all of the problems within the six sigma black beltInstructionsYou need to understand how to send your assignments (deliverables)to your instructor. The tabs (bottom of each sheet) in thisdocument contain all of the deliverables expected of you.If you need help along the way, look for these special cells that have a red indicatorRead mein 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.SoftwareWe are using Excel software for the projects. You may use other softwareto complete your projects, but please ‘report’ your answers in the Excel formatdescribed 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 2003and Excel 2007. (Slide your cursor over the red-cornered cells to read)Excel 2003Excel 2007Excel Novice – Please readProject TimelineFollow the submission scheduled posted on the Main Discussion Board!! Remember that the entire project must be100% correct and complete by no later than midnight EST one week (7 days) BEFORE the last day of class.THIS MEANS THAT ALL REQUIRED CORRECTIONS MUST HAVE BEEN COMPLETED CORRECTLY – JUST TURNINGIN THE ASSIGNMENT IS NOT SUFFICIENT IF THERE ARE ANY ERRORS ON IT. Most people require 2 – 3 attemptsper assignment to make all necessary corrections – so plan your time accordingly!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 8 or sooner)ANOVA (week 9 or sooner)Scatter diagram (week 10 or sooner)DOE (week 11 or sooner)Control chart (XmR) (12 or sooner)Pp Ppk (week 13 or sooner )How to submit an AssignmentIn response to customers like you, we have added a peach-colored boxfor each deliverable. We have done this to make it clear (and consistent) theareas of the project that will be reviewed to your instructor.Project:Deliverable:Student last name:Manufacturing ProjectImprove phase – gen. sol.JohnsonWhat is the control chart telling you?There is a point out of control atsubgroup #15. I would try to figureout why that happened. We wouldalso recalculate the control limitsbecause there is evidence theprocess has changed.What is the average of subgroup 1?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?2234232225232927Read this!To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag toReadthe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – ASSIGNMENT NAME – PROJECT NAME” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. It will straighten out after you hit SEND.7. SEND Check your SENT ITEMS folder afterward to see how it straightened out.8. DO NOT SEND ANY ATTACHMENTS UNLESS YOUR INSTRUCTOR SPECIFICALLY ASKS YOU TO!!VERY IMPORTANT!! Be sure to submit your assignments for grading as you completeeach one and following the submission scheduled posted on the message board – DONOT WAIT UNTIL THE END OF THE COURSE TO SEND THEM ALL IN. NOTE THAT THEENTIRE PROJECT MUST BE 100% CORRECT BY ONE WEEK BEFORE THE END OFCLASS OR YOU WILL FAIL THE PROJECT AND THE COURSE. This means that you mustsubmit ALL of your assignments far enough in advance of the project completiondeadline to allow time for all necessary corrections to be made. Following thesubmission schedule is the best way to ensure that you have enough time to finish theproject by the completion deadline – failure to meet the submission due dates can resultin failing the course. Very few assignments are correct on the first submission and manyrequire multiple rework attempts, so don’t procrastinate!this!Manufacturing ProjectLovell Levelers, Inc. is a major provider of specialized partsfor the automotive industry. LLI’s biggest customer, Specific Motorswas not a delighted customer this month. In fact, lastMonday, the executive vice president of Specific Motors headquarters,Phyllis Kendall was diverted from a return trip from Singaporeto drop in unexpectedly at the LLI plant. There was nothingroutine about this visit. She made it explicitly clear thatSpecific Motors was disappointed with the level of quality relativeto the leveler plates. In particular, she was disappointed with thecurrent average of rejects at the rate of 1,350 defects per millionopportunities (DPMO) that has created a cost of poor quality of just over $256,000per quarter for them. She said the industry standard is 50 DPMO andif we do not get the level of quality to the industry standard within the nextsix months, LLI will lose Specific Motors as a customer.The student will be a Black Belt working for LLI. The specifics about their company:CEOBill LovellGMMary NicholsSponsorJohn HoppsFinanceCindy JenkinsProcess ownerLeroy MillerMaster BBDennis KensManufacturingMitch FreeseDesign