This document analyzes wait times at two Starbucks locations to determine if the beverage delivery process is reliable. Wait time data was collected from each store and analyzed to determine if it followed a Weibull, gamma, or normal distribution. The data did not follow a normal distribution but did fit a Weibull or gamma model. Process capability calculations showed the process was not capable of meeting the target wait time less than 5 minutes at the New Brunswick location based on either distribution. The document concludes an analysis of the beverage making process is also needed.
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
Lung Transplantation - Where we are and Where we are goingDoctors Republic
Overview of Lung Transplantation
Changing the practice of clinical lung transplantation
Ex vivo lung perfusion, personalized medicine for the organ, engineering "super organs"
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The document discusses a study conducted on customer satisfaction at Kanan Hotels restaurant. It provides background on customer satisfaction, objectives of the study such as analyzing customer satisfaction and services. It also includes an industry profile on the growth of restaurants in India and company profile of Kanan Hotels. The study uses tools like SWOT analysis, hypothesis testing, chi-square test and analyzes customer feedback on various aspects. In conclusion, the project helps understand customer preferences and satisfaction levels but has limitations due to time constraints.
Internet of Things and Large-scale Data Analytics PayamBarnaghi
This document discusses Internet of Things (IoT) and large-scale data analytics. It begins by noting the increasing capabilities of computing devices over time, from early mainframes to modern smartphones. It then discusses the growing number of connected sensors, devices, and "things" that are part of the IoT. The document outlines some of the challenges around IoT and big data, such as heterogeneous, noisy data from many sources. It presents examples of applying IoT and analytics to problems in smart cities. Specifically, it discusses using sensor data for applications like transportation optimization and power grid management. The conclusion emphasizes that IoT analytics requires approaches that can handle resource constraints and cross-layer optimizations across the network architecture.
This document summarizes accelerated testing methods for assessing the reliability of components over a simulated 2-year storage period. It discusses using thermal cycling and constant temperature exposure to accelerate aging, and references statistical models for analyzing the results, including the Arrhenius model. Graphs show data from tests of current draw over thermal cycling cycles and time at elevated temperature, with over 98% of components meeting specifications after the simulated 2-year period.
Bio manufacturing summit croughan et al jan 2010cellculturedish2
The document discusses using animal-free cell culture supplements Cellastim and Lacromin to optimize CHO cell culture performance, finding that supplementation resulted in higher viable cell densities, product titers, and volumetric productivity as well as more efficient glucose metabolism and higher protein A capture yields.
The document describes fitting a simple linear regression model to predict a student's Calculus score based on their Mathematics score. It provides the steps to perform the analysis using the NCSS statistical software. The key results are that the linear regression model is significant with a slope of 0.7656 and R-squared of 0.7052, indicating Mathematics score explains over 70% of the variation in Calculus score. Predictions using this model for Mathematics scores of 50 and 60 are also provided. Bootstrapping methods are used to estimate properties of the population model from the sample data.
Short talk on my work developing novel tagging methods in Pinto abalone at the National Shellfisheries Association Annual Meeting this year (March 2012) in Seattle.
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
Lung Transplantation - Where we are and Where we are goingDoctors Republic
Overview of Lung Transplantation
Changing the practice of clinical lung transplantation
Ex vivo lung perfusion, personalized medicine for the organ, engineering "super organs"
Project on customer satisfaction in kanan hotelsJia Chawla
The document discusses a study conducted on customer satisfaction at Kanan Hotels restaurant. It provides background on customer satisfaction, objectives of the study such as analyzing customer satisfaction and services. It also includes an industry profile on the growth of restaurants in India and company profile of Kanan Hotels. The study uses tools like SWOT analysis, hypothesis testing, chi-square test and analyzes customer feedback on various aspects. In conclusion, the project helps understand customer preferences and satisfaction levels but has limitations due to time constraints.
Internet of Things and Large-scale Data Analytics PayamBarnaghi
This document discusses Internet of Things (IoT) and large-scale data analytics. It begins by noting the increasing capabilities of computing devices over time, from early mainframes to modern smartphones. It then discusses the growing number of connected sensors, devices, and "things" that are part of the IoT. The document outlines some of the challenges around IoT and big data, such as heterogeneous, noisy data from many sources. It presents examples of applying IoT and analytics to problems in smart cities. Specifically, it discusses using sensor data for applications like transportation optimization and power grid management. The conclusion emphasizes that IoT analytics requires approaches that can handle resource constraints and cross-layer optimizations across the network architecture.
