Welcome! Please read this page (in particular) very carefully. Instructions You need to understand how to send your assignments (deliverables) to your instructor. The tabs (bottom of each sheet) in this document contain all of the deliverables expected of you. If you need help along the way, look for these special cells that have a red indicator Read me in the corner. It looks like the "Read me" box to the right: Simply slide your cursor over the red-cornered cell and you will get more information. The format for all of the deliverables is the same: The 'assignment objective' is in black font. The next segment is in green font. These are your instructions for that assignment. The blue font is the data (where applicable) for completing each the assignment. Software We are using Excel software for the projects. You may use other software to complete your projects, but please 'report' your answers in the Excel format described below. You may complete your assignments with any version of Excel software. All assignments can easily be completed with a basic copy of Excel. There is also an Add-In feature which is available for Excel that can be helpful, although it is not required. The Add-In feature comes free with each Excel package, although it may not be currently loaded into your copy. Following are the simple instruction for loading the Excel Add-ins for both Excel 2003 and Excel 2007. (Slide your cursor over the red-cornered cells to read) Excel 2003 Excel Novice - Please read Project Timeline Deliverables include: Project charter (target week 3 or sooner) Baseline sigma (week 4 or sooner) Histogram (week 5 or sooner) Expected variation (week 6 or sooner) t test ( week 7 or sooner) Chi square (week 9 or sooner) ANOVA (week 11 or sooner) DOE (week 12 or sooner) Scatter diagram (week 13 or sooner) Control chart (XmR) (14 or sooner) Pp Ppk (week 15 or sooner ) Excel 2007 How to submit an Assignment In response to customers like you, we have added a peach-colored box for each deliverable. We have done this to make it clear (and consistent) the areas of the project that will be reviewed to your instructor. Project: Deliverable: Student last name: Manufacturing Project Improve phase - gen. sol. Johnson What is the control chart telling you? There is a point out of control at subgroup #15. I would try to figure out why that happened. We would also recalculate the control limits because there is evidence the process has changed. e of Exampl What is the average of subgroup 1? liverable a de What is the average of subgroup 2? What is the average of subgroup 3? What is the average of subgroup 4? What is the average of subgroup 5? What is the average of subgroup 6? What is the average of subgroup 7? What is the average of subgroup 8? 22 34 23 22 25 23 29 27 Read this! 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Read this! This spreadsheet tab provides illustrations of adding the DATA ANALYSIS capability to your Excel software. If you see Data Analysis already listed under the Tools tab, you are set. If you do not see Data Analysis follow the instructions in the Green tab. Excel 2003 instructions Excel 2003 or earlier versions of Excel example This spreadsheet tab provides illustrations of adding the DATA ANALYSIS capability to your 2007 Excel software. If you see Data Analysis already listed under the DATA tab, you are set. If you do not see Data Analysis follow the instructions in the Green tab. Excel 2007 instructions Excel 2007 example 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) at a cost of poor quality of just over $256,000 per quarter. She said the industry standard is less than 50 DPMO and if we do not get the level of quality to the industry standard (as a minimum) within the next six months, LLI should not expect to keep the business next year. The student will be a Black Belt working for LLI. The specifics about their company: 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 The deadline for completing all project deliverables is 7 days prior to the end of the course Objective: A problem statement needs to be developed. There needs to be a business case so that management will buy-in to having the team working on the project. The scope of the project also needs to be decided