes when the sample size is 1.Stat > Control Charts > Variables Charts for Individuals > Individuals
 X Bar \ R Chart – Variable Control ChartDisplays a control chart for subgroup means (an X chart) and a control chart for subgroup ranges (an R chart) in the same graph window.Stat > Control Charts > Variables Charts for Subgroups > Xbar-R
 X Bar \ S Chart – Variable Control ChartDisplays a control chart for subgroup means (an X chart) and a control chart for subgroup standard deviations (an S chart) in the same graph window.Stat > Control Charts > Variables Charts for Subgroups > Xbar-S
NP Chart – Attribute Control ChartTracks the number of defectives and detects the presence of special causes.Stat > Control Charts > Attributes Charts > NP
P Chart – Attribute Control ChartTracks the proportion defective and detects the presence of special causes.Stat > Control Charts > Attributes Charts > P
C Chart – Attribute Control ChartTracks the number of defects and detects the presence of special causesStat > Control Charts > Attributes Charts > C
U Chart – Attribute Control ChartTracks the number of defects per unit sampled and detects the presence of special causesStat > Control Charts > Attributes Charts > U
Gage R&R (X Bar \ R Chart)Gage repeatability and reproducibility studies determine how much of your observed process variation is due to measurement system variation.Stat > Quality Tools > Gage Study > Gage R&R Study (Crossed)
Attribute Gage StudyAttribute gage studies calculate the amount of bias and repeatability of a measurement system when the response is a binary attribute variable.Stat > Quality Tools > Gage Study > Attribute Gage Study (Analytic Method)
Attribute Agreement AnalysisUse attribute agreement analysis to assess the agreement of nominal or ordinal ratings given by multiple appraisers. The measurements are subjective ratings by people rather than direct physical measurements.Stat > Quality Tools > Attribute Agreement Analysis
Normal Probability Plots – Lumped DataUse to evaluate the fit of a distribution to your data, estimate percentiles, and compare different sample distributions.Graph >Probability Plot
Individual Distribution IdentificationUse to evaluate the optimal distribution for your data based on the probability plots and goodness-of-fit tests before conducting a capability analysis study. Choose from 14 distributions.Stat > Quality Tools > Individual Distribution Identification
Box-Cox TransformationFor improved process where the data became non-Normal.Stat > Control Charts > Box-Cox Transformation.
Johnsons Transform – Capability StudyYou can try to transform your data, so it follows a normal distribution. Johnson transformation optimally selects a function from three families of distributions.Stat > Quality Tools > Johnson Transformation
Capability AnalysisUse Capability Analysis (Normal) to produce a process capability report when your data are from a normal distribution or transform the data to follow a normal distribution using a Box-Cox or Johnson transformation.Stat > Quality Tools > Capability Analysis > Normal
Capability 6 PackUse to produce process capability report when your data follow a normal distribution. To confirm process stability, normality, and capability.Stat > Quality Tools > Capability Sixpack > Normal

Lean Six Sigma Graphs and Statistics used in the Analyse, Improve and Control Phases

