Objective: We want you to determine the sigma levels with the Motorola 1.5 sigma shift for both the current and target defect levels identified for this project. You will need to refer to the tab entitled "The Project" to be able to complete this deliverable. Instructions for you: Determine the approximate baseline and target sigma levels (to 1 decimal place) based on the DPMO and with the Motorola shift. How to submit an Assignment Project: Deliverable: Baseline Sigma Student last name: TAKE YOUR SIGMA LEVEL ANSWERS TO 1 DECIMAL PLACE. USE WHOLE NUMBERS FOR THE DPMO. What is the baseline sigma for the current defect level? What is the sigma value for the target defect level? To send each assignment to your instructor: Click-and-hold the LEFT mouse button at the TOP-LEFT corner of the peach-colored box, then while holding down on that button, drag to the LOWER-RIGHT corner of the box. This will highlight the entire peach-colored box. Release the mouse button. Do a CTRL-C. This will copy what has been highlighted. Go to your Villanova website and follow this sequence: 1. COURSE MENU 2. CLASS ROSTER 3. Click on your instructor's email envelope icon 4. Type "Check My Work - BASELINE SIGMA" in the SUBJECT box. 5. Click once inside of the message box 6. Do a CTRL-V. This will paste your deliverable into this box. Don't be concerned if after you paste it, the appearance of the text is out of alignment. It will straighten out after you hit SEND. 7. SEND Check your SENT ITEMS folder afterward to see how it straightened out. Please 'hand-in' your assignments throughout the course. DO NOT SAVE THEM FOR THE END. Procrastinators: The deadline for having all project deliverables 100% correct is 7 days prior to the end of the course. Manufacturing Project the current and Lovell Levelers, Inc. is a major provider of specialized parts for the automotive industry. LLI's biggest customer, Specific Motors was not a delighted customer this month. In fact, last Monday, the executive vice president of Specific Motors headquarters, Phyllis Kendall was diverted from a return trip from Singapore to drop in unexpectedly at the LLI plant. There was nothing routine about this visit. She made it explicitly clear that Specific Motors was disappointed with the level of quality relative to the leveler plates. In particular, she was disappointed with the current average of rejects at the rate of 1,350 defects per million opportunities (DPMO) that has created a cost of poor quality of just over $256,0 HINT! Check Check per quarter for them. She said the industry standard is 50 DPMO and if we do not get the level of quality to the industry standard within the next six months, LLI will lose Specific Motors as a customer. The student will be a Black Belt working for LLI. The specifics about their com CEO Bill Lovell GM Mary Nichols Sponsor John Hopps Finance Cindy Jenkins Process owner Leroy Miller Master BB Dennis Kens Manufacturing Mitch Freese Design Engineer Al Nelson Quality Debbie Judson fic Motors adquarters, ty of just over $256,000 DPMO and within the next fics about their company: Objective: So far--so good. The process has been in control for the past four months. Phyllis isn't as well versed in Six Sigma as the team is, and it is her nature to question everything. She asks for a capability study to be performed on these parameters and asks for a calculation two key factors that affect thickness and wants to see this for the past 35 days of production. You are on the spot, but confident. You pull up the past 35 day's worth of data and you calculate Pp and Ppk for each. Is Phyllis going to be happy or is she going to be more skeptical? That is the 'question of the day.' Crunch the numbers--and you will find out. By the way--finish this deliverable AND MAKE ALL OF THE CORRECTIONS REQUIRED ON THE PREVIOUS ASSIGNMENTS and you are finished with the project! Congratulations!!! Instructions for you: "Is it possible for me to do a selfcheck?" Instructions for you: 1. Construct histograms for each of the parameters. Note: The first parameter 'thickness' is the product parameter. The second parameter is thought to affect thickness. 2. Are the processes approximately normally distributed? 3. Calculate Pp and Ppk for each. Note: The upper and lower specifications are listed at the bottom of each column. You will need these to do the calculations. 