EngineerAl NelsonQualityDebbie JudsonThe deadline for having all project assignments 100% correct is 7 days prior to the end of the courseObjective:A problem statement needs to be developed.There needs to be a business case so that management will buy-in to having the teamworking on the project. The scope of the project also needs to be decided upon. This isimportant to ensure a likely successful completion. If the scope is too broad, asuccess 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. Weare not interested in those details for this simulation, but we do want to see what youcome 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 AssignmentTARGET ASSIGNMENT Submission DATE – Submit in Week 3 or earlierProject:Deliverable:Student last name:Manufacturing 2013 LAJProject charterYour LAST name hereWhat is the business case?”Business Case?”Type in your business case here. Use no more than 2 sentences.What is the problem statement?”Problem Statement”Type in your problem statement here. Use no more than 2 sentences.What is your goal statement?”Goal Statement”Type in your goal statement here. Use no more than 2 sentences.What is the project scope?Type in the scope here. Be sure to express your scope in terms of theprocess.To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – PROJECT CHARTER” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.”The project scope?”Objective:We want you to determine the sigma levels with the Motorola 1.5 sigma shift for both the current andtarget 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 theDPMO and with the Motorola shift.Be sure to review the week 3 virtual class for more information on sigma levels before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 4 or earlierProject:Manufacturing 2013 LAJDeliverable:Baseline SigmaStudent last name:Your last name hereHINT!TAKE YOUR SIGMA LEVEL ANSWERS TO 1 DECIMAL PLACE. USEWHOLE NUMBERS FOR THE DPMO.What is the current PPM / DPMO?What is the baseline sigma for the current defect level?CheckWhat is the target PPM / DPMO?What is the sigma value for the target defect level?CheckTo send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – BASELINE SIGMA” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.Objective:The Black Belt team did a pareto analysis of the data and determined that three factors were causingover 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 it is reasonable to assume that 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 assumption of normality is reasonable.Data:Length10.6710.7410.6810.7210.6610.6910.7010.7210.6910.6810.7210.7010.7010.7310.7510.7310.6910.6810.7010.7710.7210.6910.6610.6910.6310.6810.7310.7410.6510.6910.7010.7210.7510.7110.72Upper SpecLower SpecTargetWidth1110.510.757.667.457.557.517.577.557.537.537.567.527.587.557.537.567.587.557.557.547.577.547.557.557.567.547.567.567.557.547.557.567.577.547.557.547.557.537.547.55Thickness0.5510.5460.5460.5540.5460.5420.5450.5380.5520.5470.5460.5450.5460.5480.5460.5430.5480.5450.5530.5390.5490.5410.5430.5450.5490.5460.5450.5400.5410.5450.5470.5430.5450.5460.547Histograms in Excel 2003Histograms in Excel 2007More on Bin Ranges0.560.540.55Be sure to review the week 3 & 4 virtual classes for more information on judging normality before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 5 or earlierDO NOT SEND THE ACTUAL HISTOGRAMS UNLESS YOUR INSTRUCTOR ASKS FOR THEM.Project:Manufacturing 2013 LAJDeliverable:HistogramStudent last name:Your LAST name hereIs ‘length’ approximately normally distributed?Is ‘width’approximately normally distributed?Is ‘thickness’ approximately normally distributed?Yes or NoYes or NoYes or NoHow do I determine if it’sapproximately normal?YOU DO NOT NEED TO SEND THE ACTUAL HISTOGRAMSTo send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – HISTOGRAM” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.HINT!Objective:Your boss wants to know the limits of expected variation. You know there is another shipmentcoming 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 deviationfor 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 2003The Mean and StDev in Excel 2007Expected variationInstructions 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 youmay use a calculator or other software. We explain the fundamentals of the calculations, so thatyou learn the mechanics and the meaning of standard deviation. This basic approach gives you anunderstanding of standard deviation, which then allows you to be flexible in the tools that you