Data Collected from two Starbucks location in NJ for the purposes of modeling the time between a customer walks into the store and the beverage is ordered

1. Starbucks Wait Time Analysis
Data Collected on
4/26/2012 and 4/29/2012
Brandon R. Theiss
Brandon.Theiss@gmail.com

2. Motivation
• Reliability is defined as:
– the probability of a product performing its intended
function under stated conditions for a defined period
of time.
• This definition unfortunately too narrowly defines the
term in the context of a tangible product.
• Services represent 76.8% of the overall Gross Domestic
Product of the United States or 11.9 Trillion dollars.
• A more applicable definition is therefore
– The ability of process to perform its intended function
under customer specified conditions for a customer
defined period of time.

3. Objective
• To study the reliability of the Starbucks
beverage delivery system to provide a
beverage to a customer prior to reaching
their critical wait time.

4. About Starbucks
• Founded 1971, in Seattle’s Pike Place
Market. Original name of company was
Starbucks Coffee, Tea and Spices, later
changed to Starbucks Coffee Company.
• In United States:
– 50 states, plus the District of Columbia
– 7,087 Company-operated stores
– 4,081 Licensed stores

5. Representative Stores
• Two of the 7,087 company operated
stores were selected by geographical
convenience
– Marlboro NJ
– New Brunswick NJ

6. About Marlboro NJ
Marlboro is a Township in Monmouth County, New Jersey. It has
a population of 40,191 with a median household income of
$101,322

7. About New Brunswick
New Brunswick is a city in Middlesex County, New Jersey. It has
a population of 55,181 with a median household income of
$36,080

8. Measurement System

9. Measurement Procedure
1. Click Start on 1 of 10 timers in the
Custom Application
2. Enter Identifying characteristic in textbox
3. Click Stop when the customer receives
their beverage or leaves the store. Data
is automatically recorded with times
measured in milliseconds
4. Click Reset for the next customer

10. Marlboro NJ Location

11. Marlboro Wait Time Data

12. Does the Data Follow a Weibull
Distribution?
Histogram of Time
Weibull
25 Shape 2.007
Scale 216106
N 94
20
15
Frequency
10
5
0
0 100000 200000 300000 400000 500000
Time

13. Does the Data Follow a Gamma
Distribution?
Histogram of Time
Gamma
25 Shape 3.977
Scale 47936
N 94
20
15
Frequency
10
5
0
0 100000 200000 300000 400000 500000
Time

14. Can the arrivals
of customers
be Modeled as
a Poisson
Process?
Goodness-of-Fit Test for Poisson Distribution
Data column: Marlboro
Poisson mean for Marlboro = 5.22222
Poisson Contribution
Marlboro Observed Probability Expected to Chi-Sq
<=3 7 0.235206 4.23371 1.80748
4 2 0.167197 3.00954 0.33865
5 3 0.174628 3.14330 0.00653
6 1 0.151991 2.73583 1.10135
7 1 0.113390 2.04102 0.53097
>=8 4 0.157589 2.83660 0.47716
N N* DF Chi-Sq P-Value
18 0 4 4.26215 0.372

15. Formal Test for the Data Being
Normally Distributed
Probability Plot for Time
Normal - 95% CI
99.9
Goodness of Fit Test
99
AD = 2.887
P-Value < 0.005
95
90
80
70
Percent
60
50
40
30
20
10
5
1
0.1
-200000 -100000 0 100000 200000 300000 400000 500000 600000
Time

16. Formal Test for the Data Being
Gamma Distributed
Probability Plot for Time
Gamma - 95% CI
99.9
Goodness of Fit Test
99
95 AD = 0.699
90 P-Value = 0.075
80
70
60
50
40
Percent
30
20
10
5
1
0.1
10000 100000 1000000
Time

17. Formal Test for the Data Being
Weibull Distributed
Probability Plot for Time
Weibull - 95% CI
99.9
99 Goodness of Fit Test
90
AD = 1.509
80
70 P-Value < 0.010
60
50
40
30
20
Percent
10
5
3
2
1
0.1
10000 100000 1000000
Time

18. Mean Time To Beverage and
“Reliability” at Marlboro
Biased Unbiased
190652.872424565 ms 190652.916039948 ms
3.17754787374275 min 3.1775486006658 min
Biased Unbiased
0.8727 0.8754

19. Is the Process Capable Based
Upon a Gamma Model?
Process Capability of Time
Calculations Based on Gamma Distribution Model
LB USL
P rocess D ata O v erall C apability
LB 0 Pp *
Target * PPL *
USL 300000 PPU 0.29
S ample M ean 190653 P pk 0.29
S ample N 94
Exp. O v erall P erformance
S hape 3.97724
P P M < LB *
S cale 47936
P P M > U S L 127306.05
O bserv ed P erformance P P M Total 127306.05
P P M < LB 0.00
P P M > U S L 95744.68
P P M Total 95744.68
0 100000 200000 300000 400000 500000

