Six Sigma Analysis of Daily Cycling Commute

Six Sigma Analysis of Daily Cycling Commute 2015 ASQ Lean and Six Sigma Conference

March 3, 2015

Brandon Theiss, [email protected]

Motivation

• Nationally the average one-way commuting distance is 12.6 miles with 0.6% commuting via bicycle

• In the Washington DC metro area, where the case study was performed, the average commuting time is 33.4 minutes with 3.1% of commuters riding a bicycle.

Goals For The Talk

1. Demonstrate that Six Sigma can be applied to non-traditional applications (i.e. physical training or commuting)

2. Show that Control Charts are particularly useful in analyzing commuting times

3. Illustrate a Multifactor regression model that considers departure time, wind speed, weather, day of the week and improvement in physical conditioning.

The RouteDepart

Arrive

Weather Station

The Data Collection

• Cycle Data Collected by Garmin Edge 500• Records

• Distance, Speed, Location, Calories and Elevation

• Data collected over a 9 week period (6/15/2014- 8/15/2014)

Weather StationData• Weather data by the

National Weather Service at the weather station at Reagan National Airport

Weather Data

312825221 91 61 31 0741

84

78

72

66

60

Observation

Ind

ivid

ua

l Va

lue

_X=74.00

UCL=83.61

LCL=64.38

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=3.62

UCL=11.81

LCL=0

1

I-MR Chart of Temp °F

1 st Quartile 71 .350

Median 75.000

3rd Quartile 76.450

Maximum 82.000

72.51 1 75.483

73.000 75.900

3.370 5.543

A-Squared 0.68

P-Value 0.069

Mean 73.997

StDev 4.191

Variance 17.560

Skewness -1 .04088

Kurtosis 2.75658

N 33

Minimum 60.100

Anderson-Darling Normality Test

95% Confidence Interval for Mean

95% Confidence Interval for Median

95% Confidence Interval for StDev

8075706560

Median

Mean

76757473

95% Confidence Intervals

Summary Report for Temp °F

Temperature (°F)

1 st Quartile 0.69000

Median 0.78000

3rd Quartile 0.80000

Maximum 0.84000

0.71922 0.77593

0.73000 0.79000

0.06430 0.10577

A-Squared 1 .55

P-Value <0.005

Mean 0.74758

StDev 0.07996

Variance 0.00639

Skewness -0.865595

Kurtosis -0.453918

N 33

Minimum 0.58000





84.00%78.00%72.00%66.00%60.00%

Median

Mean

80.00%78.00%76.00%74.00%72.00%


Summary Report for Humidity

312825221 91 61 31 0741

90.00%

80.00%

70.00%

60.00%

Observation

Ind

ivid

ua

l Va

lue

_X=74.76%

UCL=92.21%

LCL=57.30%

312825221 91 61 31 0741

20.00%

1 5.00%

1 0.00%

5.00%

0.00%

Observation

Mo

vin

g R

an

ge

__MR=6.56%

UCL=21.44%

LCL=0.00%

1

I-MR Chart of Humidity

Relative Humidity (%)


Median 30.853

3rd Quartile 32.695

Maximum 35.746

28.459 31 .388

28.514 32.419

3.322 5.464

A-Squared 0.77

P-Value 0.040

Mean 29.923

StDev 4.131

Variance 17.067

Skewness -1 .18627

Kurtosis 1 .78258

N 33

Minimum 17.181





35302520

Median

Mean

333231302928


Summary Report for Human Index

312825221 91 61 31 0741

40

35

30

25

20

Observation

Ind

ivid

ua

l Va

lue

_X=29.92

UCL=39.32

LCL=20.53

312825221 91 61 31 0741

1 0.0

7.5

5.0

2.5

0.0

Observation

Mo

vin

g R

an

ge

__MR=3.53

UCL=11.54

LCL=0

1

I-MR Chart of Human Index

Humidex

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10987654321

1

0

Day

Rain

Individual Value Plot of Rain

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10987654321

1 0

5

0

-5

-1 0

Day

Win

d

Head Wind (Positive) / Tail Wind (Negative)