This document summarizes accelerated testing methods for assessing the reliability of components over a simulated 2-year storage period. It discusses using thermal cycling and constant temperature exposure to accelerate aging, and references statistical models for analyzing the results, including the Arrhenius model. Graphs show data from tests of current draw over thermal cycling cycles and time at elevated temperature, with over 98% of components meeting specifications after the simulated 2-year period.
Bio manufacturing summit croughan et al jan 2010cellculturedish2
The document discusses using animal-free cell culture supplements Cellastim and Lacromin to optimize CHO cell culture performance, finding that supplementation resulted in higher viable cell densities, product titers, and volumetric productivity as well as more efficient glucose metabolism and higher protein A capture yields.
The document describes fitting a simple linear regression model to predict a student's Calculus score based on their Mathematics score. It provides the steps to perform the analysis using the NCSS statistical software. The key results are that the linear regression model is significant with a slope of 0.7656 and R-squared of 0.7052, indicating Mathematics score explains over 70% of the variation in Calculus score. Predictions using this model for Mathematics scores of 50 and 60 are also provided. Bootstrapping methods are used to estimate properties of the population model from the sample data.
Short talk on my work developing novel tagging methods in Pinto abalone at the National Shellfisheries Association Annual Meeting this year (March 2012) in Seattle.
This session presents a novel usage of the tools techniques and methods of Six Sigma to the vexing problem of mobile data overages. Learn about an individual's daily data usage collected over the span of one year and applies control charts, hypothesis testing, and process capability to determine the optimal monthly number of gigabytes of data to purchase. The case extensively uses nonparametric testing and simulation to predict the most appropriate data plan to purchase
A case study utilizing the Six Sigma data analysis toolkit to examine a 15.5-mile daily morning commute completed on bicycle. The case first explores the usage of control charts to examine the total completion time in addition to various waypoints along the route. It then utilizes hypothesis testing to attempt to prove if a statistically significant improvement has occurred. It then demonstrates a multifactor regression model to predict the time needed to traverse the route. Finally it does a cost comparison between cycling, taking the metro and driving to work.
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Terrorism is endemic to the modern world. It is impossible to board an airplane, attend a sporting event, or walk into a public building without experiencing its symptoms. However, is the incidence rate of such horrific events actually increasing? This paper draws data from The Global Terrorism Database, which collects information on terrorist events around the world (1970 through 2011), and attempts to answer this very question. This research applies G- Control Charts, most commonly used for monitoring of workplace accidents and various health care application, to determine if the time between incidences of terrorism has in fact decreased. Though not intended as a basis for policy decisions, the paper demonstrates a novel use of control charts and provides a basis for a better informed debate.
Presentation for the 16th QMOD conference which details a novel approach of using the tools techniques and methods of Six Sigma to improve students learning of Six Sigma
The document describes an experiment conducted by Brandon Theiss to analyze customer wait times at a Starbucks location in New Brunswick, NJ. Over 5 weeks, Theiss measured the time customers spent waiting in line, ordering drinks, and receiving drinks. The objective was to determine the probability of receiving a drink in under 5 minutes between 8-9 AM on weekdays. Theiss found the arrival rate followed a Poisson distribution but the wait times were best described by a 3-parameter Gamma distribution. Both arrival time and day of week significantly impacted wait times. On average, it took 4.21 minutes to receive a drink once ordered.
This document summarizes a presentation on teaching Six Sigma using a DMAIC approach. The presentation applies Six Sigma methodology to improving the process of teaching Six Sigma. Students in the class aim to pass a Six Sigma Green Belt certification exam. Data from pre-tests is analyzed using statistical process control charts to identify issues and drive improvements. Various brainstorming techniques are taught and used to gather additional potential causes of pre-test failures. The goal is to help students achieve Green Belt certification by continuously measuring performance, identifying problems, and enacting improvements to the teaching process.