20. Is the Process Capable Based
Upon a Weibull Model?
Process Capability of Time
Calculations Based on Weibull Distribution Model
LB USL
P rocess D ata O v erall C apability
LB 0 Pp *
Target * PPL *
USL 300000 PPU 0.32
S ample M ean 190653 P pk 0.32
S ample N 94
Exp. O v erall P erformance
S hape 2.00713
P P M < LB *
S cale 216106
P P M > U S L 144910.81
O bserv ed P erformance P P M Total 144910.81
P P M < LB 0.00
P P M > U S L 95744.68
P P M Total 95744.68
0 100000 200000 300000 400000 500000

21. Is the Beverage Delivery
Process in Control?
I-MR Chart of Marlboro I-MR Chart of Marlboro
Using Box-Cox Transformation With Lambda = 0.50
600000
1
1 1 1 800
1 1 1
1 1 1
Individual V alue
450000
U C L=407256 UCL=679.6
Individual Value
600
300000
_
_
X=190653 X=422.7
150000 400
0
LC L=-25950 200
LCL=165.8
1 10 19 28 37 46 55 64 73 82 91
O bser vation 1 10 19 28 37 46 55 64 73 82 91
Observation
1
11 11 1
400000 450
M oving Range
300000
UCL=315.6
Moving Range
U C L=266097 300
200000
__ 150 __
100000
M R=81443 MR=96.6
0 LC L=0 0 LCL=0
1 10 19 28 37 46 55 64 73 82 91 1 10 19 28 37 46 55 64 73 82 91
O bser vation Observation

22. New Brunswick NJ Location

23. New Brunswick Wait Time Data

24. Does the Data Follow a Weibull
Distribution?
Histogram of Time
Weibull
40 Shape 1.994
Scale 273830
N 198
30
Frequency
20
10
0
0 100000 200000 300000 400000 500000 600000
Time

25. Does the Data Follow a Gamma
Distribution?
Histogram of Time
Gamma
40 Shape 3.080
Scale 78771
N 198
30
Frequency
20
10
0
0 100000 200000 300000 400000 500000 600000
Time

26. Can the arrivals
of customers
be Modeled as
a Poisson
Process?
Goodness-of-Fit Test for Poisson Distribution
Data column: New Brunswick
Poisson mean for New Brunswick = 9.9
New Poisson Contribution
Brunswick Observed Probability Expected to Chi-Sq
<=6 4 0.136574 2.73148 0.589107
7 - 8 3 0.207617 4.15235 0.319795
9 - 10 5 0.251357 5.02715 0.000147
11 - 12 4 0.205390 4.10780 0.002829
>=13 4 0.199062 3.98123 0.000088
N N* DF Chi-Sq P-Value
20 0 3 0.911967 0.823

27. Formal Test for the Data Being
Normally Distributed
Probability Plot for Time
Normal - 95% CI
99.9
Goodness of Fit Test
99
AD = 1.680
95 P-Value < 0.005
90
80
70
Percent
60
50
40
30
20
10
5
1
0.1
00 00 0 00 00 00 00 00 00 00
000 0 00 00 00 00 00 00 00 00
-2 -1 10 20 30 40 50 60 70
Time

28. Formal Test for the Data Being
Gamma Distributed
Probability Plot for Time
Gamma - 95% CI
99.9
Goodness of Fit Test
99
95 AD = 0.911
90 P-Value = 0.023
80
70
60
50
40
Percent
30
20
10
5
1
0.1
10000 100000 1000000
Time

29. Formal Test for the Data Being
Weibull Distributed
Probability Plot for Time
Weibull - 95% CI
99.9
99 Goodness of Fit Test
90
AD = 0.441
80
70 P-Value > 0.250
60
50
40
30
20
Percent
10
5
3
2
1
0.1
10000 100000 1000000
Time

30. Why Might the Data Not Follow
a Gamma?
Poisson Gamma ?
Gamma * ? =?
Make Drink
Wait in Line
Process
Arrival Deliver
To Store Order Drink
Drink
What We Measured

31. Is the Process Capable Based
Upon a Weibull Model?
Process Capability of Time
Calculations Based on Weibull Distribution Model
LB USL
P rocess D ata O v erall C apability
LB 0 Pp *
Target * PPL *
USL 300000 PPU 0.15
S ample M ean 242647 P pk 0.15
S ample N 198
E xp. O v erall P erformance
S hape 1.99408
P P M < LB *
S cale 273830
P P M > U S L 301307.05
O bserv ed P erformance P P M Total 301307.05
P P M < LB 0.00
P P M > U SL 303030.30
P P M Total 303030.30
0 100000 200000 300000 400000 500000 600000

