Lean Six Sigma Green Belt (LSSGB)


Final Exam Review




· The answers should be typed in order and submitted as one PDF file (with charts/graphs done using Microsoft Excel, Minitab, and/or VISIO and inserted into a WORD file) along with one Excel and/or one Minitab file(s) with one sheet per question, as appropriate. The WORD file should be converted to PDF before submission. ALL the answers should be explained in the WORD/PDF file. Please do not expect us to look for your answers/justifications in the Excel/Minitab files.





· If any references or external sources are used in solving any of the questions, those should be appropriately cited and included in a References section.



Question 1 [430 Points]: Read the case study carefully below and provide answers to the questions that follow.


According to Binghamton University’s Hospital CFO newsletter, labor costs have typically averaged 50 percent of hospitals’ total operating revenue for the past decade. The American Hospital Association also reported in 2012 that growing labor costs are the most important factor in increasing hospital care costs and found that wages and benefits accounted for more than 59 percent of hospital costs in 2014. Improving the shift changes for nursing staff is one of the areas of opportunity to control hospital staffing costs while maximizing operational efficiency. A 600-bed hospital in Binghamton, NY, initiated a project to improve its nursing shift change process to cut labor costs without negatively affecting the quality of patient care. This hospital has a formal operational excellence department that primarily uses the Lean Six Sigma methodology. The project was approved and facilitated by this department as well as the service line director of nursing. Working with Mr. John Doe, a Lean Six Sigma Black Belt as their mentor, the nurse manager and day nurse supervisor for the medicine and surgery unit led the project.


The shift-change nursing report is the primary tool used to ensure continuity of care as staff change happens every 12 hours. The report contains pertinent patient information and is given to the arriving nurse before the previous nurse on duty leaves at the end of a shift. Nursing assignments are given to the arriving nurse and include the list of patients they are to care for. The process of nursing shift change begins with staff punching in, then their belongings are put away before they get assignments. Then, the current nurses need to give assignments and shift-change reports to the next shift nurses. There are typically five registered nurses on the team. Often the five nurses from the day shift have to interact with each of the five nurses on the night shift as dictated by the patient assignments. The outputs of the process are time, Hospital








Consumer Assessment of Healthcare Providers and Systems (HCAHPS) scores, employee satisfaction, salary, etc. The customers are the service line director and patients.


In order to measure improvement, the team decided to call upon the overall time it took to produce the nursing report. The cycle time of staff punch in is 10 seconds, the Transaction Time I before they put away their belongings is another 10 seconds, and they need 2 minutes to put away the belongings. And 10 more seconds are needed to get the assignment after 2 minutes Transaction Time II. The report is given individually, so the cycle time of reporting with the 1st nurse is 7 minutes, reporting with the 2nd nurse is 6 minutes, and reporting with the 3rd nurse is also 6 minutes. There are transaction times between each procedure, so Transaction Times III, IV, V are all 5 minutes. The total lead time of the current nursing shift change process is 43 minutes, which is considered as a defect. The objective of this effort is to decrease it to 30 minutes.


To begin addressing potential solutions for non-value-added (NVA) wait time, the team completed a failure mode and effects analysis (FMEA) chart. This analysis is a complete and quantified cause and effect chart that pinpoints potential reasons why the shift-change report is taking so long to complete. Included in the FMEA is a risk priority number, which suggests the factors that should take the highest priority in promoting change. There are six steps for completing the FMEA:

1. Analyze what may be causing a long nursing report.

2. Identify how the step can go wrong.

3. Identify what impact the step has on the nursing report.

4. Determine potential causes for the problem.

5. Assess potential controls that exist for the problem.

6. Identify how to reduce the likelihood of the problem.


Upon observing and analyzing the data, the team identified a key area for most effectively eliminating waste. It was clear that the most significant and controllable source of unnecessary payroll expenditures existed in the number of nurses involved in producing the shift-change reports. After deploying the process change, the average lead time to complete the nursing shift change report has been reduced to 30 minutes.


