Starbucks Wait Time Analysis

Starbucks Wait Time Analysis

Data Collected on

4/26/2012 and 4/29/2012

Brandon R. Theiss [email protected]

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– 7,087 Company-operated stores– 4,081 Licensed stores

Representative Stores

• Two of the 7,087 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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Frequency

Shape 2.007Scale 216106N 94

Histogram of TimeWeibull

Does the Data Follow a Gamma Distribution?

5000004000003000002000001000000

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Frequency


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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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

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Perc

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AD = 0.699 P-Value = 0.075

Probability Plot for TimeGamma - 95% CI

Formal Test for the Data Being Weibull Distributed

100000010000010000

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Perc

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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



Process DataPp *


Overall Capability

PPM < LB 0.00

PPM > USL 95744.68PPM Total 95744.68


PPM < LB *

PPM > USL 144910.81PPM Total 144910.81


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

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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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Observation

Movin

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__MR=81443

UCL=266097

LCL=0

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I-MR Chart of Marlboro

New Brunswick NJ Location

New Brunswick Wait Time Data


6000005000004000003000002000001000000

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Shape 1.994Scale 273830N 198

Histogram of TimeWeibull


6000005000004000003000002000001000000

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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




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Perc

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AD = 1.680 P-Value < 0.005

Probability Plot for TimeNormal - 95% CI


100000010000010000

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Perc

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AD = 0.911 P-Value = 0.023

Probability Plot for TimeGamma - 95% CI


100000010000010000

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Perc

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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


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


PPM < LB *PPM > USL 301307.05PPM Total 301307.05


Process Capability of TimeCalculations Based on Weibull Distribution 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


PPM < LB *PPM > USL 283036.30PPM Total 283036.30


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

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idual V

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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

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11

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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

Is there a difference between Marlboro and New Brunswick?

6000005000004000003000002000001000000

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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)

Combined Wait Time Data


6000005000004000003000002000001000000

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Combined

Frequency

Shape 1.954Scale 255391N 292

Histogram of CombinedWeibull


6000005000004000003000002000001000000

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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



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


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Perc

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AD = 4.293 P-Value < 0.005

Probability Plot for CombinedNormal - 95% CI


100000010000010000

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Perc

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AD = 0.594 P-Value = 0.141

Probability Plot for CombinedGamma - 95% CI


100000010000010000

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Perc

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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


6000005000004000003000002000001000000

LB USL

LB 0



Process DataPp *


Overall Capability

PPM < LB 0.00

PPM > USL 236301.37PPM Total 236301.37


PPM < LB *

PPM > USL 237100.41PPM Total 237100.41


Process Capability of CombinedCalculations Based on Gamma Distribution Model


6000005000004000003000002000001000000

LB USL

LB 0



Process DataPp *


Overall Capability

PPM < LB 0.00

PPM > USL 236301.37PPM Total 236301.37


PPM < LB *

PPM > USL 254194.23PPM Total 254194.23


Process Capability of CombinedCalculations Based on Weibull Distribution Model


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


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

About the Author• Academics

– 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

Starbucks Wait Time Analysis

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