NameUsed ForWhere in Minitab
CorrelationCalculates the Pearson product-moment correlation coefficient between each pair of variables you list.Stat > Basic Statistics > Correlation
Regression – Fitted Line Plot This procedure performs regression with linear and polynomial (second or third order) terms if requested of a single predictor variable and plots a regression line through the data on the actual or log10 scale.Stat > Regression > Fitted Line Plot
Regression – Best SubsetBest subsets regression identifies the subset models that produce the highest R values from a full set of the predictor variables that you specify. Best subsets regression is an efficient way to identify models that achieve your goals with as few predictors as possible.Stat > Regression > Best Subsets
Regression AnalysisYou can use Regression to perform simple and multiple regression using least squares.Stat > Regression > Regression
Regression – Residual plotsUse to examine the goodness of model fit in regression and ANOVA. Examining residual plots helps determine if the ordinary least squares assumptions are being met. Stat> Regression>Residual Plots
Test of Equal VarianceUse variance test to perform hypothesis tests for equality or homogeneity of variance using Bartlett’s and Levene’s tests. An F Test replaces Bartlett’s test when you have just two levels.Stat > ANOVA > Test for Equal Variances
Chi-SqrUse Chi-Square Goodness-of-Fit Test to test the hypotheses: H0: Data follow a multinomial distribution with certain proportions. H1: Data do not follow a multinomial distribution with certain proportionsStat > Tables > Chi-Square Goodness-of-Fit Test (One Variable)
One-Tailed t-testPerforms a one-sample t-test or t-confidence interval for the mean.Stat > Basic Statistics > 1-Sample t
2 Sample t-testComputes a confidence interval & performs a hypothesis test of the difference b/w two population means when std. Deviations are unknown, and samples are drawn independently from each other.Stat > Basic Statistics > 2-Sample t
Paired tPerforms a paired t-test. This is appropriate for testing the mean difference between paired observations when the paired differences follow a normal distribution.Stat > Basic Statistics > Paired t
1 Sample SignYou can perform a 1-sample sign test of the median or calculate the corresponding point estimate and confidence interval.Stat > Nonparametrics > 1-Sample Sign
      Mann.WhitneyYou can perform a 2-sample rank test (also called the Mann- Whitney test or the two-sample Wilcoxon rank-sum test) of the equality of two population medians and calculate the corresponding point estimate and confidence interval.Stat > Nonparametrics > Mann- Whitney
Kruskal WallisYou can perform a Kruskal-Wallis test of the equality of medians for two or more populations.Stat > Nonparametrics > Kruskal- Wallis
Mood’s MedianMood’s median test can be used to test the equality of medians from two or more populations and, like the Kruskal- Wallis Test, provides a nonparametric alternative to the one-way analysis of variance. Mood’s median test is sometimes called a median test or sign scores test.Stat > Nonparametrics > Mood’s Median Test
Pairwise NonparametricPairwise Averages calculates and stores the average for each possible pair of values in a single column, including each value with itself.Stat > Nonparametrics > Pairwise Averages
One-way ANOVAPerforms a one-way analysis of variance, with the response variable in one column, factor levels in another.Stat > ANOVA > One-way
ANOVA Main Effects PlotUse Main Effects Plot to plot data means when you have multiple factors. The points in the plot are the means of the response variable at the various levels of each factor, with a reference line drawn at the grand mean of the response data.Stat > ANOVA > Main Effects Plot
ANOVA Interval PlotUse to plot means and either confidence intervals or error bars for one or more variables. An interval plot illustrates both a measure of central tendency and variability of the data.Graph > Interval Plot   Stat > ANOVA > Interval Plot
ANOVAInteraction PlotInteractions Plot creates a single interaction plot for two factors or a matrix of interaction plots for three to nine factors. An interactions plot is a plot of means for each level of a factor with a second factor held constant.Stat > ANOVA > Interactions Plot
MultiVari StudiesMinitab draws multi-vari charts for up to four factors. Multi- vari charts are a way of presenting the analysis of variance data in a graphical form providing a “visual” alternative to the analysis of variance.Stat > Quality Tools > Multi-Vari Chart
Factorial Design – Normal PlotCan’t analyze the full factorial using ANOVA procedures. Effects associated with, i.e. Temp and Temp * Chip interaction are important. We need to evaluate the highest order interaction and not worry about the Main Effect.Stat > DOE > Factorial > Analyze Variability
Factorial Design – Pareto ChartCan’t analyze the full factorial using ANOVA procedures. Effects associated with, i.e. Temp and Temp * Chip interaction are important. We need to evaluate the highest order interaction and not worry about the Main Effect.Stat > DOE > Factorial > Analyze Variability
DOE Interaction PlotWhen the effect of one factor depends on the level of the other factor, you can use an interaction plot to visualize possible interactions.Stat > DOE > Factorial > Factorial Plots
DOE Main Effects PlotUse in conjunction with an analysis of variance and design of experiments to examine differences among level means for one or more factors. The main effect is present when different levels of a factor affect the response differently.Stat > DOE > Factorial > Factorial Plots
Cube PlotCube plots can be used to show the relationships among two to eight factors – with or without a response measure – for two-level factorial or Plackett-Burman designs.Stat > DOE > Factorial > Factorial Plots
Response OptimizerUse response optimization to help identify the combination of input variable settings that jointly optimize a single response or a set of responses.Stat > DOE > Factorial > Response Optimizer
Area GraphUse to evaluate trends in multiple time series and each series’ contribution to the sum. Minitab can generate calendar values, clock values, or index values for the time scale, or you can use your own column of stamp values.Graph > Area Graph
Contour PlotIn a contour plot, the values for two variables are represented on the x- and y-axes. In contrast, the values for a third variable are represented by shaded regions, called contours. A contour plot is like a topographical map in which x-, y-, and z-values are plotted instead of longitude, latitude, and altitude.Graph > Contour Plot
3D Surface PlotUse to evaluate relationships between three variables at once. Like a 3D scatterplot, a 3D surface plot has three axes. In addition, a 3D Surface Plot uses interpolation to produce a continuous surface (surface plot) or grid (wireframe plot) of z-values that fits your data.Graph > 3D Surface Plot
3D Scatter PlotUse to evaluate relationships between three variables at once by plotting data on three axes.Graph > 3D Scatterplot
Control ChartsSee Define and Measure phase 
Capability AnalysisSee Define and Measure phase 

We trust you found this article on Lean Six Sigma Graphs and Statistics of value. You might also find our article containing all the relevant Lean Six Sigma Terminologies of value too.

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