As a Lean Six Sigma Green Belt, please answer the following questions (feel free to state any assumptions that might be necessary for you to address the following questions):


1. Identify the stakeholders and their roles in this project and discuss their potential impact or concerns (30 points).


2. Based on the information in the case study, develop a Project Charter for this project. Please use the template provided in the LSSGB_Final_Exam_December_2021.xls Excel file. For the milestones, assume that the project’s start date is January 1 and the end date is June 30 (30 points).

3. Based on the provided information only, develop a process map for the nursing shift change process (30 points).


4. Develop a VSM based on your developed process map for the nursing shift change process, and then identify the value-added and non-value-added activities (30 points).


5. Based on the provided information only, develop a SIPOC diagram for the nursing shift change process (30 points).


6. Perform a cause-and-effect analysis for the problem identified (30 points).


7. Based on your understanding of the problem, develop a preliminary Why-Why diagram (30 points).


8. The hospital analyzed the assessments from HCAHPS. Create a Pareto chart based on the given data and comment on the results. There are 361 received complaints, which are grouped into nine categories. The data is shown in the following table and is also available in the LSSGB_Final_Exam_December_2021.xls Excel file (30 points).


Complaint Type

Solving Time 61
Information Provided 35
Received Treatment 50
Too Many Formalities 34
Timetable 65
Waiting Time 41
Personal Skill 18
Others 15
Forms Missing 42



9. To begin addressing potential solutions for NVA wait time, the team completed a failure mode and effects analysis (FMEA). The incomplete FMEA is given in the table below, which is also provided in the LSSGB_Final_Exam_December_2021.xls Excel file. Complete the FMEA based on your understanding (You are encouraged to make any necessary assumptions) (50 points).


Failure Mode Failure Severity Potential Occurr Current Detection RPN Actions
  Effects   Causes ence Controls     Recommended
Too many                
staff nurses to         None      
give a report                
Report is         Potential      
          to off-put      
given based                
          off going/      
on staff nurse                
Timing of                
charge nurse         None      
in report                
Doesn’t         Don’t      
          utilize the      
report time                
Relationship         Potential      
development         to off-put      
versus actual         off going      
report         nurse      



10. Develop a ‘matrix diagram’ based on your developed FMEA analysis (you are encouraged to make any necessary assumptions) (25 points). This was not covered in the program, so you might need to read about matrix diagrams before answering the question.


11. Calculate 90%, 95%, and 99% confidence intervals for the parameters below. The required data is provided in the LSSGB_Final_Exam_December_2021.xls Excel file (30 points):

· Number of Received Complaints per Month

· Improved Nursing Shift Change Duration (minutes)

· Number of Arrival Patients per Week


12. After finishing the Six Sigma Project for nursing shift change, the hospital is also interested in improving the medication order entry process. The team decided to use quality function deployment (QFD) to link the needs of the customers with the design and development of the process functions.


Calculate the absolute value and relative value for the QFD provided below. (MAR = medication administration record, TAT = turnaround time) (30 points).
































13. Fifty observations of nursing shift change duration are collected for the period before the Lean Six Sigma Project (Pre Shift Change Time) and after the Lean Six Sigma Project (Post Shift Change Time). Construct an I-chart (Hint: The individual chart (I-Chart) is used to detect trends and shifts in the data, and thus in the process.) for both pre-process and post-process for the nursing shift change duration based on the data provided in the LSSGB_Final_Exam_December_2021.xls Excel file (25 points). This was not covered in the program, so you might need to read about I-Charts before answering the question.


14. Based on your understanding of the problem, list at least five ideas as your improvement plan? What would you recommend in your control plan to ensure sustainable improvements? (30 points)


Question 2 [50 Points]: Andy is a quality manager in a display development company. He found some quality issues about a heatsink hole on the printed circuit board (PCB) when developing the heatsink. A heatsink absorbs and dissipates heat from an electronic component through contact with PCB, or thermal interface material, which increases the thermal mass and heat dissipation (conduction/convection). To improve the manufacturing process of the heatsink hole, he measures the

precision of the system and performs a Gauge R&R study to investigate the uncertainty of the process. Two operators are chosen for the study. Each operator measures ten surface areas of the heatsink two times. The tolerance specification is 0.6 in2 and the study variation is 5.15 in2. The measurements are recorded in the table below. The data is also provided in the LSSGB_Final_Exam_December_2021.xls Excel file. Conduct a Gage R&R study and comment on the results. (Hint: The Excel template provided in the course is only applicable for three operators. You are expected to modify the template or use Minitab to solve this question.)


