An introduction to SigmaXL's various Graphical tools Established in 1998, SigmaXL Inc. is a leading provider of user friendly Excel Add-ins for Lean Six Sigma graphical and statistical tools and Monte Carlo simulation. SigmaXL® customers include market leaders like Agilent, Diebold, FedEx, Microsoft, Motorola and Shell. SigmaXL® software is also used by numerous colleges, universities and government agencies. Our flagship product, SigmaXL®, was designed from the ground up to be a cost-effective, powerful, but easy to use tool that enables users to measure, analyze, improve and control their service, transactional, and manufacturing processes. As an add-in to the already familiar Microsoft Excel, SigmaXL® is ideal for Lean Six Sigma training and application, or use in a college statistics course.  DiscoverSim™ enables you to quantify your risk through Monte Carlo simulation and minimize your risk with global optimization. Business decisions are often based on assumptions with a single point value estimate or an average, resulting in unexpected outcomes. DiscoverSim™ allows you to model the uncertainty in your inputs so that you know what to expect in your outputs.

1. Graphical Tools SigmaXL® Version 6.1
Basic and Advanced (Multiple) Pareto Charts
EZ-Pivot/Pivot Charts
Multiple Boxplots and Dotplots
Multiple Normal Probability Plots (with
95% confidence intervals to ease
interpretation of normality/non-normality)
Run Charts (with Nonparametric Runs Test
allowing you to test for Clustering, Mixtures,
Lack of Randomness, Trends and Oscillation.)
Multi-Vari Charts
Basic Histogram
Multiple Histograms and Descriptive Statistics
(includes Confidence Interval for Mean and StDev.,
as well as Anderson-Darling Normality Test)
Multiple Histograms and Process Capability
(Pp, Ppk, Cpm, ppm, %)
Scatter Plots (with linear regression and
optional 95% confidence intervals and
prediction intervals)
Scatter Plot Matrix

2. Graphical Tools:
Multiple Pareto Charts
2
Customer Type - Customer Type: # 1 - Size of Customer:
Large
6
4
2
Ordertakestoo-long
Notavailable
Wrongcolor
Difficultto-order
Returncalls
0
Customer Type - Customer Type: # 1 - Size of Customer:
Small
Ordertakestoo-long
10
8
6
4
2
0
Ordertakestoo-long
8
12
Notavailable
10
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
14
Count
12
Count
Customer Type - Customer Type: # 2 - Size of Customer:
Large
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
14
Notavailable
0
Ordertakestoo-long
Notavailable
Wrongcolor
Difficultto-order
Returncalls
0
4
Wrongcolor
2
6
Wrongcolor
4
8
Difficultto-order
6
10
Difficultto-order
8
12
Returncalls
Count
10
Returncalls
12
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
14
Count
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
14
Customer Type - Customer Type: # 2 - Size of Customer:
Small
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3. Graphical Tools: EZ-Pivot/Pivot
Charts – The power of Excel’s
Pivot Table and Charts are now
easy to use!
Size of Customer (All)
70
Count of Major-Complaint
60
50
40
Customer Type
3
2
1
30
20
10
0
Difficult-to-order
Not-available
Order-takes-too-long
Return-calls
Wrong-color
Major-Complaint
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Index

4. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
9
109
0
Run Chart - Avg days Order to delivery time
Graphical Tools:
Run Charts with
Nonparametric Runs Test
67.40
62.40
57.40
52.40
Median: 49.00
47.40
42.40
37.40
32.40
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Index

5. Basic Histogram
Count = 100
Mean = 3.530
Stdev = 0.904031
Minimum = 1
45
25th Percentile (Q1) = 3
50th Percentile (Median) = 4
40
95% CI Mean = 3.351 to 3.709
95% CI Sigma = 0.793746 to
1.050191
35
Anderson-Darling Normality Test:
A-Squared = 5.417
25
20
15
10
5
6.00
Loyalty - Likely to Recommend
5.00
4.00
3.00
2.00
0
1.00
Frequency
30
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Index