upon. This is important to ensure a likely successful completion. If the scope is too broad, a success may not be realized for years, or may not happen at all. Instructions for you: Create a project charter based "Create a charter?" upon the information in the introduction. (see "The project" tab below) In reality, you would fill in a charter with team members' names, stake holders, etc. We are not interested in those details for this simulation, but we do want to see what you come up with for four (4) items: Problem statement, business case, goal and project scope. Be sure to review the week 2 virtual class for more information on project charters before you submit this! How to submit an Assignment TARGET ASSIGNMENT DATE - Submit in Week 3 or earlier Project: Deliverable: Student last name: Manufacturing Project Project charter Jeffries What is the business case? One of our largest customers, Specific Motors, will discontinue business with us next year due to their dissastifaction of the level of quality of the leveler plates and the high rate of rejection, resulting in over $256,000 of lost revenue each quarter. What is the problem statement? Each quarter, we have produced an average of 1,350 DPMO of rejected leveler plates, which has resulted in reduced customer satisfaction, resulting in over $256,000 in lost revenue each quarter. What is your goal statement? By January 1, 2012, we will have a process in place to reduce rejected leveler plates from 1,350 DPMO to less than 50 DPMO identified in our analysis. What is the project scope? The process boundaries are Incoming Material to Inspection of the Leveler Plate. The project has to be completed under 6 months with 20 hours a week being utilized. Additional money and equipment based on good data after discussion with the Champion. "Business Case?" "Problem Statement" "Goal Statement" "Project Scope?" 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Objective: We want you to determine baseline sigma for both the current defect level and the new target defect level. (approximate is okay) You will need to refer to the tab below entitled "The Project" for this deliverable. Instructions for you: Calculate baseline sigma. Sigma Levels 6 sigma 3.4 dissatisfied customer experiences per million (DPMO) 5 sigma 233 DPMO 4 sigma 6,210 DPMO 3 sigma 66,807 DPMO 2 sigma 308,538 DPMO 1 sigma 691,462 DPMO How to submit an Assignment Target Assignment Date - Submit in Week 4 or earlier Project: Manufacturing Deliverable: Baseline Sigma Student last name: Jeffries Baseline sigma for current defect level:: 4.5 Baseline sigma for the new target defect level 5.4 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Help? Objective: The Black Belt team did a pareto analysis of the data and determined that three factors were causing over 95% of the problem with the leveler plates. Those factors are, the length of the plates, the width of the plates, and the thickness of the plates. You need to know if the data from these three 'product parameters' are normally distributed. Instructions for you: 1. Construct three (3) histograms for the three data sets. 2. Interpret each of the histograms to determine whether the variables are random or normally distributed. Data: Length 10.67 10.74 10.68 10.72 10.66 10.69 10.70 10.72 10.69 10.68 10.72 10.70 10.70 10.73 10.75 10.73 10.69 10.68 10.70 10.77 10.72 10.69 10.66 10.69 10.63 10.68 10.73 10.74 10.65 10.69 10.70 10.72 10.75 10.71 10.72 Upper Spec Lower Spec Target Width 11 10.5 10.75 7.66 7.45 7.55 7.51 7.57 7.55 7.53 7.53 7.56 7.52 7.58 7.55 7.53 7.56 7.58 7.55 7.55 7.54 7.57 7.54 7.55 7.55 7.56 7.54 7.56 7.56 7.55 7.54 7.55 7.56 7.57 7.54 7.55 7.54 7.55 7.53 7.54 7.55 Thickness 0.551 0.546 0.546 0.554 0.546 0.542 0.545 0.538 0.552 0.547 0.546 0.545 0.546 0.548 0.546 0.543 0.548 0.545 0.553 0.539 0.549 0.541 0.543 0.545 0.549 0.546 0.545 0.540 0.541 0.545 0.547 0.543 0.545 0.546 0.547 Histograms in Excel 2003 Histograms in Excel 2007 More on Bin Ranges 0.56 0.54 0.55 How to submit an Assignment Target Assignment Date - Submit in Week 5 or earlier YOU DO NOT NEED TO SEND THE ACTUAL HISTOGRAMS Project: Manufacturing Deliverable: Histogram Student last name: Jeffries Is 'length' normally distributed? Is 'width' normally distributed? Is 'thickness' normally distributed? NO YES YES YOU DO NOT NEED TO SEND THE ACTUAL HISTOGRAMS 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. "Normal?" 