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 ...
Objective• To study the reliability of the Starbucks  beverage delivery system to provide a  beverage to a customer prior ...
About Starbucks• Founded 1971, in Seattle’s Pike Place Market.  Original name of company was Starbucks  Coffee, Tea and Sp...
Representative Stores• Two of the 6,075 company operated  stores were selected by geographical  convenience  – Marlboro NJ...
About Marlboro NJMarlboro is a Township in Monmouth County, New Jersey. It hasa population of 40,191 with a median househo...
About New BrunswickNew Brunswick is a city in Middlesex County, New Jersey. It hasa population of 55,181 with a median hou...
Measurement System
Measurement Procedure1. Click Start on 1 of 10 timers in the   Custom Application2. Enter Identifying characteristic in te...
Marlboro NJ Location
Marlboro Wait Time Data
Does the Data Follow a Weibull         Distribution?                                      Hi st ogr am of Ti me           ...
Does the Data Follow a Gamma         Distribution?                                     Hi st ogr am of Ti me              ...
Can the arrivals of customersbe Modeled as  a Poisson   Process?Goodness-of-Fit Test for Poisson DistributionData column: ...
Formal Test for the Data Being    Normally Distributed                                         Pr obabi l i t y Pl ot f or...
Formal Test for the Data Being    Gamma Distributed                        Pr obabi l i t y Pl ot f or Ti me              ...
Formal Test for the Data Being    Weibull Distributed                              Pr obabi l i t y Pl ot f or Ti me      ...
Mean Time To Beverage and  “Reliability” at Marlboro Biased                 Unbiased 190652.872424565 ms    190652.9160399...
Is the Process Capable Based    Upon a Gamma Model?                                        Pr ocess Capabi l i t y of Ti m...
Is the Process Capable Based    Upon a Weibull Model?                                        Pr ocess Capabi l i t y of Ti...
Is the Beverage Delivery                                                         Process in Control?                      ...
New Brunswick NJ Location
New Brunswick Wait Time Data
Does the Data Follow a Weibull         Distribution?                                        Hi st ogr am of Ti me         ...
Does the Data Follow a Gamma         Distribution?                                       Hi st ogr am of Ti me            ...
Can the arrivals of customersbe Modeled as  a Poisson   Process?Goodness-of-Fit Test for Poisson DistributionData column: ...
Formal Test for the Data Being    Normally Distributed                                          Pr obabi l i t y Pl ot f o...
Formal Test for the Data Being    Gamma Distributed                             Pr obabi l i t y Pl ot f or Ti me         ...
Formal Test for the Data Being    Weibull Distributed                              Pr obabi l i t y Pl ot f or Ti me      ...
Why Might the Data Not Follow        a Gamma?Poisson    Gamma                       ?                                     ...
Is the Process Capable Based    Upon a Weibull Model?                                    Pr ocess Capabi l i t y of Ti me ...
Is the Process Capable Based    Upon a Gamma Model?                                   Pr ocess Capabi l i t y of Ti me    ...
Mean Time To Beverage and“Reliability” at New Brunswick  Biased           Unbiased  242688.9419 ms   242371.0724 ms  4.044...
Is the Beverage Delivery                                                    Process in Control?                           ...
Marlboro   New BrunswickStarbucks Wait Time AnalysisCOMBINED
Combined Wait Time Data
Is there a difference betweenMarlboro and New Brunswick?                              Hi st ogr am of Mar l bor o, New Br ...
Is there a difference betweenMarlboro and New Brunswick?  Kruskal-Wallis Test: Wait Times versus Location  Kruskal-Wallis ...
Does the Data Follow a Weibull         Distribution?                                      Hi st ogr am of Combi ned       ...
Does the Data Follow a Gamma         Distribution?                                      Hi st ogr am of Combi ned         ...
Are the Arrival Rates the Same?                                 Hi st ogr am of Mar l bor o, New Br unsw i ck             ...
Are the Arrival Rates the Same?  Kruskal-Wallis Test: Arrivals versus Location  Kruskal-Wallis Test on Arrivals  Location ...
Can the arrivals of customersbe Modeled as  a Poisson   Process?Goodness-of-Fit Test for Poisson DistributionData column: ...
Why Might the data set of Combined  Arrivals Not Represent a Poisson              Process?• Not a large enough data set of...
Formal Test for the Data Being    Normally Distributed                                       Pr obabi l i t y Pl ot f or C...
Formal Test for the Data Being    Gamma Distributed                         Pr obabi l i t y Pl ot f or Combi ned         ...
Formal Test for the Data Being    Weibull Distributed                              Pr obabi l i t y Pl ot f or Combi ned  ...
Mean Time To Beverage and       “Reliability” Biased           Unbiased 225908.8493 ms   226153.1587 ms 3.7651 mins      3...
Is the Process Capable Based    Upon a Gamma Model?                                     Pr ocess Capabi l i t y of Combi n...
Is the Process Capable Based    Upon a Weibull Model?                                      Pr ocess Capabi l i t y of Comb...
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...