6. Graphical Tools:
Multiple Histograms &
Descriptive Statistics
12
Overall Satisfaction - Customer Type: 1
10
Count = 31
Mean = 3.3935
Stdev = 0.824680
Range = 3.1
8
6
Minimum = 1.7200
25th Percentile (Q1) = 2.8100
50th Percentile (Median) = 3.5600
75th Percentile (Q3) = 4.0200
Maximum = 4.8
4
2
4.98
4.71
4.44
4.17
3.90
3.62
3.35
3.08
2.81
2.54
2.26
1.99
1.72
0
Overall Satisfaction - Customer Type: 1
95% CI Mean = 3.09 to 3.7
95% CI Sigma = 0.659012 to 1.102328
Anderson-Darling Normality Test:
A-Squared = 0.312776; P-value = 0.5306
12
Overall Satisfaction - Customer Type: 2
10
Count = 42
Mean = 4.2052
Stdev = 0.621200
Range = 2.6
8
6
Minimum = 2.4200
25th Percentile (Q1) = 3.8275
50th Percentile (Median) = 4.3400
75th Percentile (Q3) = 4.7250
Maximum = 4.98
4
2
Overall Satisfaction - Customer Type: 2
4.98
4.71
4.44
4.17
3.90
3.62
3.35
3.08
2.81
2.54
2.26
1.99
1.72
0
95% CI Mean = 4.01 to 4.4
95% CI Sigma = 0.511126 to 0.792132
Anderson-Darling Normality Test:
A-Squared = 0.826259; P-value = 0.0302
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Index

7. Graphical Tools:
Multiple Histograms &
Process Capability
Histogram and Process Capability Report
Room Service Delivery Time: Before Improvement (Baseline)
LSL = -10
Target = 0
USL = 10
160
140
120
Count = 725
Mean = 6.0036
Stdev (Overall) = 7.1616
USL = 10; Target = 0; LSL = -10
Capability Indices using Overall Standard Deviation
Pp = 0.47
Ppu = 0.19; Ppl = 0.74
Ppk = 0.19
Cpm = 0.36
Sigma Level = 2.02
Expected Overall Performance
ppm > USL = 288409.3
ppm < LSL = 12720.5
ppm Total = 301129.8
% > USL = 28.84%
% < LSL = 1.27%
% Total = 30.11%
100
80
60
Actual (Empirical) Performance
% > USL = 26.90%
% < LSL = 1.38%
% Total = 28.28%
40
20
0
Delivery Time Deviation
Histogram and Process Capability Report
Room Service Delivery Time: After Improvement
LSL = -10
Target = 0
USL = 10
Anderson-Darling Normality Test
A-Squared = 0.708616; P-value = 0.0641
Count = 725
Mean = 0.09732
Stdev (Overall) = 2.3856
USL = 10; Target = 0; LSL = -10
Capability Indices using Overall Standard Deviation
Pp = 1.40
Ppu = 1.38; Ppl = 1.41
Ppk = 1.38
Cpm = 1.40
Sigma Level = 5.53
160
140
120
Expected Overall Performance
ppm > USL = 16.5
ppm < LSL = 11.5
ppm Total = 28.1
% > USL = 0.00%
% < LSL = 0.00%
% Total = 0.00%
100
80
60
40
Actual (Empirical) Performance
% > USL = 0.00%
% < LSL = 0.00%
% Total = 0.00%
20
0
Delivery Time Deviation
Anderson-Darling Normality Test
A-Squared = 0.189932; P-value = 0.8991
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Index

8. Graphical Tools:
Multiple Boxplots
5
Overall Satisfaction
Overall Satisfaction
5
4
3
2
1
4
3
2
1
1
2
Customer Type - Size of Customer: Large
3
1
2
3
Customer Type - Size of Customer: Small
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Index

9. Graphical Tools:
Multiple Normal Probability
Plots
2
1
1
NSCORE
3
2
NSCORE
3
0
0
-1
-1
-2
-2
-3
-3
1
2
3
4
Overall Satisfaction - Customer Type: 1
5
6
2.1
2.6
3.1
3.6
4.1
4.6
5.1
5.6
6.1
Overall Satisfaction - Customer Type: 2
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Index