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, you can calculate/predict the limits of expected variation by calculating the mean and standard deviation. 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, width and thickness. 2. Calculate the standard deviation for each. 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 Upper Spec Lower Spec Target Length 10.67 10.74 10.68 10.72 10.66 10.69 10.70 10.72 10.69 10.68 10.72 10.70 10.70 10.73 10.75 10.73 10.69 10.68 10.70 10.77 10.72 10.69 10.66 10.69 10.63 10.68 10.73 10.74 10.65 10.69 10.70 10.72 10.75 10.71 10.72 11 10.5 10.75 Width Thickness 7.51 0.551 7.57 0.546 7.55 0.546 7.53 0.554 7.53 0.546 7.56 0.542 7.52 0.545 7.58 0.538 7.55 0.552 7.53 0.547 7.56 0.546 7.58 0.545 7.55 0.546 7.55 0.548 7.54 0.546 7.57 0.543 7.54 0.548 7.55 0.545 7.55 0.553 7.56 0.539 7.54 0.549 7.56 0.541 7.56 0.543 7.55 0.545 7.54 0.549 7.55 0.546 7.56 0.545 7.57 0.540 7.54 0.541 7.55 0.545 7.54 0.547 7.55 0.543 7.53 0.545 7.54 0.546 7.55 0.547 7.66 7.45 7.55 Decimal places in Excel Excel STORES the full decimal value of a number in its cells. 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 spreadsheet number to display the value to 4 decimal places, 2.4558. Following are the instructions for re-setting the number of decimal places that are visible in Excel for both Excel 2003 and Excel 2007. NOTE: Try to not use 'rounded' data during your calculations. In your final result, you may round to one more decimal place than your raw data. Excel 2003 Excel 2007 0.56 0.54 0.55 How to submit an Assignment Target Assignment Date - Submit in Week 6 or earlier Project: Manufacturing Deliverable: Expected variation Student last name: Jeffries REPORT ALL OF THE RESULTS TO AT LEAST 4 DECIMAL PLACES! Mean for LENGTH::: 10.7029 Standard deviation for LENGTH::: 0.0305 What is the lowest point of expected variation? 10.6114 What is the upper point of expected variation? 10.7944 Mean for WIDTH::: Standard deviation for WIDTH::: What is the lowest point of expected variation? What is the upper point of expected variation? 7.5489 0.0157 7.5018 7.5960 Mean for THICKNESS::: Standard deviation for THICKNESS::: What is the lowest point of expected variation? What is the upper point of expected variation? 0.5457 0.0036 0.5349 0.5565 Help 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Objective: There is thought among some people at your facility that the old method and the new method are producing product at different thicknesses. You DO NOT WANT the methods to be different. In fact, you want the methods to be producing products that are the same. To address this, you suggest using a T test. If the methods are significantly different, you have a problem. If the null is NOT rejected--that is good news! The team agrees that a sample size of 25 is adequate for the test. Remember...You are hoping the null does not get rejected. The team decides a significance level at 0.05 for the test. Instructions for you: Step 1. You need 4 numbers: Old method's average: = .012576 New method's average: x-bar (you need to calculate it from the data below) Standard deviation of sample data 's' (you need to calculate it from the data below) n number of samples 'n' (you need to count them yourself from the data below) Step 2. State the null and alternate hypothesis. Step 3. Calculate the T test statistic from the formula found in the t test lecture in your white manuals. (Use ALL of the available digits, DO NOT ROUND!) Step 4. Determine the critical T value (refer to the T-distribution Table in the Online Textbook.) [Hint: (n - 1) is 25 - 1 = 24 df] and considering a 95% confidence. Step 5. What is your conclusion? "How did you come up with ?" "How can I find x-bar?" "How can I find S?" "Hypothesis statement?" "How much help is Excel for this?" "My conclusion?" "I'm lost in calculating the Test Statistic" "What's the difference between 1-tail or 2?" Data: New method 0.009 0.010 0.011 0.011 0.010 0.011 0.011 0.013 0.008 0.012 0.010 0.013 0.014 0.012 0.009 0.014 0.011 0.015 0.011 0.012 0.015 0.011 0.011 0.012 0.008 How to submit an Assignment Target