Sample Operator 1 Operator 2
  R1 R2 R1 R2
1 12.37 12.36 12.35 12.34
2 12.33 12.29 12.35 12.32
3 12.32 12.31 12.29 12.30
4 12.30 12.30 12.32 12.31
5 12.31 12.31 12.31 12.28
6 12.34 12.35 12.34 12.33
7 12.35 12.34 12.35 12.35
8 12.32 12.31 12.29 12.30
9 12.31 12.33 12.29 12.32
10 12.35 12.34 12.32 12.32


Question 3 [55 Points]: Printed Circuit Boards (PCBs) are becoming more sophisticated due to the increasing market demands on complex electronics. Therefore, it is very crucial to maintain an excellent quality while manufacturing PSBs. An innovation PCBs manufacturing company manufactures multilayer’s PCBs using surface-mounted technology (SMT). The major manufacturing processes in the company are solder screening, component placement, and solder reflow. Solder screening is the most critical process in PCB manufacturing which is performed to avoid any defect in the solder joint during manufacturing that may cause a circuit failure. The solder paste volume (height) transferred onto the


PCB is the most important factor that needs to be controlled carefully to maintain a low level of variation. The solder screening process transferred the solder pasted onto the solder pad of the PCB. The application method of solder paste is printing, and the printing technique used is off-contact printing in which there is a snap-off distance between a stencil and a PCB. The type of screening The machine used to manufacture products is semi-automatic. As the squeegee system consists of the front and back blades, there are two types of printing, front printing, and back printing. In current practice, both front and back printing are used alternatively during printing. During a printing process, two PCBs are placed side-by-side on the holder of a screening machine. The solder paste is then manually placed onto a stencil before printing. The front/back blade makes line contact with the stencil and close contact with the given amount of solder paste. The solder paste is then rolled in front of the front/back blade. So, solder paste is pressed against the stencil and transferred onto the solder pad through the stencil openings.
















The Lean Six Sigma team found that the screening process during PCB manufacturing has a low capability and needed to be improved. Many DMAIC approaches were used to increase the screening process capability. DOE was performed to determine which of the critical-to-quality factors mostly affect the screening process capability by studying the solder past height. Five factors were tested using DOE. A full factorial experiment was carried out. There were 48 types of printing, and two PCBs were measured for


each type of printing. In total, 96 PCBs were measured, and 480 solder paste height data were collected for analysis. The experimental conditions are as follows: (1) Room temperature: 25 oC, (2) Room humidity: 58%, (3) Machine number: 12, (4) Stencil number: 25 (new), (5) Number of operators: 1, (6) Model: Neptune, (7) Snap-off distance: nearly zero, (8) Point locations: J1, U1, U1, U2, U2, and (9) Specification: (4.5-7) mil. The factors and their levels in the experiment are given in below. Please review the results and then answer the questions below:


































1. Name the factors that were tested and list their levels? (10 points)

2. What are the significant factors that affect the process? (10 points)

3. Explain the main effects plot and the interaction effects plot? (15 points)


4. What can be concluded from the previous analysis? What is the optimal solder height variation that results from the best combination of variables? (20 points)


Question 4 [125 points]: In a hospital radiology department, the radiology report turnaround times have been a concern to the department. Doctors have been complaining about the long turnaround time of their ordered radiology reports for patients. The radiology department staff decided to investigate the problem and collect turnaround time data on 10 randomly selected reports every day for one month (data are shown in the table below, also available in the exam excel sheet LSSGB_Final_Exam_December_2021.xls. [Hint: You can use Minitab to validate your answers if you like, but you are expected to solve those questions using Excel]


1. Calculate the following measures of variability for wait times: standard deviation, variance, mean absolute deviation, and range. Comment on the results. Do these calculations for each day (ten observations per day) and the entire month (25 points).