32. Is the Process Capable Based
Upon a Gamma Model?
Process Capability of Time
Calculations Based on Gamma Distribution Model
LB USL
P rocess D ata O v erall C apability
LB 0 Pp *
Target * PPL *
USL 300000 PPU 0.13
S ample M ean 242647 P pk 0.13
S ample N 198
E xp. O v erall P erformance
S hape 3.0804
P P M < LB *
S cale 78771.2
P P M > U S L 283036.30
O bserv ed P erformance P P M Total 283036.30
P P M < LB 0.00
P P M > U S L 303030.30
P P M Total 303030.30
0 100000 200000 300000 400000 500000 600000

33. Mean Time To Beverage and
“Reliability” at New Brunswick
Biased Unbiased
242688.9419 ms 242371.0724 ms
4.0448 mins 4.0395 mins
Biased Unbiased
0.6987 0.6993

34. Is the Beverage Delivery
Process in Control?
I-MR Chart of New Brunswick I-MR Chart of New Brunswick
1 1
Using Box-Cox Transformation With Lambda = 0.50
600000 11
1 1 1
1 1 800 11 1
U C L=485623 UCL=733.1
Individual V alue
450000
Individual Value
600
300000 _ _
X=242647 X=473.9
400
150000
0 LC L=-330 200 LCL=214.7
1 1 1 1 1 1
1 1
1 21 41 61 81 101 121 141 161 181 1
O bser vation 1 21 41 61 81 101 121 141 161 181
Observation
1
480000 1 11
1
1 600
1 1 1
1
360000 1 1
Moving Range
1 1
11 1
Moving Range
1 1
U C L=298497 400 1
240000 UCL=318.4
__ 200
120000 __
M R=91359
MR=97.4
0 LC L=0 0 LCL=0
1 21 41 61 81 101 121 141 161 181 1 21 41 61 81 101 121 141 161 181
O bser vation Observation

35. Marlboro New Brunswick
Starbucks Wait Time Analysis
COMBINED

36. Is there a difference between
Marlboro and New Brunswick?
Histogram of Marlboro, New Brunswick
Gamma
40 Variable
Marlboro
New Brunswick
Shape Scale N
30 3.977 47936 94
3.080 78771 198
Frequency
20
10
0
0 100000 200000 300000 400000 500000 600000
Data

37. Is there a difference between
Marlboro and New Brunswick?
Kruskal-Wallis Test: Wait Times versus Location
Kruskal-Wallis Test on C2
Subscripts N Median Ave Rank Z
Marlboro 94 173350 121.6 -3.47
New Brunswick 198 216245 158.3 3.47
Overall 292 146.5
H = 12.04 DF = 1 P = 0.001
H = 12.04 DF = 1 P = 0.001 (adjusted for
ties)

38. Combined Wait Time Data

39. Does the Data Follow a Weibull
Distribution?
Histogram of Combined
Weibull
35 Shape 1.954
Scale 255391
N 292
30
25
Frequency
20
15
10
5
0
0 100000 200000 300000 400000 500000 600000
Combined

40. Does the Data Follow a Gamma
Distribution?
Histogram of Combined
Gamma
35 Shape 3.201
Scale 70580
N 292
30
25
Frequency
20
15
10
5
0
0 100000 200000 300000 400000 500000 600000
Combined

41. Are the Arrival Rates the Same?
Histogram of Marlboro, New Brunswick
2 4 6 8 10 12 14 16
Marlboro New Brunswick
9
8
7
6
Frequency
5
4
3
2
1
0
2 4 6 8 10 12 14 16

42. Are the Arrival Rates the Same?
Kruskal-Wallis Test: Arrivals versus Location
Kruskal-Wallis Test on Arrivals
Location N Median Ave Rank Z
Marlboro 18 4.500 12.4 -3.76
New Brunswick 20 10.000 25.9 3.76
Overall 38 19.5
H = 14.11 DF = 1 P = 0.000
H = 14.26 DF = 1 P = 0.000 (adjusted for
ties)

43. Can the arrivals
of customers
be Modeled as
a Poisson
Process?
Goodness-of-Fit Test for Poisson Distribution
Data column: Combined
Poisson mean for Combined = 7.68421
Poisson Contribution
Combined Observed Probability Expected to Chi-Sq
<=4 10 0.119196 4.52945 6.60719
5 3 0.102708 3.90291 0.20888
6 4 0.131538 4.99846 0.19945
7 2 0.144396 5.48703 2.21602
8 4 0.138696 5.27044 0.30624
9 3 0.118419 4.49991 0.49995
10 3 0.090995 3.45782 0.06062
11 1 0.063566 2.41551 0.82950
>=12 8 0.090486 3.43846 6.05144
N N* DF Chi-Sq P-Value
38 0 7 16.9793 0.018