Assignment Date - Submit in Week 7 or earlier Project: Manufacturing Deliverable: T Test Student last name: Jeffries REPORT ALL OF THE RESULTS TO AT LEAST 4 DECIMAL PLACES! Old method average::: 0.0126 New method average::: 0.0114 Standard deviation (s)::: 0.0019 n = ::: 25 State the null hypothesis::: State the alt. hypothesis::: T test statistic::: One tail or two? Critical value::: Reject the null? (yes, or no?)::: Check Check Check The Null Hypothesis is the new method thickness = the old method thickness The Alternative Hypothesis is the new method thickness does not equal the old method thickness -3.1795 Two 2.0640 Yes Please write the hypothesis conclusion::: Since the test statistic falls in the left-hand reject region, the null hypothesis is rejected. With 95% confidence it concludes that the two methods are producing different thicknesses. Check Check 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Objective: Going down the DMAIC road, you and your team are continuing to try to get a handle on what is causing additional defects in the leveler plates. You are trying to reduce the variation in that process. One of the team members suggested that defects of type A or B is dependent upon the test sites. In other words, he thinks that one or more of the three test sites may be influencing the defect rate of type A and/or type B. One way to find out is through the use of the Chi Square test for independence. There are three test sites that are designed to detect two types of defects. There have been arguments that Site 3 is not able to detect as many Type A defects as the other test stations. You have been asked to prove (or disprove) that test site and defect type are independent of each other. Test at 95% confidence. Instructions for you: We highly recommend working through the practice example in yellow below before tackling this deliverable. 1. State the practical problem. 2. State the null and alternate hypotheses. 3. Compute the chi-square statistic. 4. Determine the chi-square critical value. 5. What conclusions can you draw? "Hypothesis statement?" "Write-up my conclusion? Sample Exercise in shaded area (not required, but helpful) See manufacturing project assignment data in blue below this example Some help for you using an practice example: You first need to calculate the expected values. It is best to make a table as step 1. For example, males and females watch various TV stations. Let's say that we want to find out if gender is dependent or independent of television station preferences. The practice data follows: WKBW WBEN WGR Totals Males 62 54 25 141 Females 44 50 15 109 Totals 106 104 40 250 Step 1. Calculate each of the 'expected values.' We will do the first two for you. a. Probability of viewer being male is 141 / 250 = 0.564 (refer to the cells in the table above) b. Probability of viewer preferring WKBW is 106 / 250 = 0.424 c. Probability of viewer preferring WKBW AND being male is 0.564 x 0.424 = 0.239 d. Expected number of viewers in this cell is 0.239 x 250 = 59.8 etc... a. Probability of viewer being female is 109 / 250 = 0.436 b. Probability of viewer preferring WKBW is 106 / 250 = 0.424 c. Probability of viewer preferring WKBW AND being female is 0.436 x 0.424 = 0.185 d. Expected number of viewers in this cell is 0.185 x 250 = 46.3 etc... Repeat this for all six cells. To check your work, the totals (across and down) should add up very close to the (across and and down) totals of the observed values. Here is how your chart should appear when finished: The 'expected values' are in [brackets.] Males Females Totals WKBW WBEN WGR Totals 62 [59.8] 54 [58.8] 25 [22.5] 141 44 [46.3] 50 [45.3] 15 [17.5] 109 106 104 40 250 Step 2. Compare the OBSERVED [EXPECTED] Example: For the first cell (Males/WKBW), the formula is: Observed minus [Expected] Squared divided by [Expected] as follows: (62-59.8)2 divided by 59.8 = 0.0809 For the 2nd value... (54-58.8)2 divided by 58.8 = 0.3918 For the 3rd value... (25-22.5)2 divided by 22.5 = 0.2778 For the 4th value... (44-46.3)2 divided by 46.3 = 0.1143 For the 5th value... (50-45.3)2 divided by 45.3 = 0.4876 For the 6th value... (15-17.5)2 divided by 17.5 = 0.3571 Step 3. Add those chi-square values and you should get 1.7095 This is your