2. Calculate the coefficient of variation. Comment on the results (10 points).


3. Construct an X-bar and R control chart. Is the process in statistical control? The values of control limits and center lines should be clearly seen on the figures and/or written below it (25 points).


4. If the clinicians feel that any time over 24 hours is unacceptable, what are the Cp and Cpk of this process? (15 points)

5. What are the next steps for the laboratory manager? (10 points)


6. The performance improvement specialist on your team suggests several process changes that result in reducing the turnaround time by 6 hours for each report. Reconstruct the X-bar and R charts and comment on the results (25 points).


7. Based on your answers in Parts 3 and 6, plot the control charts for the ‘before’ and ‘after’ situation on the same chart (using Excel) (15 points).



Observations (Turnaround time in hours)

Day 1 2 3 4 5 6 7 8 9 10
1 11 12 21 18 35 16 18 22 11 23
2 13 19 20 18 16 6 21 5 15 5
3 8 1 16 8 16 23 12 5 7 22
4 7 9 19 9 11 10 21 17 19 6
5 1 14 9 18 18 22 20 8 11 16
6 13 4 17 5 6 22 17 5 18 26
7 15 15 9 6 21 23 16 7 3 9
8 17 3 5 13 23 3 11 22 15 5
9 5 2 12 17 8 14 21 21 20 19
10 17 19 7 8 22 17 7 14 14 21
11 20 20 18 23 15 11 23 8 15 33
12 10 6 23 22 3 6 17 19 12 9
13 1 23 24 7 8 3 20 11 22 1
14 12 25 23 13 16 8 21 13 12 4
15 7 17 4 13 2 17 4 4 15 6
16 4 14 20 5 1 10 21 14 21 13
17 3 11 13 14 6 11 15 23 23 20
18 20 1 13 11 10 19 19 21 21 16
19 19 3 5 12 22 9 15 2 22 7
20 13 11 5 17 21 20 18 11 17 8
21 14 23 8 12 18 8 19 9 30 6
22 12 22 11 17 20 3 2 1 23 3
23 11 12 21 18 35 16 18 22 11 23
24 7 1 11 20 8 28 20 15 11 14
25 13 30 12 2 3 6 9 6 7 17
26 13 6 8 16 11 23 21 2 13 21
27 2 12 19 14 15 22 7 11 8 15
28 14 14 10 16 15 19 20 12 4 15
29 9 12 4 18 17 1 3 15 13 6
30 14 1 9 9 4 23 11 15 16 5



Question 5 [35 points]: Efficient design of specific types of municipal waste incinerators requires that information about the energy content of the waste be available. A study was performed in order to model this energy content of municipal solid waste. In this study, y is the energy content, x1 represents the % plastics, x2 is the % paper, x3 is the % garbage, x4 represents the % moisture where all of these percentages are by weight for waste specimens from a specific region. The results are shown below and also are available in the LSSGB_Final_Exam_December_2021.xls Excel file.


Observation x1 x2 x3 x4 y
1 18.69 15.65 45.01 58.21 947
2 19.43 23.51 39.69 46.31 1407
3 19.24 24.23 43.16 46.63 1452




22.64 22.2 35.67 45.85 1553
5 16.54 23.56 41.2 55.14 989
6 21.44 23.65 35.56 54.24 1162
7 19.53 24.45 40.18 47.2 1466
8 23.97 19.39 44.11 43.82 1656
9 21.45 23.84 35.41 51.01 1254
10 20.34 26.5 34.21 49.06 1336
11 17.03 23.46 32.45 53.23 1097
12 21.03 26.99 38.19 51.78 1266
13 20.49 19.87 41.35 46.69 1401
14 20.45 23.03 43.59 53.57 1223
15 18.81 22.62 42.2 52.98 1216



1. Find the correlation between the energy content and each of the four independent variables (10 points).


2. Find the correlation between the four independent variables and show the results in a table. Develop a scatter diagram between x3 and x4 and comment on the results (10 points).


3. Develop a regression model to identify the relationship between energy content and each of the independent variables (separately). In each case, provide the regression equation and R-square value. Comment on the accuracy of your regression models. Please note that you are not asked to do a multiple regression here but only separate first-order polynomial models (15 points).