10. Overall Satisfaction (Mean
Options)
Graphical Tools:
Multi-Vari Charts
4.634
4.634
4.634
4.634
4.134
4.134
4.134
4.134
3.634
3.634
3.634
3.634
3.134
3.134
3.134
3.134
2.634
2.634
2.634
2.634
2.134
2.134
2.134
2.134
1.634
1.634
#1
#2
#3
Standard Deviation
Customer Type - Size of Customer:
Large - Product Type: Consumer
1.634
#1
#2
#3
Customer Type - Size of Customer: Small Product Type: Consumer
1.634
#1
#2
#3
Customer Type - Size of Customer: Large Product Type: Manufacturer
#1
#2
#3
Customer Type - Size of Customer: Small Product Type: Manufacturer
1.00
1.00
1.00
1.00
0.80
0.80
0.80
0.80
0.60
0.60
0.60
0.60
0.40
0.40
0.40
0.40
0.20
0.20
0.20
0.20
0.00
0.00
0.00
#1
#2
#3
Customer Type - Size of Customer:
Large - Product Type: Consumer
#1
#2
#3
Customer Type - Size of Customer: Small Product Type: Consumer
0.00
#1
#2
#3
Customer Type - Size of Customer: Large Product Type: Manufacturer
#1
#2
#3
Customer Type - Size of Customer: Small Product Type: Manufacturer
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11. Graphical Tools:
Multiple Scatterplots with
Linear Regression
5.1
4.6
y = 0.5238x + 1.6066
R2 = 0.6864
5.1
y = 0.5639x + 1.822
R2 = 0.6994
4.6
Overall Satisfaction
Overall Satisfaction
4.1
3.6
3.1
2.6
4.1
3.6
3.1
2.1
2.6
1.6
1.1
1.01
1.51
2.01
2.51
3.01
3.51
Responsive to Calls - Customer Type: 1
4.01
4.51
2.1
1.88
2.38
2.88
3.38
3.88
4.38
4.88
Responsive to Calls - Customer Type: 2
Linear Regression with 95%
Confidence Interval and Prediction Interval
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12. y = 0.567x + 1.6103
R2 = 0.6827
3.7200
2.7200
1.7200
1.0000
2.0000
3.0000
4.0000
3.7200
2.7200
1.7200
1.4000
5.0000
Responsive to Calls
y = 1.2041x - 0.7127
R2 = 0.6827
2.0000
1.0000
1.7200 2.2200 2.7200 3.2200 3.7200 4.2200 4.7200
3.0000
2.0000
1.4000
1.7200 2.2200 2.7200 3.2200 3.7200 4.2200 4.7200
2.0000
3.0000
4.0000
5.0000
0.9600
1.7200 2.2200 2.7200 3.2200 3.7200 4.2200 4.7200
Overall Satisfaction
3.9600
y = 0.0799x + 2.9889
R2 = 0.0071
2.9600
1.9600
0.9600
1.0000
4.9600
y = 0.0893x + 3.57
R2 = 0.0071
3.0000
2.0000
1.9600
2.9600
3.9600
4.9600
Staff Knowledge
4.4000
y = 0.0428x + 3.6071
R2 = 0.0026
3.4000
2.4000
1.4000
0.9600
1.9600
2.9600
3.9600
4.9600
4.9600
2.0000
3.0000
4.0000
Responsive to Calls
5.0000
Staff Knowledge
1.9600
3.9600
Staff Knowledge
4.9600
Staff Knowledge
Staff Knowledge
2.9600
y = 0.303x + 2.5773
R2 = 0.1437
2.4000
1.4000
1.0000
2.9600
4.0000
1.0000
0.9600
4.4000
Responsive to Calls
4.9600
y = 0.1055x + 2.8965
R2 = 0.0059
3.4000
3.4000
Overall Satisfaction
3.9600
2.4000
Ease of Communications
2.4000
4.4000
1.9600
Staff Knowledge
Ease of Communications
Ease of Communications
Ease of Communications
Overall Satisfaction
3.4000
2.7200
5.0000
y = 0.4743x + 2.0867
R2 = 0.1437
4.0000
1.0000
1.4000
y = 0.0555x + 3.6181
R2 = 0.0059
3.7200
1.7200
0.9600
4.4000
Responsive to Calls
3.0000
y = 0.8682x + 0.4478
R2 = 0.5556
3.4000
5.0000
4.0000
4.4000
2.4000
4.7200
Ease of Communications
Responsive to Calls
Responsive to Calls
5.0000
y = 0.64x + 1.4026
R2 = 0.5556
4.7200
Overall Satisfaction
4.7200
Overall Satisfaction
Overall Satisfaction
Graphical Tools:
Scatterplot Matrix
3.9600
y = 0.0599x + 3.0732
R2 = 0.0026
2.9600
1.9600
0.9600
1.4000
2.4000
3.4000
4.4000
Ease of Communications
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