4. Are the processes acceptable? "I'm lost" "Can I do this with the Data Analysis Toolpak in Excel 2003?" "Can I do this with the Data Analysis Toolpak in Excel 2007?" Data: Data: Thicknes s 0.548 0.550 0.552 0.554 0.552 0.547 0.547 0.552 0.549 0.548 0.549 0.549 0.550 0.551 0.549 0.550 0.551 R.P.M. 4400 4400 4400 4400 4450 4450 4450 4450 4450 4450 4450 4450 4450 4500 4500 4500 4550 0.550 0.550 0.553 0.548 0.552 0.551 0.550 0.549 0.551 0.551 0.550 0.551 0.550 0.549 0.550 0.551 0.549 0.550 Thicknes s Upper Spe 0.5600 Lower Spe 0.5400 4600 4650 4650 4650 4700 4700 4700 4700 4700 4700 4700 4700 4700 4700 4750 4750 4750 4800 R.P.M. 8000 2000 How to submit an Assignment YOU DO NOT NEED TO CREATE CONTROL CHARTS TO COMPLETE THIS ASSIGNMENT!! DO NOT SEND THE ACTUAL HISTOGRAMS UNLESS YOUR INSTRUCTOR ASKS YOU TO. Project: Deliverable: Pp Ppk Student last name: INSTRUCTIONS: (1) IF YOU SAY THE DISTRIBUTION IS NOT APPROXIMATELY NORMAL, GIVE THE CORRECT NAME FOR THE PATTERN YOU SEE IN YOUR HISTOGRAM. (2) BASE YOUR DECISION ON ACCEPTABILITY ON THE ASSUMPTIONS AND CRITERIA FOR Pp and Ppk DISCUSSED IN THE RECORDED LECTURES AND VIRTUAL CLASSES ON CAPABILITY. YOU DO NOT NEED TO CREATE CONTROL CHARTS FOR THIS ASSIGNMENT!! ThicknessPp (use 6 decimal places) Ppk (use 6 decimal places) Is this distribution approximately Normal? If it's not normal, what is the shape? Is this process acceptable? Explain your decision on acceptability. Check HINT! HINT! HINT! Round your Pp and Ppk results to 6 decimal places R.P.M. Pp (use 6 decimal places) Ppk (use 6 decimal places) Is this distribution approximately Normal? If it's not normal, what is the shape? Is this process acceptable? Explain your decision on acceptability. Check HINT! HINT! HINT! Objective: Although many things have been learned to this point and we have made progress, but we are not quite there. Earlier in the project the team determined that thickness was the main problem relating to the high level defects in the leveler plates. The analysis has been completed. Now, we want to IMPROVE the process. You recommend using a design of experiments approach to hopefully realize a breakthrough improvement. The team brainstorms a long list of possible reasons why the thickness is not capable. From that list, the team has reduced it down to five factors they want to include in an experiment. They suspect interactions, so they conclude a full factorial will be required. They refer to the resolution matrix (found in your reading materials and in the Fractional Factorial Designs Lecture) and they find they can learn about the effects of those five factors in 32 experiments. The factors for the experiment were Depth, Temp, Pressure, R.P.M. and Time. Instructions for you: From the factorial experiment (below) calculate the interactions to determine confounding. 1. Fill in the interaction columns. (shaded in peach color) You will need to do this to answer #1 in the peach-colored area below. 2. Is the initial design below a resolution III, IV, V or Full Factorial (no resolution)? 3. The initial design below is a design that an consultant is recommending. Unfortunately, you learn some bad ne Your management has set your budget only allowing for 8 runs because the trials cost $600 a piece. Big Hint: One of the factors MAY be dropped from the study for economic reasons. What specific experimental design would you recommend? (You do not need to decide which factor to drop at 4. Using the resolution matrix found in your online textbook, what is the resolution for the design you're recomme 5. Based on your new recommendation, what will the confounding pattern be in your results? Data: Factor Depth Temp Pressure R.P.M. Time (-) 85 140 850 4400 30 (+) 150 155 2500 4800 45 Factor A Factor B - + + + I try to enter + or - and it does not work. Trial 1 2 3 4 5 6 7 8 9 10 11 Factor C + + + + - Factor D Factor E + + + + + + + + + + - AX B AX C AX D 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + + + + + + + + + - + + + + + + + + + + How to submit an Assignment DO NOT SUBMIT THE DESIGNED EXPERIMENT!! Project: Deliverable: DOE Design Choice Student last name: 1. What is the sign (+ or -) for the AxC interaction for the 4th trial? 2. What is the resolution as shown above? (III, IV, or V, or Full) 3. Given the teams goals and budget, what is your recommendation for the final design of this experiment? BE SPECIFIC AND USE THE CORRECT DESIGN NOTATION AND/OR TERMINOLOGY!! 