The document summarizes a Six Sigma Green Belt certification course offered at Rutgers University. The course was designed to teach students the Six Sigma methodology and prepare them to pass the ASQ Green Belt certification exam in a cost-effective way, as typical certification courses can be prohibitively expensive. The course applied the Six Sigma DMAIC process of Define, Measure, Analyze, Improve, Control to both the material covered and the pedagogical method of instruction. Pre- and post-test data was collected to analyze the effectiveness of the course and students' improvement.
The document discusses a Six Sigma Green Belt certification course taught over 11 weeks. Key points:
- Students took a pre-test on the first day which showed their initial knowledge and the process capability was very poor, with high failure rates.
- Midway through the course, students re-took portions of the test, showing some improvement in scores on covered material but not uncovered material.
- At the end of the course, students re-took the full test. While scores improved overall, the distribution was bimodal due to issues with some students' work experience preventing certification. Test scores and process capability both significantly improved from the start.
The document provides information about a course to prepare students to pass the ASQ Certified Six Sigma Green Belt exam. It discusses challenges in teaching Lean Six Sigma concepts in an academic setting and outlines how the course applied the DMAIC methodology to the process of passing the exam. It summarizes the course structure, demographics of enrolled students, pre-test results which were analyzed using statistical process control charts, and techniques taught such as brainstorming, process mapping, and control charts. The goal was for students to learn and apply Six Sigma tools and strategies to improve their exam performance.
The document outlines an agenda for a guest lecture on quality control topics, including introductions, an overview of the speaker's background and qualifications, and a schedule of activities covering quality tools and methods like measuring processes, defining problems, brainstorming solutions, creating control charts, process mapping, and data analysis. The speaker intends to demonstrate how these tools can help attendees see and solve problems differently. Hands-on activities are included to have participants apply various quality improvement techniques to defining and analyzing the coffee ordering and receiving process at Starbucks.
The document describes an agenda for a Rutgers Governor School event on industrial engineering and quality. The agenda includes an introduction, defining key terms, examining how to measure the quality of coffee, analyzing coffee quality data, making control charts, mapping coffee-making processes, conducting hypothesis testing, and concluding. The slides for the event are available online, as is a feedback survey.
Brandon Theiss presented on how quality decisions require quality data. He discussed limitations of traditional data collection methods and provided case studies showing how new technologies enabled real-time data collection. This improved process understanding and quality. For example, adding scales and scanners to production lines eliminated transcription errors and provided visibility into issues. The key is linking data collection to business goals and using tools like Lean Six Sigma to reveal truths from quality data.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
This session presents a novel usage of the tools techniques and methods of Six Sigma to the vexing problem of mobile data overages. Learn about an individual's daily data usage collected over the span of one year and applies control charts, hypothesis testing, and process capability to determine the optimal monthly number of gigabytes of data to purchase. The case extensively uses nonparametric testing and simulation to predict the most appropriate data plan to purchase
A case study utilizing the Six Sigma data analysis toolkit to examine a 15.5-mile daily morning commute completed on bicycle. The case first explores the usage of control charts to examine the total completion time in addition to various waypoints along the route. It then utilizes hypothesis testing to attempt to prove if a statistically significant improvement has occurred. It then demonstrates a multifactor regression model to predict the time needed to traverse the route. Finally it does a cost comparison between cycling, taking the metro and driving to work.
Teaching tactical industrial engineering to high school studentsBrandon Theiss, PE
Case study of a group of high school students who worked with a replacement window manufacturer to apply six sigma to improve their manufacturing process
Terrorism is endemic to the modern world. It is impossible to board an airplane, attend a sporting event, or walk into a public building without experiencing its symptoms. However, is the incidence rate of such horrific events actually increasing? This paper draws data from The Global Terrorism Database, which collects information on terrorist events around the world (1970 through 2011), and attempts to answer this very question. This research applies G- Control Charts, most commonly used for monitoring of workplace accidents and various health care application, to determine if the time between incidences of terrorism has in fact decreased. Though not intended as a basis for policy decisions, the paper demonstrates a novel use of control charts and provides a basis for a better informed debate.