Departure Time

312825221 91 61 31 0741

7:00

6:40

6:20

6:00

5:40

Observation

Ind

ivid

ua

l Va

lue

_X=6:15

UCL=6:54

LCL=5:37

312825221 91 61 31 0741

0.04

0.03

0.02

0.01

0.00

Observation

Mo

vin

g R

an

ge

__MR=0.01009

UCL=0.03297

LCL=0

11

1

I-MR Chart of Departure Time

I had an early meeting

312825221 91 61 31 0741

50

25

0

-25

-50

Observation

Ind

ivid

ua

l Va

lue

_X=-0.7

UCL=37.9

LCL=-39.3

312825221 91 61 31 0741

60

45

30

1 5

0

Observation

Mo

vin

g R

an

ge

__MR=14.53

UCL=47.48

LCL=0

11

1

I-MR Chart of 6:15 Target

ThuWedTueMon

40

30

20

1 0

0

-1 0

-20

-30

DayofWeek

6:1

5 T

arg

et

0.875-1.22222-5

2.625

Boxplot of 6:15 Target

987654321

40

30

20

1 0

0

-1 0

-20

-30

Weeknum

6:1

5 T

arg

et

-2.5

-8.33333

1

-17.25

-3.75-4.75

5.25

-2

23.25

Boxplot of 6:15 Target

Cycling Data

Segment 0

Start

Finish

• Departure from Benning Rd Northeast

• Segment finished under Capital East

• Segment Distance 1.1 miles


Median 5.9700

3rd Quartile 6.6550

Maximum 7.4800

5.4088 6.31 18

5.5498 6.3255

1 .0241 1 .6844

A-Squared 1 .25

P-Value <0.005

Mean 5.8603

StDev 1 .2735

Variance 1 .6217

Skewness -2.09994

Kurtosis 7.23867

N 33

Minimum 0.7800





7654321

Median

Mean

6.46.26.05.85.65.4


Summary Report for Stage 0 (1 .1 )

312825221 91 61 31 0741

8

6

4

2

0

Observation

Ind

ivid

ua

l Va

lue _

X=5.860

UCL=8.893

LCL=2.828

312825221 91 61 31 0741

4.8

3.6

2.4

1 .2

0.0

Observation

Mo

vin

g R

an

ge

__MR=1.140

UCL=3.726

LCL=0

1

11

I-MR Chart of Stage 0 (1 .1 )

GPS Did Not Always Start Recording Immediately

• Garmin Edge 500 did not get a GPS lock immediately.

• Consequently data collection started at different points

Segment 1 Start

Finish

• Segment Started at East Capital• Segment Finished at Nationals Park• Segment Distance 3.5 miles• Total Distance 4.6 miles


Median 14.800

3rd Quartile 15.350

Maximum 16.400

14.353 15.032

14.210 15.215

0.771 1 .267

A-Squared 0.16

P-Value 0.945

Mean 14.692

StDev 0.958

Variance 0.918

Skewness -0.253076

Kurtosis -0.427336

N 33

Minimum 12.600





16151413

Median

Mean

15.215.014.814.614.414.2


Summary Report for Stage 1 (3.5)

312825221 91 61 31 0741

1 7

1 6

1 5

1 4

1 3

Observation

Ind

ivid

ua

l Va

lue

_X=14.692

UCL=17.030

LCL=12.355

312825221 91 61 31 0741

3

2

1

0

Observation

Mo

vin

g R

an

ge

__MR=0.879

UCL=2.871

LCL=0

1

I-MR Chart of Stage 1 (3.5)

987654321

1 6.5

1 6.0

1 5.5

1 5.0

1 4.5

1 4.0

1 3.5

1 3.0

1 2.5

Weeknum

Sta

ge 1

(3

.5)

13.44

15.84

13.3825

14.3225

15.32

14.37

15.2

14.525

15.4925

Boxplot of Stage 1 (3.5)

One-way ANOVA: Stage 1 (3.5) versus Weeknum

Factor Information

Factor Levels Values

Weeknum 9 1, 2, 3, 4, 5, 6, 7, 8, 9

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Weeknum 8 20.193 2.5242 6.59 0.000

Error 24 9.187 0.3828

Total 32 29.380

Was There A Significant Difference Between Weeks?