use.Data:DataLength10.6710.7410.6810.7210.6610.6910.7010.7210.6910.6810.7210.7010.7010.7310.7510.7310.6910.6810.7010.7710.7210.6910.6610.6910.6310.6810.7310.7410.6510.6910.7010.7210.7510.7110.72Upper SpecLower SpecTarget1110.510.75WidthThickness7.510.5517.570.5467.550.5467.530.5547.530.5467.560.5427.520.5457.580.5387.550.5527.530.5477.560.5467.580.5457.550.5467.550.5487.540.5467.570.5437.540.5487.550.5457.550.5537.560.5397.540.5497.560.5417.560.5437.550.5457.540.5497.550.5467.560.5457.570.5407.540.5417.550.5457.540.5477.550.5437.530.5457.540.5467.550.5477.667.457.55Decimal places in ExcelExcel STORES the full decimal value of a number in its cells.But, you can adjust how many decimal valuesare VISIBLE in your spreadsheet. For example,if your average/mean was 2.4557643, Excelcould display that number. Or, you can set your spreadsheetnumber to display the value to 4 decimal places, 2.4558.Following are the instructions for re-setting the number ofdecimal places that are visible in Excel for both Excel 2003 andExcel 2007. NOTE: Try to not use ’rounded’ data during yourcalculations. In your final result, you may round to onemore decimal place than your raw data.Excel 2003Excel 20070.560.540.55Be sure to review the week 3 and 4 virtual classes for more information on expected variation before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 6 or earlierProject:Deliverable:Student last name:Manufacturing 2013 LAJExpected variationYour last name hereMean for LENGTH:Standard deviation for LENGTH:::What is the lowest point of expected variation?What is the upper point of expected variation?Mean for WIDTH:Standard deviation for WIDTH:::What is the lowest point of expected variation?What is the upper point of expected variation?Mean for THICKNESS:Standard deviation for THICKNESS:::What is the lowest point of expected variation?What is the upper point of expected variation?HINT!!HelpCheckCheckCheckCheckROUND ALL FINAL RESULTS TO3 DECIMAL PLACES.CheckCheckHelpCheckCheckHelpTo send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – EXPECTED VARIATION” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.CheckCheckCheckCheckObjective:There is thought among some people at your facility that the old methodand 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 beproducing products that have the same average. If the method averages are significantlydifferent, you have a problem! To address this, you suggest using a T test.If the null is NOT rejected–that is good news! The team agrees that a sample sizeof 25 is adequate for the sample from the new process for this test. You already knowthe mean for the old process. The team decides to use a significance level of 0.05 for the test.Instructions for you:Step 1. You need 4 numbers:Old method’s average:m = 0.0126New 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 lecturein your white manuals.Step 4. Determine the critical T value[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 µ?””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 method0.0090.0100.0110.0110.0100.0110.0110.0130.0080.0120.0100.0130.0140.0120.0090.0140.0110.0150.0110.0120.0150.0110.0110.0120.008Be sure to review the week 3 and 5 virtual classes for more information on descriptive statistics and t tests before yousubmit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 7 or earlierProject:Deliverable:Student last name:Manufacturing 2013 LAJT TestYour last name hereOld method average:New method average:Standard deviation (s):n=Enter hereEnter hereWhat is s?What is n?Round all your final results to4 decimal places.CheckCheckCheckState the null hypothesis:::Write the null hypothesis here.State the alt. hypothesis:::Write the alternative hypothesis here.T test statistic:One tail or two?Critical value:Reject the null? Yes or NoWhat is it?1 or 2?What is it?Yes or NoCheckRound your final results to 4decimal places.CheckState your bottom-line conclusion in the words of the problem addressedby this study. HINT: What would you say to your Sponsor?Type your conclusion bottom-line conclusion in the words ofthe problem here.To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – t test” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.HINT!Objective:Going down the DMAIC road, you and your team are continuing to tryto get a handle on what is causing additional defects in theleveler plates. You are trying to reduce the variation in that process.There are three test sites that are designed to detect both Type A and Type B defects.People have suggested