4. [Bonus] Develop a multiple regression model to determine the relationship between y and the other factors (10 points).


Question 6 [70 points]: A manufacturing company is measuring the diameter of a ball bearing by 12 inspectors, each using two different kinds of calipers to test the difference between the sample means of the two calipers used. Data is shown below and available in the LSSGB_Final_Exam_December_2021.xls Excel file.


1. Is there a significant difference between the means of the population of measurements from which the two samples were selected? Use α = 0.01, 0.05, 0.1 and comment on the results (30 points).

2. What is the P-value for the test in part (1)? (10 points)


3. Construct 90%, 95%, and 99% confidence intervals (CIs) on the difference in mean diameter measurements for the two types of calipers. Comment on the results (30 points).


Inspector Caliper 1 Caliper 2
1 0.473 0.518
2 0.512 0.552
3 0.518 0.545
4 0.492 0.521
5 0.484 0.511
6 0.512 0.492
7 0.513 0.558
8 0.536 0.545
9 0.481 0.5
10 0.533 0.575
11 0.536 0.554
12 0.538 0.515




0.539 0.577
14 0.523 0.55
15 0.535 0.566
16 0.513 0.562
17 0.553 0.505
18 0.544 0.527
19 0.585 0.479
20 0.527 0.484



Question 7 [120 points]: Value stream mapping (VSM) has shown its effectiveness on the manufacturing processes to maximize customer value. However, nonproduction activities, such as design and engineering, appear to have a significant influence on production cost and lead time so a good number of industrial participants are trying to engage in applying lean principles in nonproduction activities. Such nonproduction activities involve some knowledge-based areas, like design, new product introduction, engineering, and product development. In the wood products industry, lean principles and techniques have shown effectiveness, especially in enhancing the productivity of the furniture manufacturing process. VSM also showed its importance in streamlining the manufacturing process for the wood industry. On the other hand, lean principles could also create benefits to nonproduction processes in the secondary wood products industry like the engineering process. The impact of the engineering process on the production cost is extremely important. A study was done to evaluate the current state VSM of furniture engineering processes in a certain company to identify both value-added and non–value-added engineering activities toward fulfilling customer requirements. The VSM is shown in the following figure.
























Notes: 1) C/T = cycle time; 2) The numbers on the timeline at the bottom of the figure are the processing times. They are just the cycle times multiplied by the number of operators.


1. What is the cycle time for the CNC process? (5 points)


2. What is the cycle time for the entire process or system (i.e., summation of all cycle times)? (10 points)


3. What is the system cycle time? (10 points)


4. What is the throughput time? (10 points)


5. What is the percent value-added time in this process? What is the percent non-value-added time in this process? Based on your understanding of the problem, which of the activities can be considered value-enabling (reasonable assumptions are accepted here), and based on your answer, what is the percent value-enabling time in this process? (20 points)


6. Given that the output of the system is measured by the number of parts. If the system operates a net time of 15 hours a day with an assumed average of three parts being ordered every working day, what is the takt time? (10 points)


7. If the demand becomes four parts per day, what is the takt time? (10 points)


8. What would you do in the second situation (referenced in part 7)? (10 points)


9. Develop a histogram showing the value-adding times in the system. Be sure to create a dotted line for the takt time calculated in part 8. According to the level loading lean technique (Heijunka), what are the steps that should be taken to achieve a balanced workflow? Please comment on the results and explain your rationale (25 points).


10. Discuss your results and comment on the system’s ability to handle the demand (10 points).


Question 8 [30 points]: The effect of illumination levels on the performance of tasks has been investigated where subjects were required to insert a probe that is fine-tipped into the eyeholes of a certain number of needles in rapid succession for both a low light level that has a black background and also a higher light level with a white background. The resulting data is shown below and is also available in the LSSGB_Final_Exam_December_2021.xls Excel file where each value is the time (in seconds) required to complete the task. Conduct an appropriate hypothesis test to check if using the higher level of illumination with white background results in a decrease of more than 5 seconds using α = 0.05. Clearly state your conclusions.


