1. Applying Six Sigma resources to reduce the time to resolve complaints for an existing customer support call center by looking at the most common reasons for complaints and improving the training of call center staff to apply best practices toward resolving these issues would most likely fall under which of the following types of Six Sigma Projects: a. b. c. d. DMAIC Manufacturing Six Sigma Project DMADV Design for Six Sigma Project DMAIC Transactional Six Sigma Project IDD Transactional Design for Six Sigma Project 2. Suppose you work for a company that sells and distributes DVDs through the internet. The company performs an audit on 20% of all orders over the last three months. For each order, they have identified four possible defect types (wrong DVD title, DVD in-stock but order filled late, Damaged DVD, Missing DVD (Assume this requirement ONLY applies to multiple DVD orders as they would not ship an order without at least one DVD packed). In the past six months they audit 270 purchased orders with single DVD requests and 670 orders with multiple DVD requests. The obtain the following data\" Category 1: Wrong DVD - had 21 defects Category 2: DVD in-stock but late - had 78 defects Category 3: Damaged DVD: had 2 defects Category 4: Missing DVD (multiple orders): had 14 defects Note: an individual order could have more than 1 defect 1 Which of the following would best reflect 'current state process capability'? a. b. c. d. 32,951 DPMO 35,530 DPMO 165,000 DPMO Yield = 84% 3. Suppose you monitor the number of minutes to complete a task. You obtain results from 200 samples and produce the following Graphical Summary Analysis using Minitab. Which of the following would most likely be inferred from these results? (Assume alpha = 0.05) a. b. c. d. Data appear to be Skewed Right Data appear to be Skewed Left Data appear to be Normally Distributed Data appear to be strictly increasing over time (data collection order) 2 S & S Inc provides consulting services to various clients. One of their biggest problems is past due account receivables. An account is considered past due if it is more than 45 days beyond the invoice date (USL = 45). To analyze the problem, they obtain a sample of 263 invoices. The data are plotted as below. Summary for Days outstanding A nderson-D arling N ormality T est A -S quared 0.063 M ean S tD ev V ariance 39.183 8.353 69.776 S kew ness K urtosis N 15.0 22.5 30.0 37.5 45.0 52.5 60.0 0.71 P -V alue 0.0803911 -0.0215217 263 M inimum 1st Q uartile 17.000 34.000 M edian 3rd Q uartile M aximum 39.000 44.000 60.000 95% C onfidence Interv al for M ean 38.168 40.197 95% C onfidence Interv al for M edian 38.000 9 5 % C onfide nce Inte r v als 40.000 95% C onfidence Interv al for S tD ev Mean 7.695 9.135 Median 38.0 38.5 39.0 39.5 40.0 40.5 3 Process Capability of Days outstanding USL P rocess D ata LS L * T arget * USL 45 S ample M ean S ample N S tD ev (Within) S tD ev (O v erall) W ithin O v erall P otential (Within) C apability Cp * C PL * C P U 0.25 C pk 0.25 39.1825 263 7.81631 8.36116 O v erall C apability Pp * PPL * PPU P pk C pm 22.5 O bserv ed P erformance 30.0 37.5 45.0 52.5 E xp. Within P erformance E xp. O v erall P erformance P P M < LS L PPM > USL P P M T otal P P M < LS L PPM > USL P P M T otal 0.23 0.23 * 60.0 P P M < LS L PPM > USL P P M T otal * 220532.32 220532.32 * 228354.72 228354.72 * 243284.73 243284.73 4. Suppose that an account receivable with more than 45 days outstanding is considered a defect. Which of the following best describes the above current state of the process in terms of PPM Defective? (Note: I First conduct an Anderson-Darling (AD) Normality Test and assumed type I alpha = 0.05) a. b. c. d. Data are not Normal, Expected PPM Defective = 220K Data are not Normal, Observed PPM Defective = 228K Data are Normal, Expected PPM Defective = 243K Data are Normal, Observed PPM Defective = 208K 5. The data was Subset to only consider those accounts that are defective. What is the average 'days outstanding' for these accounts (round to the nearest tenth)? Based on MINITAB output below. Descriptive Statistics: Days outstanding Total Variable Count Mean StDev Range Days outstanding 58 50.931 3.820 14.000 a. b. c. d. 39.2 days 35.9 days 50.9 days 60.0 days 4 A recent patient satisfaction survey at the University Urology Outpatient Clinic indicated that 25% of the patients rated satisfaction with wait times as 'poor'. An additional 28% rated wait times as 'below average'. The clinic has three teams of physicians who see approximately 75 to 100 patients per day. Each team represents a specialty area. Team A specializes in treating infertility, Team B treats general urological problems and Team C specializes in urologic cancers. The staff decided to study office visit processes to identify sources of delay that lead to extended wait times. The Urology Clinic manager is disturbed by the satisfaction survey findings and concerned about the long wait times. She made calls to colleagues at other university urology outpatient clinics across the country and discovered that most have shorter wait times and see approximately 33% more patients with the same number of staff. Because of these findings, she wants to reach an average goal of total wait times during each patient's entire clinic visit of 30 minutes or less with a maximum allowable total wait time of 40. Initially, the team decides to study all of the patients seen over the course of a typical day. Using the information from MINITAB plotted below, answer the following questions. 