that the number of Type A or B defects detected depends onwhich test site is doing the testing. In other words, one or more of the test sitesmay not be using the same criteria, method, etc. to detect Type A or B defects and thisis causing the defect rate to be reported inconsistently across the three sites.You have been asked to test the defect rates from the three test sites and settle the debate.One way to find out is through the use of the Chi-Square test for independence.Test at 95% confidence.Chi SquareInstructions for you:We highly recommend working through the practice example in yellow belowbefore 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 exampleSome help for you using an practice example:You first need to calculate the expected values. It is best to makea table as step 1. For example, males and females watch variousTV stations. Let’s say that we want to find out if gender is dependentor independent of television station preferences.The practice data follows:WKBW WBENWGRTotalsMales625425141Females445015109Totals10610440250Step 1. Calculate each of the ‘expected values.’ We will dothe 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 = 0.424c. Probability of viewer preferring WKBW AND being maleis 0.564 x 0.424 = 0.239d. Expected number of viewers in this cell is 0.239 x 250 = 59.8etc…a. Probability of viewer being female is 109 / 250 = 0.436b. Probability of viewer preferring WKBW is 106 / 250 = 0.424c. Probability of viewer preferring WKBW AND beingfemale is 0.436 x 0.424 = 0.185d. Expected number of viewers in this cell is 0.185 x 250 = 46.3etc…Repeat this for all six cells. To check your work, the totals(across and down) should add up very close to the (across andand down) totals of the observed values. Here is how yourchart should appear when finished: The ‘expected valuesare in [brackets.]MalesFemalesTotalsWKBWWBENWGRTotals62 [59.8] 54 [58.8] 25 [22.5] 14144 [46.3] 50 [45.3] 15 [17.5] 10910610440250Step 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 = 0.0809For the 2nd value…(54-58.8)2 divided by 58.8 = 0.3918For the 3rd value… (25-22.5)2 divided by 22.5 = 0.2778For the 4th value… (44-46.3)2 divided by 46.3 = 0.1143For the 5th value… (50-45.3)2 divided by 45.3 = 0.4876For the 6th value… (15-17.5)2 divided by 17.5 = 0.3571Step 3. Add those chi-square values and you should get 1.7095This is your calculated chi-square 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 basedupon what level of risk they are willing to live with.Step 5. Determine the Degrees of Freedom (df) for the rows andthe columns. You will need this to find the critical value inthe table in the textbook.df=(number of rows minus 1) multiplied bythe (number of columns minus 1) So, in this particularcase it would be (2-1 multiplied by 3-1) = 2Step 6. Go to the chi-square table in a textbook and determinethe critical value. You already knowthe calculated statistic (1.7095). All you need now is that criticalvalue to see if the calculated statistic is greater than that criticalvalue. If it is greater than the critical value, you can reject thenull. If not, then you fail to reject the null.Data:Data for this deliverable:Site 1Defect Type A8Defect Type B9Excel 2003Site 2810Site 378Excel 2007Please review the week 7 virtual class on chi square tests for more information before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 8 or earlierProject: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? (Yes or No)Manufacturing 2013 LAJChi SquareYour LAST name hereRound all finalresults to 2 decimalplaces.CheckCheckCheckCheckCheckCheckCheck1 or 2CheckYes or NoState your bottom-line conclusion in the words of the problem addressedby this study. HINT: What would you say to your Sponsor?HINT!Type your bottom-line conclusion in the words of the problem here.To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – Chi Square” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.Objective:In an effort to stabilize the process, there has been some discussion about 3 machinesthat appear to be causing variation in the mean part thicknesses (measuredprior to plating). It appears that these 3 machines may be producing parts with different averagematerial thickness even though they are supposed to be producing parts with the same average thickness.It was suggested that a One-Way ANOVA be used to compare the mean thicknessesproduced by these 3 machines. You will be checking for significant differences betweenthe mean material thicknesses produced by these 3 machines. Use