Starbucks Wait Time Analysis

Brandon R. Theiss

Mathew Brown

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.

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.

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– 6,075 Company-operated stores– 4,082 Licensed stores

• Outside US– 2,326 Company Stores– 3,890 Licensed stores

Representative Stores• Two of the 6,075 company operated

stores were selected by geographical convenience– Marlboro NJ– New Brunswick NJ

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

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

Measurement System

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

Marlboro NJ Location

Marlboro Wait Time Data

Does the Data Follow a Weibull Distribution?

5000004000003000002000001000000

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Time

Frequency

Shape 2.007Scale 216106N 94

Histogram of TimeWeibull

Does the Data Follow a Gamma Distribution?

5000004000003000002000001000000

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0

Time

Frequency

Shape 3.977Scale 47936N 94

Histogram of TimeGamma

Can the arrivals of customers

be Modeled as a Poisson Process?

Goodness-of-Fit Test for Poisson Distribution Data column: MarlboroPoisson mean for Marlboro = 5.22222 Poisson ContributionMarlboro Observed Probability Expected to Chi-Sq<=3 7 0.235206 4.23371 1.807484 2 0.167197 3.00954 0.338655 3 0.174628 3.14330 0.006536 1 0.151991 2.73583 1.101357 1 0.113390 2.04102 0.53097>=8 4 0.157589 2.83660 0.47716 N N* DF Chi-Sq P-Value18 0 4 4.26215 0.372

Formal Test for the Data Being Normally Distributed

6000005000004000003000002000001000000-100000-200000

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Time

Perc

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Goodness of Fit Test

AD = 2.887 P-Value < 0.005

Probability Plot for TimeNormal - 95% CI

Formal Test for the Data Being Gamma Distributed

100000010000010000

99.9

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9590

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Perc

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Goodness of Fit Test

AD = 0.699 P-Value = 0.075

Probability Plot for TimeGamma - 95% CI

Formal Test for the Data Being Weibull Distributed

100000010000010000

99.999

9080706050403020

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Time

Perc

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Goodness of Fit Test

AD = 1.509 P-Value < 0.010

Probability Plot for TimeWeibull - 95% CI

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

Is the Process Capable Based Upon a Gamma Model?

5000004000003000002000001000000

LB USL

LB 0

Target *USL 300000Sample Mean 190653

Sample N 94Shape 3.97724Scale 47936

Process DataPp *

PPL *PPU 0.29Ppk 0.29

Overall Capability

PPM < LB 0.00

PPM > USL 95744.68PPM Total 95744.68

Observed Performance

PPM < LB *

PPM > USL 127306.05PPM Total 127306.05

Exp. Overall Performance

Process Capability of TimeCalculations Based on Gamma Distribution Model

Is the Process Capable Based Upon a Weibull Model?

5000004000003000002000001000000

LB USL

LB 0

Target *USL 300000Sample Mean 190653

Sample N 94Shape 2.00713Scale 216106

Process DataPp *

PPL *PPU 0.32Ppk 0.32

Overall Capability

PPM < LB 0.00

PPM > USL 95744.68PPM Total 95744.68

Observed Performance

PPM < LB *

PPM > USL 144910.81PPM Total 144910.81

Exp. Overall Performance

Process Capability of TimeCalculations Based on Weibull Distribution Model

Is the Beverage Delivery Process in Control?

918273645546372819101

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Observation

Indiv

idual V

alu

e

_X=422.7

UCL=679.6

LCL=165.8

918273645546372819101

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Observation

Movin

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ange

__MR=96.6

UCL=315.6

LCL=0

1111

111

I-MR Chart of MarlboroUsing Box-Cox Transformation With Lambda = 0.50

918273645546372819101

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Observation

Indiv

idual V

alu

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_X=190653

UCL=407256

LCL=-25950

918273645546372819101

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300000

200000

100000

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Observation

Movin

g R

ange

__MR=81443

UCL=266097

LCL=0

111

111

111

I-MR Chart of Marlboro

New Brunswick NJ Location

New Brunswick Wait Time Data

Does the Data Follow a Weibull Distribution?