4. What would the new resolution be under your recommendation in #3 above? (III, IV, or V) ::: 5. In one sentence, what will the generic confounding pattern be for your final design? (Do NOT give us the design generators or alias sets!) III, IV, V or Full Type your SPECIFIC recommendation here and use the correct design you recommend. III, IV, or V Based on the Five Finger rule, describe the GENERIC confoun this design resolution. HINT: We do not want the alias sets or de This should be a complete sentence describing the top two e are not quite there. he high level the process. gh improvement. om that list, the matrix (found in your , you learn some bad news. $600 a piece. which factor to drop at this point.) design you're recommending? d it does not work. AX E BXC BXD BXE CXD CXE DXE + or III, IV, V or Full "I'm lost" HINT! HINT! here and use the correct notation for the recommend. III, IV, or V e the GENERIC confounding pattern for want the alias sets or design generators. describing the top two effects in DOE. HINT! HINT! Objective: Lovell Levelers just reported that Specific Motors is a satisfied customer. The leveler plate quality is no longer an issue. In fact, they have not seen a single defect in six months! Phyllis Kendall made another surprise visit, but this time for a more pleasant reason. She presented each member of the team with a crisp, new $100 bill as a show of appreciation. But she also pointed out that we need to have a way to ensure that this problem will not crop up again. The team is one step ahead of her and explained that the thickness of the leveler plates is being monitored and controlled with an on-going XmR (Individuals and Moving Range) chart so that any assignable causes of variation will be detected and addressed quickly. The parameters affecting the product thickness are also being monitored with a capability study. Instructions for you: We want to make sure you can calculate control limits. You may construct the control chart by hand, or you may use a charting function in Excel. There are blank forms in the back of your notebook . Control Charts in Excel 2003 Control Charts in Excel 2007 1. What is the upper control limit for the range? Help 2. What is the upper control limit for the individuals? 3. What is the lower control limit for the individuals? 4. What would you do with the process? a. What would you recommend? b. Is the measurement system discriminate? c. Is thickness in statistical control? "I have no idea about this "I have no one" idea about this one" Data: Thickness data for XMR control chart. SAMPLE SIZE IS 1!! 0.551 0.546 1a. CalcuCalculating R-bar in Excel 2003 0.547 0.548 Self check 0.547 0.547 1b. CalculCalculating R-bar in Excel 2007 0.538 upper control limit 0.546 for the range 0.542 "How do I do that?" 0.543 Self check 0.545 0.547 2 & 3. Calculate the 0.543 control limits for the 0.548 individuals 0.545 "How do I do that?" 0.554 Self check 0.549 0.546 0.545 0.553 0.549 0.541 0.542 0.545 0.546 0.552 0.546 0.546 0.545 0.547 0.548 0.547 0.545 0.54 0.545 YOU DO NOT NEED TO SUBMIT THE XmR CHART Project: Deliverable: XmR Chart Student last name: Calculated R-Bar: Upper control limit for the range: Upper control limit for the individuals: Lower control limit for the individuals: Is there adequate discrimination? Explain your answer: Which chart did you use and exactly how many strata are there on that chart? What is the minumum number of strata for adequate discrimination? ROUND YOUR FINAL RESULTS TO 6 DECIMAL PLACES. Type your answer here. Include which chart you used (remember that there are 2 charts here), how many strata there are on that chart, and how many strata you need for adequate discrimination. Check Check Check Check Help Based upon your analysis of the stability of this control chart, what would you do next? Help Type your answer here. ving Range) Check Objective: Your boss wants to know the limits of expected variation. You know there is another shipment coming in next week and based upon this week's run, and assuming that the process is normally distributed, you can calculate/predict the limits of expected variation by calculating the mean and standard deviation for this data and then using the properties of the normal distribution to estimate the limits of the expected variation The Mean and StDev in Excel 2003 The Mean and StDev in Excel 2007 Expected variation Instructions for you: 1. Calculate the average for length. 2. Calculate the standard deviation for length. 