44. Why Might the data set of Combined
Arrivals Not Represent a Poisson
Process?
• Not a large enough data set
• Not constant arrival rate
– Different demand for Beverages at different
stores at different times
• Other factors are influencing the
independence of events
– Traffic lights

45. Formal Test for the Data Being
Normally Distributed
Probability Plot for Combined
Normal - 95% CI
99.9
Goodness of Fit Test
99
AD = 4.293
95 P-Value < 0.005
90
80
70
Percent
60
50
40
30
20
10
5
1
0.1
0 00 0 0 0 0 0 0 0 0
00 00 00 00 00 00 00 00 00
00 10 00 00 00 00 00 00 00
-2 - 1 2 3 4 5 6 7
Combined

46. Formal Test for the Data Being
Gamma Distributed
Probability Plot for Combined
Gamma - 95% CI
99.9
Goodness of Fit Test
99
95 AD = 0.594
90 P-Value = 0.141
80
70
60
50
40
Percent
30
20
10
5
1
0.1
10000 100000 1000000
Combined

47. Formal Test for the Data Being
Weibull Distributed
Probability Plot for Combined
Weibull - 95% CI
99.9
99 Goodness of Fit Test
90
AD = 0.959
80
70 P-Value = 0.016
60
50
40
30
20
Percent
10
5
3
2
1
0.1
10000 100000 1000000
Combined

48. Mean Time To Beverage and
“Reliability”
Biased Unbiased
225908.8493 ms 226153.1587 ms
3.7651 mins 3.7692 mins
Biased Unbiased
0.7629 0.7617

49. Is the Process Capable Based
Upon a Gamma Model?
Process Capability of Combined
Calculations Based on Gamma Distribution Model
LB USL
P rocess D ata O v erall C apability
LB 0 Pp *
Target * PPL *
USL 300000 PPU 0.16
S ample M ean 225909 P pk 0.16
S ample N 292
Exp. O v erall P erformance
S hape 3.20075
P P M < LB *
S cale 70580
P P M > U S L 237100.41
O bserv ed P erformance P P M Total 237100.41
P P M < LB 0.00
P P M > U S L 236301.37
P P M Total 236301.37
0 100000 200000 300000 400000 500000 600000

50. Is the Process Capable Based
Upon a Weibull Model?
Process Capability of Combined
Calculations Based on Weibull Distribution Model
LB USL
P rocess D ata O v erall C apability
LB 0 Pp *
Target * PPL *
USL 300000 PPU 0.19
S ample M ean 225909 P pk 0.19
S ample N 292
Exp. O v erall P erformance
S hape 1.95393
P P M < LB *
S cale 255391
P P M > U S L 254194.23
O bserv ed P erformance P P M Total 254194.23
P P M < LB 0.00
P P M > U S L 236301.37
P P M Total 236301.37
0 100000 200000 300000 400000 500000 600000

51. Is the Process Capable Based
Upon a Weibull Model?
The corresponds to a Sigma level of 4. The Goal is 6!

52. Is the Process Capable Based
Upon a Gamma Model?
The corresponds to a Sigma level of 2. The Goal is 6!

53. Conclusions
• The amount of time a customer waits at a Starbucks is
dependent on which location they visit.
• Regardless of location, Starbucks is incapable of reliably
delivering a beverage in less than 5 minutes
• There is evidence to suggest that the arrivals follow a
Poisson distribution which is supported by the literature
• There is evidence to suggest that the wait times follow a
gamma distribution which the literature would suggest

54. • Academics
About the Author
– MS Industrial Engineering Rutgers University
– BS Electrical & Computer Engineering Rutgers University
– BA Physics Rutgers University
• Awards
– ASQ Top 40 Leader in Quality Under 40.
• Professional
– Principal Industrial Engineer -Medtronic
– Master Black belt- American Standard Brands
– Systems Engineer- Johnson Scale Co
• Certifications
– ASQ Certified Manager of Quality/ Org Excellence Cert # 13788
– ASQ Certified Quality Auditor Cert # 41232
– ASQ Certified Quality Engineer Cert # 56176
– ASQ Certified Reliability Engineer Cert #7203
– ASQ Certified Six Sigma Green Belt Cert # 3962
– ASQ Certified Six Sigma Black Belt Cert # 9641
– ASQ Certified Software Quality Engineer Cert # 4941
• Publications
– Going with the Flow- The importance of collecting data without holding up your processes-
Quality Progress March 2011
– "Numbers Are Not Enough: Improved Manufacturing Comes From Using Quality Data the
Right Way" (cover story). Industrial Engineering Magazine- Journal of the Institute of
Industrial Engineers September (2011): 28-33. Print

55. ?