calculated chi-square test statistic. Step 4. Determine the significance level. (e.g., .05 or .01 or .1) This is up to the discretion of the team and the team's choice is based upon what level of risk they are willing to live with. Step 5. Determine the Degrees of Freedom (df) for the rows and the columns. You will need this to find the critical value in the table in the textbook. df=(number of rows minus 1) multiplied by the (number of columns minus 1) So, in this particular case it would be (2-1 multiplied by 3-1) = 2 Step 6. Go to the chi-square table in the Online textbook and determine the critical value. Let's assume a 95% confidence level, and we know we have 2 df (from above), using the table we find the respective critical value of 5.99. We now can compare the calculated test statistic (1.7095) to the critical value (5.99). If the test statistic is greater than the critical value, you can conclude 'reject' the null. If not, then you conclude 'fail to reject' the null hypothesis. Data: Data for this deliverable: Site 1 Defect Type A 8 Defect Type B 9 Excel 2003 Site 2 8 10 Site 3 7 8 Excel 2007 How to submit an Assignment Target Assignment Date - Submit in Week 9 or earlier Deliverable: Student last name: Site 1 / Type A expected::: Site 2 / Type A expected::: Site 3 / Type A expected::: Site 1 / Type B expected::: Site 2 / Type B expected::: Site 3 / Type B expected::: Chi Square statistic::: One tail or two?::: Critical value::: Reject the null? (Y or N)::: Chi Square Jeffries ::: ::: 7.8200 8.2800 6.9000 9.1800 9.7200 8.1000 0.0279 One 5.9900 No Please write the hypothesis conclusion is statistical language::: Fail to reject the null hyupothesis. Check Check Check 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. 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). It is thought that these machines were affecting the overall material thickness in varying degrees. It was suggested to compare the machines' performance 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 1 Machine 2 Machine 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 CM df F MS SS ANalysis Of VAriance Correction for the Mean degrees of freedom F statistic used to compare with the F-table value (aka 'critical value') Mean Square 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 = 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 = 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? Help Help Help Help Help Help Help How to submit an Assignment Target Assignment Date - Submit in Week 11 or earlier Project: Deliverable: Student last name: Manufacturing Project ANOVA Jeffries What is the SUM of SQUARES (SS) for FACTOR? What is the SUM of SQUARES (SS) for ERROR? What is the SUM of SQUARES (SS) TOTAL? What is the Degrees of Freedom (Df) for FACTOR? What is the Degrees of Freedom (Df) for the ERROR term? What is the Degrees of Freedom (Df) TOTAL? What is the MEAN SQUARED (MS) for FACTOR? What is the MEAN SQUARED (MS) for the ERROR term? What is the F Calculated value? What is F Critical value (from the table)? Write up your conclusion - in statistic terms: 0.000650 0.004164 0.004814 2 9 11 0.000325 0.000463 0.702450 4.2565 Because the F Statisitic is not greater than the F Critical I fail to reject the null hypothesis. Therefore I cannot conclude that any one of the machines affect the mean of the material thickness. Check 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Objective: Although many things have been learned to this point and we have made progress, 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 (in your workbook - page 542 (Book 3 of your white manuals 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 design below a resolution III, IV, V or Full Factorial (no resolution)? 