? Brandon R. Theissbtheiss@rutgers.edu
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15th QMOD conference on Quality and Service Sciences 9/07/2012

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15th QMOD conference on Quality and Service Sciences 9/07/2012

  1. 1. Starbucks Wait Time Analysis Brandon R. Theiss Mathew Brown
  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 – 6,075 Company-operated stores – 4,082 Licensed stores• Outside US – 2,326 Company Stores – 3,890 Licensed stores
  5. 5. Representative Stores• Two of the 6,075 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? Hi st ogr am of Ti me Weibull 25 Shape 2.007 Scale 216106 N 94 20 15 Fr equency 10 5 0 0 100000 200000 300000 400000 500000 Time
  13. 13. Does the Data Follow a Gamma Distribution? Hi st ogr am of Ti me Gamma 25 Shape 3.977 Scale 47936 N 94 20 15 Fr equency 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 Pr obabi l i t y Pl ot f or Ti me Normal - 95% CI 99.9 Goodness of Fit Test 99 AD = 2.887 P-Value < 0.005 95 90 80 70 Per cent 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 Pr obabi l i t y Pl ot f or Ti me Gamma - 95% CI 99.9 Goodness of Fit Test 99 95 AD = 0.699 90 P-Value = 0.075 80 70 60 50 40 Per cent 30 20 10 5 1 0.1 10000 100000 1000000 Time
  17. 17. Formal Test for the Data Being Weibull Distributed Pr obabi l i t y Pl ot f or Ti me 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 Per cent 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? Pr ocess Capabi l i t y of Ti me Calculations Based on Gamma Distribution Model LB USL Process Data O v erall Capability LB 0 Pp * Target * PPL * USL 300000 PPU 0.29 Sample Mean 190653 Ppk 0.29 Sample N 94 Exp. O v erall Performance Shape 3.97724 PPM < LB * Scale 47936 PPM > USL 127306.05 O bserv ed Performance PPM Total 127306.05 PPM < LB 0.00 PPM > USL 95744.68 PPM Total 95744.68 0 100000 200000 300000 400000 500000
  20. 20. Is the Process Capable Based Upon a Weibull Model? Pr ocess Capabi l i t y of Ti me Calculations Based on Weibull Distribution Model LB USL Process Data O v erall Capability LB 0 Pp * Target * PPL * USL 300000 PPU 0.32 Sample Mean 190653 Ppk 0.32 Sample N 94 Exp. O v erall Performance Shape 2.00713 PPM < LB * Scale 216106 PPM > USL 144910.81 O bserv ed Performance PPM Total 144910.81 PPM < LB 0.00 PPM > USL 95744.68 PPM Total 95744.68 0 100000 200000 300000 400000 500000
  21. 21. Is the Beverage Delivery Process in Control? I -MR Char t of Mar l bor o I -MR Char t of Mar l bor o Using Box-Cox Transformation With Lambda = 0.50 600000 1 1 1 1 800 1 1 1 450000 1 1 1I n d i v i d u a l V a lu e UCL= 407256 UCL= 679.6 I ndiv idual Value 600 300000 _ _ X= 190653 X= 422.7 150000 400 0 LCL= -25950 200 LCL= 165.8 1 10 19 28 37 46 55 64 73 82 91 O b se r v a t io n 1 10 19 28 37 46 55 64 73 82 91 Observ at ion 1 11 11 1 400000 450M o v in g Ra n g e 300000 UCL= 315.6 Mov ing Range UCL= 266097 300 200000 __ 150 __ 100000 MR= 81443 MR= 96.6 0 LCL= 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 b se r v a t io n Observ at ion
  22. 22. New Brunswick NJ Location
  23. 23. New Brunswick Wait Time Data
  24. 24. Does the Data Follow a Weibull Distribution? Hi st ogr am of Ti me Weibull 40 Shape 1.994 Scale 273830 N 198 30 Fr equency 20 10 0 0 100000 200000 300000 400000 500000 600000 Time
  25. 25. Does the Data Follow a Gamma Distribution? Hi st ogr am of Ti me Gamma 40 Shape 3.080 Scale 78771 N 198 30 Fr equency 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 Pr obabi l i t y Pl ot f or Ti me Normal - 95% CI 99.9 Goodness of Fit Test 99 AD = 1.680 95 P-Value < 0.005 90 80 70 Per cent 60 50 40 30 20 10 5 1 0.1 00 00 0 00 00 00 00 00 00 00 000 000 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 Pr obabi l i t y Pl ot f or Ti me Gamma - 95% CI 99.9 Goodness of Fit Test 99 95 AD = 0.911 90 P-Value = 0.023 80 70 60 50 40 30 Per cent 20 10 5 1 0.1 10000 100000 1000000 Time
  29. 29. Formal Test for the Data Being Weibull Distributed Pr obabi l i t y Pl ot f or Ti me 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 Per cent 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? Pr ocess Capabi l i t y of Ti me Calculations Based on Weibull Distribution Model LB USL Process Data O v erall Capability LB 0 Pp * Target * PPL * USL 300000 PPU 0.15 Sample Mean 242647 Ppk 0.15 Sample N 198 Exp. O v erall Performance Shape 1.99408 PPM < LB * Scale 273830 PPM > USL 301307.05 O bserv ed Performance PPM Total 301307.05 PPM < LB 0.00 PPM > USL 303030.30 PPM Total 303030.30 0 100000 200000 300000 400000 500000 600000