Sample Number Low light with black background Higher light level with white background
1 25.85 18.23
2 28.84 20.84
3 32.05 22.96
4 25.74 19.68
5 20.89 19.50
6 41.05 24.98
7 25.01 16.61
8 24.96 16.07
9 27.47 24.59



Question 9a [40 points]: Stainless steel pipe comes in many lengths and widths. These measurements vary between applications, and different sizes of pipe require different tools for cutting. Two machines are used for cutting the stainless-steel pipes with a length of 16.0 inches. The cutting process for the two machines can be assumed to be normal, with standard deviations of 0.015 (Machine 1) and 0.018 (Machine 2). Bill, a quality engineer, suspects that both machines cut the pipes into the same length, whether the length is 16.0 inches. An experiment is performed by taking a random sample from the output of each machine. The collected data is shown below and is also provided in the LSSGB_Final_Exam_December_2021.xls Excel file.


Machine 1 Machine 2
16.03 16.01 16.02 16.03
16.04 15.96 15.97 16.04




15.98 15.96 16.02
16.05 16.02 16.01 16.01
16.02 15.99 15.99 16.00



1. State the hypotheses that should be tested in this experiment? (10 points)


2. Test these hypotheses using α = 0.05. Comment on your results (10 points).


3. What is the P-value for the test? (5 points)


4. Find a 95% confidence interval on the difference in the mean cutting length for the two cutting machines (please keep four decimal places in your answers(15 points).


Question 9b [25 points]: A vendor claim that the average weight of a shipment of n parts is 1.84. The customer randomly chooses 64 parts and finds that the sample has an average weight of 1.88. Suppose that the standard deviation of the population is known to be 0.03. Should the customer reject the lot? Assume 90%, 95%, 99% confidence intervals and comment on your answers.


Question 10 [40 Points]: Answer the following questions with no more than 1-4 paragraphs on each (when appropriate, examples and/or illustrations are encouraged).


1. Discuss the differences between ‘special cause’ and ‘common cause’ variation, giving at least one example of each type (10 points).


2. List the seven types of waste and give at least one example for each from your daily life (10 points).


3. Compare Lean with Six Sigma, and then describe the strengths and weaknesses of the Lean Six Sigma method. Use an example to explain how Lean and Six Sigma work together in a way that your non-engineering colleagues and/or friends/family members will appreciate/understand (10 points).


4. Define the meaning of “cost of poor quality”? Give examples to support your definition? Suggest some prevention techniques to prevent the cost of poor quality (10 points).


Question 11 [57 Points]: Are the following statements True or False? Please provide a very short justification (1-2 sentences) to support your answers.


1. Cpk can exceed Cp.


2. Cp and Cpk can be negative.


3. If the mean is larger than the median, the distribution is right-skewed.


4. DPMO is used to show the ratio of defects to units.


5. DPU is calculated by dividing the number of defects by the number of units.


6. A process operating at 6 Sigma will only generate 3.4 defects per million opportunities.


7. A hypothesis test is a statistical method in which a specific hypothesis is formulated about the population, and the decision of whether to reject the hypothesis is made based on sample data.


8. A critical to quality (CTQ) tree is used to translate broad requirements into specific requirements.


9. An ‘affinity diagram’ is used extensively in quality function deployment (QFD).


10. In the normal distribution, 68% of the data will occur within ±3 standard deviations.


11. The Voice of the Customer indicates the control limits in a control chart.


12. Histogram is a bar chart that depicts the frequencies of numerical or measurement data.


13. An arithmetic mean is the middle value of a dataset when the values are arranged in either ascending or descending order.


14. A “pull” production system is a production system where you make as much product as you can regardless of whether the customer needs it or not.


15. A Kanban system supports a “pull” system.


16. A VSM enables all stakeholders of an organization from the ground up to easily visualize and understand the process.


17. Type I error is a situation wherein a hypothesis test fails to reject a null hypothesis that is false.


18. The dependent variable (DV) is the variable expected to predict or cause a change in another variable.


19. Jidoka is the ability of employees to stop a production process that is not meeting standards.

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