3. The design below is a design that an consultant is recommending. Unfortunately, you learn some bad news. Your management has set your budget only allowing for 8 runs because the trials cost $600 a piece. What would you recommend? Big Hint: One of the factors MAY be dropped from the study - for economic reasons. (please provide your answer in the peach-colored area below) You do not have to determine which factor to drop. 4. Using the resolution matrix on page 542 (Book 3 of the white manuals), what resolution would your recommendation be? 5. Based on your new recommendation, what are you giving up? Explain (briefly in the peach area) "I'm lost" Data: Factor Depth Temp Pressure R.P.M. Time (-) 85 140 850 4400 30 (+) 150 155 2500 4800 45 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 I try to enter + or - and it does not work. Factor Factor Factor Factor Factor A X B A X C A X D A X E B X C B X D B X E C X D C X E D X E C A B D E + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Entering + + + + + + + + or - does + + + + + + not work + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + How to submit an Assignment Target Assignment Date - Submit in Week 12 or earlier YOU DO NOT NEED TO SUBMIT THE DESIGNED EXPERIMENT Project: Manufacturing Deliverable: DOE Design Choice Student last name: Jeffries 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. What is your recommendation? "I'm lost" I am recommending a Fractional Factorial DOE because of the budget that I am alotted is restricted. I will drop one of the factors and set my DOE to 8 Trials in Run Order. 4. What would the new resolution be? (III, IV, or V) ::: 5. What would you be giving up? What confounding will you see? + Full Factorial Resolution IV I am giving up less interactions that could be important . The two confounding structures that will be identified are main effect confounded with a 3 way interaction and a two way interaction confounded with a two way interaction. YOU DO NOT NEED TO SUBMIT THE DESIGNED EXPERIMENT Hint: 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Objective: A team member has been saying since day one that there is a correlation between temperature and the thickness. Should the team have listened? Construct a scatter diagram to see if she is correct. Instructions for you: Construct a scatter diagram to see if she is correct. And, if she is, we may have found a smoking gun toward a solution. Data: Data: Temp 154 153 152 152 151 151 151 151 151 151 151 151 151 151 151 151 150 150 150 150 150 150 150 150 149 149 149 148 148 148 147 147 146 146 145 Thickness 0.554 0.553 0.552 0.551 0.549 0.549 0.548 0.548 0.548 0.547 0.547 0.547 0.547 0.547 0.547 0.546 0.546 0.546 0.546 0.546 0.546 0.545 0.545 0.545 0.545 0.545 0.545 0.545 0.543 0.543 0.542 0.542 0.541 0.54 0.538 Scatter diagrams in Excel 2003 Scatter diagrams in Excel 2007 Correlation Coefficient - Excel 2003 Correlation Coefficient - Excel 2007 How to submit an Assignment Target Assignment Date - Submit in Week 13 or earlier YOU DO NOT NEED TO SUBMIT THE SCATTER DIAGRAM Project: Manufacturing Deliverable: Scatter Diagram Student last name: Jeffries Is there correlation? Positive or negative correlation? Yes Positive 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. 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 it was 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 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 key process parameters that effect the thickness of the leveler plates have been controlled with an on-going XmR chart and is being monitored with a capability study. Since thickness was the end-product parameter of interest, the team wanted to determine whether there is any assignable-cause variation. They chose to use an XmR chart. 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. 2. 3. 4. What is the upper control limit for the range? What is the upper control limit for the individuals? What is the lower control limit for the individuals? What would you do with the process? a. What would you recommend? b. Is the measurement system discriminate? c. Is thickness in statistical control? Help "I have no idea about this one" Data: Calculating R-bar in Excel 2003 Calculating R-bar in Excel 2007 Thickness data for XMR control chart 0.551 0.546 1a. Calculate R-bar 0.547 0.548 Self check 0.547 0.547 1b. Calculate the 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 How to submit an Assignment Target Assignment Date - Submit in Week 14 or earlier YOU DO NOT NEED TO SUBMIT THE XmR CHART Project: Manufacturing - XmR Chart Deliverable: XmR Chart Student last name: Jeffries REPORT ALL OF THE RESULTS TO AT LEAST 4 DECIMAL PLACES! Calculated R-Bar::: 0.0035 Upper control limit for the range::: 0.0113 Upper control limit for the