  32. 32. Is the Process Capable Based Upon a Gamma Model? Pr ocess Capabi l i t y of Ti me Calculations Based on Gamma Distribution Model LB USL Process Data O v erall Capability LB 0 Pp * Target * PPL * USL 300000 PPU 0.13 Sample Mean 242647 Ppk 0.13 Sample N 198 Exp. O v erall Performance Shape 3.0804 PPM < LB * Scale 78771.2 PPM > USL 283036.30 O bserv ed Performance PPM Total 283036.30 PPM < LB 0.00 PPM > USL 303030.30 PPM 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 Char t of New Br unsw i ck I -MR Char t of New Br unsw i ck 1 1 Using Box-Cox Transformation With Lambda = 0.50 600000 11 1 1 1 1 1 800 11 1 UCL= 485623 UCL= 733.1I n d iv i d u a l V a l u e 450000 I ndiv idual Value 600 300000 _ _ X= 242647 X= 473.9 400 150000 0 LCL= -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 b se r v a t io n 1 21 41 61 81 101 121 141 161 181 Observ at ion 1 480000 1 11 1 1 600 1 1 1 1 360000 1 1M o v in g Ra n g e 1 1 11 1 1 1 Mov ing Range UCL= 298497 400 1 240000 UCL= 318.4 __ 200 120000 __ MR= 91359 MR= 97.4 0 LCL= 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 b se r v a t io n Observ at ion
  35. 35. Marlboro New BrunswickStarbucks Wait Time AnalysisCOMBINED
  36. 36. Combined Wait Time Data
  37. 37. Is there a difference betweenMarlboro and New Brunswick? Hi st ogr am of Mar l bor o, New Br unsw i ck Gamma 40 Variable Marlboro New Brunswick Shape Scale N 30 3.977 47936 94 3.080 78771 198 Fr equency 20 10 0 0 100000 200000 300000 400000 500000 600000 Dat a
  38. 38. 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)
  39. 39. Does the Data Follow a Weibull Distribution? Hi st ogr am of Combi ned Weibull 35 Shape 1.954 Scale 255391 N 292 30 25 Fr equency 20 15 10 5 0 0 100000 200000 300000 400000 500000 600000 Combined
  40. 40. Does the Data Follow a Gamma Distribution? Hi st ogr am of Combi ned Gamma 35 Shape 3.201 Scale 70580 N 292 30 25 Fr equency 20 15 10 5 0 0 100000 200000 300000 400000 500000 600000 Combined
  41. 41. Are the Arrival Rates the Same? Hi st ogr am of Mar l bor o, New Br unsw i ck 2 4 6 8 10 12 14 16 Marlboro New Brunswick 9 8 7 6 Fr equency 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 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
  45. 45. Formal Test for the Data Being Normally Distributed Pr obabi l i t y Pl ot f or Combi ned Normal - 95% CI 99.9 Goodness of Fit Test 99 AD = 4.293 95 P-Value < 0.005 90 80 70 Per cent 60 50 40 30 20 10 5 1 0.1 00 00 0 00 00 00 00 00 00 00 000 000 00 00 00 00 00 00 00 -2 -1 10 20 30 40 50 60 70 Combined
  46. 46. Formal Test for the Data Being Gamma Distributed Pr obabi l i t y Pl ot f or Combi ned Gamma - 95% CI 99.9 Goodness of Fit Test 99 95 AD = 0.594 90 P-Value = 0.141 80 70 60 50 40 30 Per cent 20 10 5 1 0.1 10000 100000 1000000 Combined
  47. 47. Formal Test for the Data Being Weibull Distributed Pr obabi l i t y Pl ot f or Combi ned 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 Per cent 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? Pr ocess Capabi l i t y of Combi ned Calculations Based on Gamma Distribution Model LB USL Process Data O v erall Capability LB 0 Pp * Target * PPL * USL 300000 PPU 0.16 Sample Mean 225909 Ppk 0.16 Sample N 292 Exp. O v erall Performance Shape 3.20075 PPM < LB * Scale 70580 PPM > USL 237100.41 O bserv ed Performance PPM Total 237100.41 PPM < LB 0.00 PPM > USL 236301.37 PPM Total 236301.37 0 100000 200000 300000 400000 500000 600000
  50. 50. Is the Process Capable Based Upon a Weibull Model? Pr ocess Capabi l i t y of Combi ned Calculations Based on Weibull Distribution Model LB USL Process Data O v erall Capability LB 0 Pp * Target * PPL * USL 300000 PPU 0.19 Sample Mean 225909 Ppk 0.19 Sample N 292 Exp. O v erall Performance Shape 1.95393 PPM < LB * Scale 255391 PPM > USL 254194.23 O bserv ed Performance PPM Total 254194.23 PPM < LB 0.00 PPM > USL 236301.37 PPM 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. ? Brandon R. Theissbtheiss@rutgers.edu

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