6. Which of the following best describes the observed current state of the process for the variable \"Total Wait Time\"? a. b. c. d. 768,115 PPM Defective 681,159 PPM Defective Yield = 74.2% Yield = 23.2% 5 Next, I performed stratification analysis (e.g., multiple box plots, descriptive statistics by groups) of the total wait time decomposed by the three key waiting periods (time in wait room, time waiting for clinician 1, and time waiting for clinician 2) AND also by each of the teams (Team A, B, and C). I also record the time of arrival for each person. From the plots and analysis shown below Boxplot of TotalWaitTime 160 140 TotalWaitTime 120 100 80 60 40 20 0 A B Team C 6 7. Which of the following may be reasonably inferred as the main problem that needs to be address? a. Need to reduce the average time in waiting room across all teams b. Need to focus on reducing variation across the three waiting periods across all team (i.e., have a consistent wait time less than 10 minutes for each step) c. Need to focus on reducing the average wait time for Team A d. Need to focus on reducing both the waiting room average time and variation for Team C (get patients through the waiting room faster) 8. True or False: Higher sigma level means higher defect rate 9. True or False: A process operating at 1 sigma level will generate defect-free products 70% of the time 7 10. Ultimately, the Analyze phase establishes a reliable hypothesis for improvement solutions using A. B. C. D. Establish transfer function Y = f(X) Validated lists of critical X's and impacts Beta improvement plan (e.g. pilot plan) All of the above 11. A team for a large research and development company conducts a study on their proposal effectiveness across all divisions. Based on previous customer feedback and their own knowledge of the proposal process, they created 5 main defect categories (reasons why proposals were denied). Each proposal may fail any of the defect categories. (Assume defect categories are independent of the others). Using inspection data from 248 proposals, defects were classified and decomposed as follows: 1) 2) 3) 4) 5) Unrealistic budget: 112 Deadline for submission not met: 14 Poor formatting: 51 Poor writing quality: 27 Proposed area of study is not company's strength: 1 Which of the following metrics would best describe the current state of this process? a. b. c. d. PPM Defective (DPM) = 826,613 DPMO = 206,653 DPMO = 165,323 Yield = 85% 12. A company studies their order processing system. They obtain data from 4 measurable points in the process. They track ~2500 orders and record performance at each of these steps. Assume each order is either OK or noncompliant (binary outcome)? 8 Given these results, what is the rolled yield and normalized yield for this process? a. b. c. d. Rolled Yield = 75.2%, Normalized Yield = 93.1% Rolled Yield = 74.0%, Normalized Yield = 92.7% Rolled Yield = 93.1%, Normalized Yield = 75.2% Rolled Yield = 49.9%, Normalized Yield = 80.1% A manufacturer of injection molded parts measures the output characteristic, strength, for one of their products. Their current sampling strategy is to measure 5 parts every two hours, or after a new setup occurs. They collect 20 subgroups. The strength (psi) measurements are in the control charts are plotted below 9 13. Which of the following control charts would be used to assess the stability of the within subgroup variation only? a. b. c. d. Moving Range Chart Range Chart Individual Chart Either (a) or (c) 14. Based on the SPC charts above, which of the following would best reflect the current state of the process in terms of statistical control/stability? Note: I Selected R-bar method for estimating control limits and use only the first four rules in Minitab for assessing control. a. b. c. d. X-bar is in-control, Range is out-control Both the between and within subgroup charts are out-control X-bar is out-control, within subgroup variation is stable Both the within and between subgroup charts are in-control 10 15. Which of the following would you recommend based on all of the information available above including the Box plot? a. Manufacturer needs to focus on reducing the inherent, common cause variation b. Manufacturer needs to focus on improving the consistency of the setup operation c. Manufacturer needs to identify those special causes which are occurring every few hours d. Manufacturer needs to tighten the specifications to produce higher quality products A scientific foundation wanted to evaluate the relation between y= salary of researcher (in thousands of dollars), x1= number of years of experience, x2= an index of publication quality, x3=sex (M=1, F=0) and x4= an index of success in obtaining grant support. A sample of 35 randomly selected researchers was used to fit the multiple regression model. Parts of the computer output appear below. 16. The least squares line fitted to the data is: 11 17. The p-value of the ANOVA F test will be: 18. The (one-sided) p-value for testing whether salary increases with years of experience is: 19. The variable that helps the most in predicting salary is: 20. Which of the following gives a 95% CI for ??1? 21. How many degrees of freedom does the t* value from the previous question have? 22. According to the assumptions, what has to have a Normal distribution and constant variance? 12 BONUS - 16 Points A Six Sigma team is testing pilot test results to see if they have made a ststistically significant improvement.They need to test this hypothesis statistically and determine the 95% Confidence Interval for the improvement.Data from the baseline and pilot test are reported in the table below: B1. State the hypothesis. 2 points B2. Test the hypothesis and state the results in statistical and business statements. 5 points B3. State the 95% confidence interval for the baseline process defect rate in %. 3 points 13 B4. State the 95% confidence interval for the improved process defect rate in %. 3 points B5. State the 95% confidence interval for the improved process defect rate in %. 3 points 14