987654321

1 6

1 5

1 4

1 3

Week Number

Sa

mp

le M

ea

n

__X=14.692

UCL=16.051

LCL=13.334

987654321

3

2

1

0

Week Number

Sa

mp

le R

an

ge

_R=0.722

UCL=2.360

LCL=0

1

1

Xbar-R Chart of Stage 1 (3.5)

Tests performed with unequal sample sizes

Segment 2

Start

Finish

• Segment Started at Nationals Park

• Segment Finished at entry onto Mount Vernon Trail

• Segment Distance 3.6 miles• Total Distance 8.2 miles


Median 18.155

3rd Quartile 18.927

Maximum 26.820

17.359 19.042

16.950 18.650

1 .871 3.103

A-Squared 1 .25

P-Value <0.005

Mean 18.200

StDev 2.334

Variance 5.448

Skewness 1 .77507

Kurtosis 5.47402

N 32

Minimum 14.650





2724211815

Median

Mean

19.018.518.017.517.0



312825221 91 61 31 0741

28

24

20

1 6

1 2

Observation

Ind

ivid

ua

l Va

lue

_X=18.20

UCL=23.89

LCL=12.51

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__

MR=2.14

UCL=6.99

LCL=0

1

11


What happened here?

I Tried A Different Route!Correct Route

Route Taken

312825221 91 61 31 0741

27

24

21

1 8

1 5

Observation

Ind

ivid

ua

l Va

lue

_X=17.92

UCL=21.76

LCL=14.08

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=1.44

UCL=4.72

LCL=0

1

1

11

I-MR Chart of Stage 2 (3.6)What happened here?

Recalculated Control Limits

I Made a Wrong Turn!

Wrong Turn

312825221 91 61 31 0741

27

24

21

1 8

1 5

Observation

Ind

ivid

ua

l Va

lue

_

X=17.74

UCL=20.96

LCL=14.52

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=1.21

UCL=3.96

LCL=0

1

1

11

11


Got a Flat took Metro

Again Recalculated Control Limits

Segment 3• Segment Started at entry

onto Mount Vernon Trail• Segment Finished at entry

onto streets of Alexandria• Segment Distance 4.6 miles• Total Distance 12.8 miles