individuals::: 0.5553 Lower control limit for the individuals::: 0.5369 Is there adequate discrimination? Check Check Check Check Help Yes there is adequate discrimination Based upon what the control chart is telling you, what would you do? Help This control Chart is in control because no rules are being violated 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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 completing all project deliverables is 7 days prior to the end of the course. Fre que nc Bin Frequency 0.547 2 0.5484 3 0.5498 7 0.5512 17 0.5526 4 More 2 Histogram Bin Frequency Bin Frequency 145 1 146.8 2 148.6 6 150.4 13 152.2 11 More 2 Histogram 15 10 5 0 145 146.8 148.6 150.4 152.2 More Bin Frequency Bin Frequency 1300 1 1420 4 1540 5 1660 10 1780 7 More 8 Histogram 15 10 5 0 1300 1420 1540 1660 1780 More Bin Fre que nc Bin Frequency 0.121 1 0.1228 2 0.1246 5 0.1264 13 0.1282 11 More 3 Histogram Bin Fre que nc Bin Frequency 0.229 2 0.2302 4 0.2314 9 0.2326 9 0.2338 5 More 6 Histogram Bin Frequency Bin Frequency 4400 4 4480 9 4560 4 4640 1 4720 13 More 4 Histogram 15 10 5 0 4400 4480 4560 4640 Bin 4720 More Frequency Bin Frequency 400 1 403.6 1 407.2 5 410.8 13 414.4 13 More 2 Histogram 15 10 5 0 400 403.6 407.2 410.8 414.4 More Bin 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 for each of the seven key process (upstream) parameters 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 you are finished with the project. Congratulations!!!! Instructions for you: "Is it possible for me to do a self-check?" Instructions for you: 1. Construct histograms for each of the parameters. Note: The first parameter 'thickness' is the product parameter. The remaining parameters are process parameters that are thought to affect thickness. 2. Are the processes random (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: Upper Specs Lower Specs Thickness 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 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 Time 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 Temp 145 146 146 147 148 148 148 149 149 149 150 150 150 150 150 150 150 150 151 151 151 151 151 153 149 152 148 147 150 151 151 151 152 152 154 Press 1300 1400 1500 1500 1500 1500 1500 1400 1800 1600 1600 1600 1600 1600 1600 1600 1600 1600 1600 1800 1800 1400 1400 1700 1700 1700 1700 1700 1700 1700 1800 1800 1900 1900 1900 0.125 dim. 0.121 0.122 0.122 0.123 0.123 0.124 0.124 0.124 0.125 0.125 0.125 0.125 0.125 0.128 0.128 0.125 0.129 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.127 0.127 0.127 0.127 0.127 0.127 0.127 0.128 0.128 0.129 0.130 0.23 dim. 0.229 0.230 0.230 0.231 0.231 0.231 0.231 0.231 0.231 0.231 0.231 0.231 0.230 0.230 0.234 0.233 0.235 0.229 0.234 0.232 0.232 0.232 0.232 0.232 0.232 0.232 0.232 0.232 0.233 0.233 0.233 0.233 0.234 0.234 0.235 R.P.M. 4400 4400 4400 4400 4450 4450 4450 4450 4450 4450 4450 4450 4450 4500 4500 4500 4550 4600 4650 4650 4650 4700 4700 4700 4700 4700 4700 4700 4700 4700 4700 4750 4750 4750 4800 HB 400 402 404 404 406 406 406 408 408 408 410 410 410 410 410 411 410 410 409 409 410 412 412 412 412 412 412 412 412 414 414 414 414 416 418 Thickness 0.5600 0.5400 Time 140 100 Temp 160 140 Press 2600 900 0.125 dim. 0.1350 0.1150 0.23 dim. 0.2400 0.2200 R.P.M. 8000 2000 HB 500 300 How to submit an Assignment Target Assignment Date - Submit in Week 15 or earlier YOU DO NOT NEED TO SEND THE ACTUAL HISTOGRAMS Project: Manufacturing Deliverable: Pp Ppk Student last name: Jeffries Thickness Pp 2.11 Ppk 2.09 Normal? Yes Acceptable? Yes Time Pp Undefined Ppk Undefined Normal? No Acceptable? Yes Temp Pp 1.66 Ppk 1.61 Normal? Yes Acceptable? Yes Pressure Pp 1.83 Ppk 1.57 Normal? Yes Acceptable? Yes 0.125 dim Pp 1.59 Ppk 1.46 Normal? Yes Acceptable? No 0.230 dim Pp 2.15 Ppk 1.75 Normal? Yes Acceptable? Yes R.P.M. Pp 7.55 Ppk 6.50 Normal? No Acceptable? Yes HB temp Pp 8.74 Ppk 7.87 Normal? Yes Acceptable? Yes 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. Click on the 'email' icon on your course home page 2. Select 'new message' 3. Click on your instructor's email envelope icon 4. Type "the respective assignment name" 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. Check Normal? Acceptable? Check Check Check Check Check Check Check