6000005000004000003000002000001000000

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30

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10

0

Time

Frequency

Shape 1.994Scale 273830N 198

Histogram of TimeWeibull

Does the Data Follow a Gamma Distribution?

6000005000004000003000002000001000000

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30

20

10

0

Time

Frequency

Shape 3.080Scale 78771N 198

Histogram of TimeGamma

Goodness-of-Fit Test for Poisson Distribution Data column: New BrunswickPoisson mean for New Brunswick = 9.9New Poisson ContributionBrunswick Observed Probability Expected to Chi-Sq<=6 4 0.136574 2.73148 0.5891077 - 8 3 0.207617 4.15235 0.3197959 - 10 5 0.251357 5.02715 0.00014711 - 12 4 0.205390 4.10780 0.002829>=13 4 0.199062 3.98123 0.000088 N N* DF Chi-Sq P-Value20 0 3 0.911967 0.823

Can the arrivals of customers

be Modeled as a Poisson Process?

Formal Test for the Data Being Normally Distributed

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Time

Perc

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Goodness of Fit Test

AD = 1.680 P-Value < 0.005

Probability Plot for TimeNormal - 95% CI

Formal Test for the Data Being Gamma Distributed

100000010000010000

99.9

99

959080706050403020

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Time

Perc

ent

Goodness of Fit Test

AD = 0.911 P-Value = 0.023

Probability Plot for TimeGamma - 95% CI

Formal Test for the Data Being Weibull Distributed

100000010000010000

99.999

9080706050403020

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Time

Perc

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Goodness of Fit Test

AD = 0.441 P-Value > 0.250

Probability Plot for TimeWeibull - 95% CI

Why Might the Data Not Follow a Gamma?

Wait in LineMake Drink

Process

Poisson

Arrival To Store

Gamma ?

Deliver Drink

Gamma * ? =?

Order Drink

What We Measured

Is the Process Capable Based Upon a Weibull Model?

6000005000004000003000002000001000000

LB USL

LB 0Target *USL 300000Sample Mean 242647Sample N 198Shape 1.99408Scale 273830

Process DataPp *PPL *PPU 0.15Ppk 0.15

Overall Capability

PPM < LB 0.00PPM > USL 303030.30PPM Total 303030.30

Observed Performance

PPM < LB *PPM > USL 301307.05PPM Total 301307.05

Exp. Overall Performance

Process Capability of TimeCalculations Based on Weibull Distribution Model

Is the Process Capable Based Upon a Gamma Model?

6000005000004000003000002000001000000

LB USL

LB 0Target *USL 300000Sample Mean 242647Sample N 198Shape 3.0804Scale 78771.2

Process DataPp *PPL *PPU 0.13Ppk 0.13

Overall Capability

PPM < LB 0.00PPM > USL 303030.30PPM Total 303030.30

Observed Performance

PPM < LB *PPM > USL 283036.30PPM Total 283036.30

Exp. Overall Performance

Process Capability of TimeCalculations Based on Gamma Distribution Model

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

Is the Beverage Delivery Process in Control?

181161141121101816141211

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Observation

Indiv

idual V

alu

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_X=473.9

UCL=733.1

LCL=214.7

181161141121101816141211

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Observation

Movin

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__MR=97.4

UCL=318.4

LCL=0

1

1

11

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1111

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I-MR Chart of New BrunswickUsing Box-Cox Transformation With Lambda = 0.50

181161141121101816141211

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Observation

Indiv

idual V

alu

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_X=242647

UCL=485623

LCL=-330

181161141121101816141211

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Observation

Movin

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__MR=91359

UCL=298497

LCL=0

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I-MR Chart of New Brunswick

COMBINEDStarbucks Wait Time Analysis

Marlboro New Brunswick

Combined Wait Time Data

Is there a difference between Marlboro and New Brunswick?