Start

Finish


Median 18.650

3rd Quartile 19.172

Maximum 29.700

18.040 19.640

18.270 19.030

1 .780 2.951

A-Squared 3.71

P-Value <0.005

Mean 18.840

StDev 2.220

Variance 4.927

Skewness 3.891 1

Kurtosis 19.4030

N 32

Minimum 15.700





2824201 6

Median

Mean

1 9.5019.2519.0018.7518.5018.2518.00



312825221 91 61 31 0741

30

25

20

1 5

Observation

Ind

ivid

ua

l Va

lue

_

X=18.84

UCL=23.08

LCL=14.60

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=1.59

UCL=5.20

LCL=0

1

11


Changed a flat tire

312825221 91 61 31 0741

30

25

20

1 5

Observation

Ind

ivid

ua

l Va

lue

_X=18.49

UCL=20.78

LCL=16.20

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=0.86

UCL=2.82

LCL=0

1

1

1

1

11


Recalculated Control Limits

Segment 4• Segment Started at entry

onto streets of Alexandria• Segment finished at US

Patent and Trademark Office

• Segment Distance 2.5 miles• Total Distance 15.3 miles

Start

Finish


Median 13.200

3rd Quartile 13.980

Maximum 16.530

12.684 13.622

12.415 13.772

1 .022 1 .709

A-Squared 0.29

P-Value 0.603

Mean 13.153

StDev 1 .279

Variance 1 .635

Skewness 0.572571

Kurtosis 0.415937

N 31

Minimum 11 .000





16151413121 1

Median

Mean

13.7513.5013.251 3.0012.751 2.50



312825221 91 61 31 0741

1 8

1 6

1 4

1 2

1 0

Observation

Ind

ivid

ua

l Va

lue

_

X=13.153

UCL=17.404

LCL=8.902

312825221 91 61 31 0741

6.0

4.5

3.0

1 .5

0.0

Observation

Mo

vin

g R

an

ge

__MR=1.598

UCL=5.222

LCL=0


Segments 1-4• Segment Started at East

Capital • Segment finished at US

Patent and Trademark Office

• Segment Distance 14.2 miles

• Removes GPS Initialization Problem

Finish

Start


Median 64.930

3rd Quartile 66.600

Maximum 75.470

63.445 66.335

63.952 66.240

3.147 5.264

A-Squared 0.65

P-Value 0.084

Mean 64.890

StDev 3.939

Variance 15.512

Skewness 0.30820

Kurtosis 1 .63438

N 31

Minimum 56.580





75706560

Median

Mean

66.566.065.565.064.564.063.5


Summary Report for Stage 1 -4

312825221 91 61 31 0741

75

70

65

60

55

Observation

Ind

ivid

ua

l Va

lue

_

X=64.89

UCL=72.75

LCL=57.03

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=2.95

UCL=9.65

LCL=0

11

1

1

11

I-MR Chart of Stage 1 -4

Different Route Changed Flat

312825221 91 61 31 0741

75

70

65

60

55

Observation

Ind

ivid

ua

l Va

lue

_

X=64.23

UCL=69.72

LCL=58.74

312825221 91 61 31 0741

1 2

9

6

3

0

Observation

Mo

vin

g R

an

ge

__MR=2.06

UCL=6.74

LCL=0

11

1

1

1

1

1

11

I-MR Chart of Stage 1 -4

One-way ANOVA: Stage 1-4 versus Weeknum

Factor Levels Values

Weeknum 9 1, 2, 3, 4, 5, 6, 7, 8, 9



Weeknum 8 243.1 30.39 3.01 0.019

Error 22 222.3 10.10

Total 30 465.4

Was There A Statistically Significant Difference Between Weeks?

987654321

75

70

65

60

55

Weeknum

Sta

ge 1

-4

59.32

65.85

59.0133

63.6

66.2465.3875

67.605

65.8625

67.86

Boxplot of Stage 1 -4

987654321

70.0

67.5

65.0

62.5

60.0

Sample

Sa

mp

le M

ea

n

__X=64.89

UCL=70.92

LCL=58.86

987654321

1 5

1 0

5

0

Sample

Sa

mp

le R

an

ge

_R=3.20

UCL=10.47

LCL=0

1

Xbar-R Chart of Stage 1 -4

Tests performed with unequal sample sizes

Week 6-9Week 1 -3

70.0

67.5

65.0

62.5

60.0

57.5

55.0

Data

66.198

62.3025

Boxplot of Week 1 -3, Week 6-9

Two-sample T for Week 1-3 vs Week 6-9

N Mean StDev SE Mean

Week 1-3 10 66.20 1.91 0.61

Week 6-9 12 62.30 3.50 1.0

Difference = μ (Week 1-3) - μ (Week 6-9)

Estimate for difference: 3.90

95% upper bound for difference: 5.95

T-Test of difference = 0 (vs <): T-Value = 3.31 P-Value = 0.998 DF = 17

Did The Times Improve Significantly?

RegressionTravel Time as a Function of Weather Conditions

Stage 1-4 = 64.534 + 0.246 X1

Step Change Step P Final P

1 Add X1 0.042 0.042

1 007550250

R-Squared(adjusted) %

Human Index

Temp °F

Wind

30201 00

Increase in R-Squared %

1050-5-10

72

66

60

Wind

Sta

ge 1

-4

Human Index

Temp °F

Wind

1 00500

R-Squared %

X1: Wind X2: Temp °F X3: Human Index

Final Model Equation

Model Building SequenceDisplays the order in which terms were added or removed.

Incremental Impact of X VariablesLong bars represent Xs that contribute the most new

information to the model.

Fitted Line Plot for WindShows the relationship between Stage 1-4 and Wind.

Each X Regressed on All Other TermsLong bars represent Xs that do not help explain

additional variation in Y.

A gray bar represents an X variable not in the model.