3. From these calculations, determine the expected variation. ( Use + or - 3 sigma) You may complete this assignment by hand, as taught in the lecture. You may use Excel, or you may use a calculator or other software. We explain the fundamentals of the calculations, so that you learn the mechanics and the meaning of standard deviation. This basic approach gives you an understanding of standard deviation, which then allows you to be flexible in the tools that you use. Data: Data Length 10.670000 10.740000 10.680000 10.720000 10.660000 10.690000 10.700000 10.720000 10.690000 10.680000 10.720000 10.700000 10.700000 10.730000 10.750000 10.730000 10.690000 10.680000 10.700000 10.770000 10.720000 10.690000 10.660000 10.690000 Decimal places in Excel Excel STORES the full decimal value of a number in its But, you can adjust how many decimal values are VISIBLE in your spreadsheet. For example, if your average/mean was 2.4557643, Excel could display that number. Or, you can set your spread number to display the value to 6 decimal places, 2.4557 Following are the instructions for re-setting the number decimal places that are visible in Excel for both Excel 2 Excel 2007. NOTE: Do not use 'rounded' data during y calculations. Excel 2003 Excel 2007 10.630000 10.680000 10.730000 10.740000 10.650000 10.690000 10.700000 10.720000 10.750000 10.710000 10.720000 Upper Spec Lower Spec Target 11.000000 10.500000 10.750000 How to submit an Assignment Project: Deliverable: Student last name: Expected variation Mean for LENGTH: Standard deviation for LENGTH: What is the lowest point of expected variation? What is the upper point of expected variation? HINT!! ROUND ALL FINAL RESULTS TO 6 DECIMAL PLACES. Help Check Check Check Check mally distributed, rd deviation the expected variation. value of a number in its cells. ecimal values et. For example, 7643, Excel you can set your spreadsheet decimal places, 2.455764. r re-setting the number of n Excel for both Excel 2003 and e 'rounded' data during your Objective: In an effort to stabilize the process, there was some discussion about "those 3 machines." These 3 machines have an 'apparent' effect on the material thickness (measured prior to plating). Prior to implementing the new process and procedures, the team wants to make sure that the three machines are not performing differently using a one-way ANOVA. You will be checking for 0.05 level of significance as to whether any of the machines significantly affect the means for material thickness. Instructions for you: Using the data below construct a one-way ANOVA. To do so, occurs in two major steps--the table step, followed by the ANOVA step. Excel 2003 Excel 2007 Data: Machine 1Machine 2Machine 3 0.546 0.573 0.573 0.526 0.592 0.57 0.587 0.571 0.527 0.563 0.556 0.572 Some help: Key to terms: ANOVA ANalysis Of VAriance CM Correction for the Mean df degrees of freedom F F statistic used to compare with the F-table value (aka 'critical value') MS Mean Square SS Sum of Squares Make a table...then fill in the ANOVA using the numbers from the table. Step 1. Make a table (it is pretty easy) Table to assist in the calculations of ANOVA Sum n Sum2/n X2 Machine 1 0.546 0.526 0.587 0.563 Help Help Help Help Machine 2 0.573 0.592 0.571 0.556 Help Help Help Help Machine 3 0.573 0.57 0.527 0.572 Help Help Help Help Totals Help Help Help Help Step 2. Determine total df. Help Step 3. Determine dfFACTOR Help Step 4. Calc. CM which is: (X)2/n (which is NOT THE SAME AS X2 listed above) Step 5. Calculate SSTOTAL: X2TOTAL - CM = Help Help Step 6. Calculate SSFACTOR: SUM2/nTOTAL (from chart above) - CM = Step 7. Calculate SSERROR: SSTOTAL - SSFACTOR = Step 8. Calculate MSFACTOR: SSFACTOR divided by dfFACTOR = Step 9. Calculate dfERROR: The dfTOTAL...subtract from that the dfFACTOR Step 10. Calculate MSERROR: SSERROR divided by dfERROR = Step 11. Calculate the F statistic: MSFACTOR divided by MSERROR = Help Help Help Help Help Step 12. The ANOVA table below should be filled in by now with the exception of the F CRITICAL value. SS df MS Calc . F F Crit. ANOVA Factor Error Total Step 13. Look up the F-table value. Help Step 14. What is your conclusion? How to submit an Assignment Project: Deliverable: Student last name: ANOVA State the null hypothesis: The Null Hypothesis is State the alternative hypothesi The Alternative Hypthesis What is the F Calculated value? (Use 6 decimal places.) What is F Critical value? Check Check State your bottom-line conclusion in the words of the problem addressed by the problem. HINT: What would you say to your sponsor? (Do not use generic hypothesis testing terms.) HINT