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Six Sigma Black Belt Training Overview of Charts and Graphs: Mini Case Overview – The Story A retail company has 3 regional shipping centers, each with its own computer system. Goal:

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Six sigma black belt training l.jpg

Six Sigma Black Belt Training

Overview of Charts and Graphs: Mini Case

Overview the story l.jpg

Overview – The Story

A retail company has 3 regional shipping centers, each with its own computer system.


To determine which of the 3 systems is most efficient, determine if it helps meet customer needs regarding shipping, and improve it further. Then, the system can be used companywide to facilitate integration and enhance efficiency.

Source: Meet Minitab


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Shipping Example Data

A few records from the dataset (total 319 records) are shown below:


Eastern3/3/2003 8:343/7/2003 15:214.28264On time255

Eastern3/3/2003 8:353/6/2003 17:053.35417On time196

Eastern3/3/2003 8:38**Back order299

Central3/3/2003 8:583/6/2003 14:593.25069On time81

Central3/3/2003 9:043/8/2003 10:125.04722On time235

Central3/3/2003 9:063/9/2003 16:136.29653Late259

Western3/3/2003 9:443/6/2003 10:083.01667On time291

Western3/3/2003 9:463/6/2003 9:503.00278On time271

Source: Minitab Software V14 Example file

Continuous (Numerical) Data

Categorical Data

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First Look at Shipping Data – Univariate Analysis

Univariate analysis simply means looking at data one variable at a time, as a precursor to multivariate analysis.


  • To understand the individual variables before exploring relationships among variables,

  • To check for extraordinary, incorrect, or missing data.

    The basic method is to graph the data to look at the distribution, and compute measures of central tendency (Mean/Median) and variation (Range, Standard Deviation).

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Individual Value Plots

The graphs below show the number of days for shipping for all data

together on the left, and separated by shippingcenter on the right. The graph on the

right also shows the mean values for each center connected by a line. At first

glance, it is evident that the Western center has the lowest mean number of days

for shipping.

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Frequency Histograms – A look at the distribution

Frequency histograms help us see how the data are distributed. At left we can see that the number of days for shipping across all centers is normally distributed with a mean of about 4, and ranging from about 1 to 8 days. At the right is the distribution of the 3 centers shown separately.

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Checking for Normality – Normal Probability Plot

The normal probability plot is a graph where the X-axis shows the

actual values of the variable, and the Y-axis is scaled such that the values

should fall (if normal) between the outer blue lines shown. A perfectly

Normal distribution would have all values on the middle blue line. This method

is especially useful when the sample is too small for a meaningful histogram.

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Box Plots – Comparing Distributions

Box plots are a useful way to compare distributions visually. Box plots

show the smallest value, the first quartile, median, third quartile, and the

Largest value of the variable. In the plots below, the Mean is also marked.

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Graphing Categorical Data – Bar/Pie Charts

The Bar chart below shows the status of orders in the sample as

A percentage. About 7-8% of the orders are on back-order, while

About 5% are shipped late overall. The Pie charts show the percent

Of back-orders and late shipments by each center.

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Descriptive Statistics

Descriptive statistics give us numerical insight into the data. Compare this

information to the graphs on the previous page.

Descriptive Statistics: Days

Results for Center = Central

Variable Status N N* Mean SE Mean StDev

Days Back order 0 6 * * *

Late 6 0 6.431 0.157 0.385

On time 93 0 3.826 0.119 1.149

Results for Center = Eastern

Variable Status N N* Mean SE Mean StDev

Days Back order 0 8 * * *

Late 9 0 6.678 0.180 0.541

On time 92 0 4.234 0.112 1.077

Results for Center = Western

Variable Status N N* Mean SE Mean StDev

Days Back order 0 3 * * *

On time 102 0 2.981 0.108 1.090

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Testing Hypotheses - ANOVA

While itlooks like the centers are different in their efficiencies, a hypothesis test can

confirm that. A one-way ANOVA tests whether the mean number of days for the 3 centers

are in fact significantly different from each other. The low p-value (almost 0) indicates that

one can conclude with great confidence (almost 100%) that there at least one of the centers

is different from the others.

One-way ANOVA: Days versus Center

Source DF SS MS F P

Center 2 114.63 57.32 39.19 0.000

Error 299 437.28 1.46

Total 301 551.92

S = 1.209 R-Sq = 20.77% R-Sq(adj) = 20.24%

Individual 95% CIs For Mean Based on

Pooled StDev

Level N Mean StDev -----+---------+---------+---------+----

Central 99 3.984 1.280 (----*---)

Eastern 101 4.452 1.252 (----*----)

Western 102 2.981 1.090 (----*---)


3.00 3.50 4.00 4.50

Pooled StDev = 1.209

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Examining relationships - scatterplot

Is the better performance of the Western center due to smaller shipping

distances than the other regions? First, a scatterplot of Number of Days for shipping

against the Distance across all centers seems to show no relationship

between the two.

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Scatterplot separated by Center

When we look at it by center, there still seems to be no relationship

between distance and number of days.

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