Multiple Regression for Stage 1 -4Model Building Report

R-squared (adjusted) 10.49% 7.69%

P-value, model 0.042* 0.124

P-value, linear term 0.042* 0.045*

P-value, quadratic term — 0.729

Residual standard deviation 3.726 3.784

Statistics Linear

Selected Model

Quadratic

Alternative Model

1 050-5-1 0

75

70

65

60

55

Wind

Sta

ge 1

-4

Large residual

Y: Stage 1-4

X: Wind

Fitted Line Plot for Linear ModelY = 64.53 + 0.2455 X

* Statistically significant (p < 0.05)

Regression for Stage 1 -4 vs WindModel Selection Report

Different Route& Fix Flat

R-squared (adjusted) 10.16% 6.85%

P-value, model 0.051 0.152

P-value, linear term 0.051 0.057

P-value, quadratic term — 0.843

Residual standard deviation 2.930 2.983

Statistics Linear

Selected Model

Quadratic

Alternative Model

1 050-5-1 0

67.5

65.0

62.5

60.0

57.5

55.0

Wind

Sta

ge 1

-4_F

Large residual

Y: Stage 1-4_F

X: Wind

Fitted Line Plot for Linear ModelY = 64.00 + 0.1874 X

Regression for Stage 1 -4_F vs WindModel Selection Report

RegressionTravel Time as a Function of Non-Weather Factors

Regression Analysis: Stage 1-4_F versus Day



Regression 1 77.36 77.361 10.98 0.003

Day 1 77.36 77.361 10.98 0.003

Error 27 190.15 7.043

Total 28 267.51

Model Summary

S R-sq R-sq(adj) R-sq(pred)

2.65380 28.92% 26.29% 14.41%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 67.40 1.08 62.59 0.000

Day -0.1797 0.0542 -3.31 0.003 1.00

Regression Equation

Stage 1-4_F = 67.40 - 0.1797 Day

RegressionTravel Time as a Function of Weather and Non Weather Factors

CostsAlternative Travel Methods

Taking the Metro

20 Miles Per Gallon$3.65 / Gallon15.4 miles per trip

=$2.81 per trip

+Parking$10/day

= $12.31

Driving

Caloric Energy Is Not Free!


Median 642.00

3rd Quartile 662.00

Maximum 724.00

614.39 648.64

607.68 656.00

37.31 62.41

A-Squared 0.27

P-Value 0.648

Mean 631 .52

StDev 46.69

Variance 2180.19

Skewness -0.072865

Kurtosis -0.507187

N 31

Minimum 544.00





700650600550

Median

Mean

660650640630620610


Summary Report for Calories

312825221 91 61 31 0741

800

700

600

500

Observation

Ind

ivid

ua

l Va

lue

_X=631.5

UCL=773.1

LCL=489.9

312825221 91 61 31 0741

200

1 50

1 00

50

0

Observation

Mo

vin

g R

an

ge

__

MR=53.2

UCL=174.0

LCL=0

I-MR Chart of Calories

Cost of Energy Needed for Cycling

• 760+710 =1470 kCal (Calories)

• $6.39+$5.99 = $12.38

• $12.38/ 1470 kCal = $ 0.0084218/ kCal

• 95% Confidence Interval of kCal per trip (614.39, 648.64) with mean631.52

• 95% Confidence Interval for the cost per trip ($5.17, $ 5.46) with mean $5.32

Comparison Of The Three Alternatives

• Cycling• One Way

• $5.32

• 1:10

• Round Trip• $10.64

• 2:20

• For 33 Days• $351.02

• 77 hours

• Driving• One Way

• $12.81

• 0:27

• Round trip• $15.62

• 0:54

• For 33 Days• $515.49

• 29.7 hours

• Metro• One Way

• $4.55

• 1:04

• Round Trip• $9.10

• 2:08

• For 33 Days• $300.30

• 70.4 hours

Questions?

Contact Information:

Brandon R. Theiss, PE

Rutgers School of Law- Camden

[email protected]

Six Sigma Analysis of Daily Cycling Commute

Education

Transcript of Six Sigma Analysis of Daily Cycling Commute