Starbucks Wait Time Analysis

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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

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Starbucks Wait Time Analysis

  1. 1. Starbucks Wait Time Analysis Data Collected on 4/26/2012 and 4/29/2012 Brandon R. Theiss Brandon.Theiss@gmail.com
  2. 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. 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. 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. 5. Representative Stores• Two of the 7,087 company operated stores were selected by geographical convenience – Marlboro NJ – New Brunswick NJ
  6. 6. About Marlboro NJMarlboro is a Township in Monmouth County, New Jersey. It hasa population of 40,191 with a median household income of$101,322
  7. 7. About New BrunswickNew Brunswick is a city in Middlesex County, New Jersey. It hasa population of 55,181 with a median household income of$36,080
  8. 8. Measurement System
  9. 9. Measurement Procedure1. Click Start on 1 of 10 timers in the Custom Application2. Enter Identifying characteristic in textbox3. Click Stop when the customer receives their beverage or leaves the store. Data is automatically recorded with times measured in milliseconds4. Click Reset for the next customer
  10. 10. Marlboro NJ Location
  11. 11. Marlboro Wait Time Data
  12. 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. 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. 14. Can the arrivals of customersbe Modeled as a Poisson Process?Goodness-of-Fit Test for Poisson DistributionData 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
  15. 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. 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. 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. 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. 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. 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. 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 1Individual 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 450M 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. 22. New Brunswick NJ Location
  23. 23. New Brunswick Wait Time Data
  24. 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. 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. 26. Can the arrivals of customersbe Modeled as a Poisson Process?Goodness-of-Fit Test for Poisson DistributionData 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
  27. 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. 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. 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. 30. Why Might the Data Not Follow a Gamma?Poisson Gamma ? Gamma * ? =? Make Drink Wait in Line ProcessArrival DeliverTo Store Order Drink Drink What We Measured
  31. 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. 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. 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. 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=733.1Individual 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 1Moving 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. 35. Marlboro New BrunswickStarbucks Wait Time AnalysisCOMBINED
  36. 36. Is there a difference betweenMarlboro 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. 37. Is there a difference betweenMarlboro 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. 38. Combined Wait Time Data
  39. 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. 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. 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. 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. 43. Can the arrivals of customersbe Modeled as a Poisson Process?Goodness-of-Fit Test for Poisson DistributionData column: CombinedPoisson 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
  44. 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. 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. 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. 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. 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. 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. 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. 51. Is the Process Capable Based Upon a Weibull Model? The corresponds to a Sigma level of 4. The Goal is 6!
  52. 52. Is the Process Capable Based Upon a Gamma Model? The corresponds to a Sigma level of 2. The Goal is 6!
  53. 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. 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
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