6000005000004000003000002000001000000

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Data

Frequency

3.977 47936 943.080 78771 198

Shape Scale N

MarlboroNew Brunswick

Variable

Histogram of Marlboro, New BrunswickGamma

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)

Does the Data Follow a Weibull Distribution?

6000005000004000003000002000001000000

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Combined

Frequency

Shape 1.954Scale 255391N 292

Histogram of CombinedWeibull

Does the Data Follow a Gamma Distribution?

6000005000004000003000002000001000000

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Combined

Frequency

Shape 3.201Scale 70580N 292

Histogram of CombinedGamma

Are the Arrival Rates the Same?

161412108642

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161412108642

Marlboro

Frequency

New Brunswick

Histogram of Marlboro, New Brunswick

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)

Goodness-of-Fit Test for Poisson Distribution

Data column: Combined

Poisson mean for Combined = 7.68421 Poisson ContributionCombined Observed Probability Expected to Chi-Sq<=4 10 0.119196 4.52945 6.607195 3 0.102708 3.90291 0.208886 4 0.131538 4.99846 0.199457 2 0.144396 5.48703 2.216028 4 0.138696 5.27044 0.306249 3 0.118419 4.49991 0.4999510 3 0.090995 3.45782 0.0606211 1 0.063566 2.41551 0.82950>=12 8 0.090486 3.43846 6.05144 N N* DF Chi-Sq P-Value38 0 7 16.9793 0.018

Can the arrivals of customers

be Modeled as a Poisson Process?

Why Might the data set of Combined Arrivals Not Represent a Poisson

Process?

• Not a large enough data set of stores

• Not constant arrival rate– Different demand for Beverages at different

stores at different times

• Other factors are influencing the independence of events– Traffic lights

Formal Test for the Data Being Normally Distributed

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Perc

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Goodness of Fit Test

AD = 4.293 P-Value < 0.005

Probability Plot for CombinedNormal - 95% CI

Formal Test for the Data Being Gamma Distributed

100000010000010000

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9590

80706050403020

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Perc

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Goodness of Fit Test

AD = 0.594 P-Value = 0.141

Probability Plot for CombinedGamma - 95% CI

Formal Test for the Data Being Weibull Distributed

100000010000010000

99.999

9080706050403020

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Combined

Perc

ent

Goodness of Fit Test

AD = 0.959 P-Value = 0.016

Probability Plot for CombinedWeibull - 95% CI

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

Is the Process Capable Based Upon a Gamma Model?

6000005000004000003000002000001000000

LB USL

LB 0

Target *USL 300000Sample Mean 225909

Sample N 292Shape 3.20075Scale 70580

Process DataPp *

PPL *PPU 0.16Ppk 0.16

Overall Capability

PPM < LB 0.00

PPM > USL 236301.37PPM Total 236301.37

Observed Performance

PPM < LB *

PPM > USL 237100.41PPM Total 237100.41

Exp. Overall Performance

Process Capability of CombinedCalculations Based on Gamma Distribution Model

Is the Process Capable Based Upon a Weibull Model?

6000005000004000003000002000001000000

LB USL

LB 0

Target *USL 300000Sample Mean 225909

Sample N 292Shape 1.95393Scale 255391

Process DataPp *

PPL *PPU 0.19Ppk 0.19

Overall Capability

PPM < LB 0.00

PPM > USL 236301.37PPM Total 236301.37

Observed Performance

PPM < LB *

PPM > USL 254194.23PPM Total 254194.23

Exp. Overall Performance

Process Capability of CombinedCalculations Based on Weibull Distribution Model

Is the Process Capable Based Upon a Weibull Model?

The corresponds to a Sigma level of 4. The Goal is 6!

Is the Process Capable Based Upon a Gamma Model?

The corresponds to a Sigma level of 2. The Goal is 6!

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

?Brandon R. Theiss

btheiss@rutgers.edu