Presentation for the 16th QMOD conference which details a novel approach of using the tools techniques and methods of Six Sigma to improve students learning of Six Sigma
The document describes an experiment conducted by Brandon Theiss to analyze customer wait times at a Starbucks location in New Brunswick, NJ. Over 5 weeks, Theiss measured the time customers spent waiting in line, ordering drinks, and receiving drinks. The objective was to determine the probability of receiving a drink in under 5 minutes between 8-9 AM on weekdays. Theiss found the arrival rate followed a Poisson distribution but the wait times were best described by a 3-parameter Gamma distribution. Both arrival time and day of week significantly impacted wait times. On average, it took 4.21 minutes to receive a drink once ordered.
This document summarizes a presentation on teaching Six Sigma using a DMAIC approach. The presentation applies Six Sigma methodology to improving the process of teaching Six Sigma. Students in the class aim to pass a Six Sigma Green Belt certification exam. Data from pre-tests is analyzed using statistical process control charts to identify issues and drive improvements. Various brainstorming techniques are taught and used to gather additional potential causes of pre-test failures. The goal is to help students achieve Green Belt certification by continuously measuring performance, identifying problems, and enacting improvements to the teaching process.
The document summarizes a Six Sigma Green Belt certification course offered at Rutgers University. The course was designed to teach students the Six Sigma methodology and prepare them to pass the ASQ Green Belt certification exam in a cost-effective way, as typical certification courses can be prohibitively expensive. The course applied the Six Sigma DMAIC process of Define, Measure, Analyze, Improve, Control to both the material covered and the pedagogical method of instruction. Pre- and post-test data was collected to analyze the effectiveness of the course and students' improvement.
The document discusses a Six Sigma Green Belt certification course taught over 11 weeks. Key points:
- Students took a pre-test on the first day which showed their initial knowledge and the process capability was very poor, with high failure rates.
- Midway through the course, students re-took portions of the test, showing some improvement in scores on covered material but not uncovered material.
- At the end of the course, students re-took the full test. While scores improved overall, the distribution was bimodal due to issues with some students' work experience preventing certification. Test scores and process capability both significantly improved from the start.
The document provides information about a course to prepare students to pass the ASQ Certified Six Sigma Green Belt exam. It discusses challenges in teaching Lean Six Sigma concepts in an academic setting and outlines how the course applied the DMAIC methodology to the process of passing the exam. It summarizes the course structure, demographics of enrolled students, pre-test results which were analyzed using statistical process control charts, and techniques taught such as brainstorming, process mapping, and control charts. The goal was for students to learn and apply Six Sigma tools and strategies to improve their exam performance.
The document outlines an agenda for a guest lecture on quality control topics, including introductions, an overview of the speaker's background and qualifications, and a schedule of activities covering quality tools and methods like measuring processes, defining problems, brainstorming solutions, creating control charts, process mapping, and data analysis. The speaker intends to demonstrate how these tools can help attendees see and solve problems differently. Hands-on activities are included to have participants apply various quality improvement techniques to defining and analyzing the coffee ordering and receiving process at Starbucks.
The document describes an agenda for a Rutgers Governor School event on industrial engineering and quality. The agenda includes an introduction, defining key terms, examining how to measure the quality of coffee, analyzing coffee quality data, making control charts, mapping coffee-making processes, conducting hypothesis testing, and concluding. The slides for the event are available online, as is a feedback survey.
Brandon Theiss presented on how quality decisions require quality data. He discussed limitations of traditional data collection methods and provided case studies showing how new technologies enabled real-time data collection. This improved process understanding and quality. For example, adding scales and scanners to production lines eliminated transcription errors and provided visibility into issues. The key is linking data collection to business goals and using tools like Lean Six Sigma to reveal truths from quality data.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
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
– 6,075 Company-operated stores
– 4,082 Licensed stores
• Outside US
– 2,326 Company Stores
– 3,890 Licensed stores
5. Representative Stores
• Two of the 6,075 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
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
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. 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. 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
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. 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. 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. 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?
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. 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. 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 1
I 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 450
M 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
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. 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. 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
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. 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. 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. 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?
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. 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. 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 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= 733.1
I 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 1
M 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. Marlboro New Brunswick
Starbucks Wait Time Analysis
COMBINED
37. Is there a difference between
Marlboro 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. 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)
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. 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. 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. 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 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. 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. 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. 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. 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?
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. 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. 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