a 5% level of significance.Instructions for you:Using the data below construct a one-way ANOVA. To do so, occursin two major steps–the table step, followed by the ANOVA step.Excel 2003Excel 2007Data:Machine 1 Machine 2Machine 30.5460.5730.5730.5260.5920.570.5870.5710.5270.5630.5560.572Some help:Key to terms:ANOVACMdfFMSSSANalysis Of VArianceCorrection for the Meandegrees of freedomF statistic used to compare with the F-table value (aka ‘critical value’)Mean SquareSum of SquaresMake 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 ANOVASumn Sum2/nSum ?X2?X2Machine 10.5460.5260.5870.563HelpHelpHelpHelpMachine 20.5730.5920.5710.556HelpHelpHelpHelpMachine 30.5730.570.5270.572HelpHelpHelpHelpTotalsHelpHelpHelpHelpStep 2. Determine total df.HelpStep 3. Determine df FACTORStep 3. Determine dfFACTORHelp2Step 4. Calc. CM which is: (?X) /n (which is NOT THE SAME AS ?X2 listed above) Step 4. Calc. CM which is:HelpStep 5. Calculate SSTOTAL: ?X2TOTAL – CM = Step 5. Calculate SSTOTAL: ?X2TOTAL – CM =HelpStep 6. Calculate SSFACTOR: SUM2/nTOTAL (from chart above) – CM = Step 6. Calculate SS FACTOR: SUMHelpStep 7. Calculate SS ERROR: SSTOTAL – SSFACTOR = Step 7. Calculate SSERROR: SSTOTAL – SSFACTOR = HelpStep 8. Calculate MSFACTOR: SSFACTOR divided by dfFACTOR = Step 8. Calculate MSFACTOR: SSFACTOR divided by dfHelpStep 9. Calculate dfERROR: The dfTOTAL…subtract from that the df FACTORStep 9.: The dfTOTAL…subtract from that the dfCalculate dfERRORStep 10. Calculate MSERROR: SSERROR divided by dfERROR = Step 10. Calculate MSERROR: SSERROR divided by dfHelpStep 11. Calculate the F statistic: MS FACTOR divided by MSERROR =HelpStep 12. The ANOVA table below should be filled in by now with theexception of the F CRITICAL value.SSdfMSCalc . FANOVAFactorErrorTotalStep 13. Look up the F-table value.HelpStep 14. What is your conclusion?F Crit.Be sure to review the week 8 virtual class for more information on One-Way ANOVA before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 9 or earlierProject:Deliverable:Student last name:Manufacturing 2013 LAJANOVAYour LAST name hereRound your results to 5 decimal places.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)?Will you reject the null? Yes or NoSS-FactorSS-ErrorSS-TotalDF-FactorDF-ErrorDF-TotalMS-FactorMS-ErrorF-CalculatedF-CriticalYes or NoCheckCheckCheckCheckCheckCheckCheckCheckCheckCheckState your bottom-line conclusion in the words of the problem addressedby this study. HINT: What would you say to your Sponsor?HINT!Type your bottom-line conclusion in the words of the problem here.To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – ANOVA” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.Objective:A team member has been saying since day one that there is a correlation betweentemperature and the thickness. Should the team have listened? Construct a scatterdiagram and calculate the correlation coefficient 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 founda smoking gun toward a solution.Data:Data:Temp154153152152151151151151151151151151151151151151150150150150150150150150149149149148148148147147146146145Thickness0.5540.5530.5520.5510.5490.5490.5480.5480.5480.5470.5470.5470.5470.5470.5470.5460.5460.5460.5460.5460.5460.5450.5450.5450.5450.5450.5450.5450.5430.5430.5420.5420.5410.540.538Scatter diagrams in Excel 2003Scatter diagrams in Excel 2007Correlation Coefficient – Excel 2003Correlation Coefficient – Excel 2007Be sure to review the week 9 virtual class on scatter plots for more information before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 12 or earlierDO NOT SUBMIT THE SCATTER DIAGRAM UNLESS YOUR INSTRUCTOR ASKS FOR IT.Project:Manufacturing 2013 LAJDeliverable:Scatter DiagramStudent last name:Your last name hereROUND RESULTS TO3 DECIMAL PLACES.What is the correlation coefficient?Is there strong correlation?HINT!Yes or NoIF there is strong correlation, is it positive or negative?(Answer with positive, negative or N/A)Positive, Negative or N/A?To send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – SCATTER” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.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 leveldefects 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, theteam has reduced it down to five factors they want to include in an experiment. They suspectinteractions, so they conclude a full factorial will be required. They refer to the resolution matrix (found in yourreading materials and in the Fractional Factorial Designs Lecture) and they find they canlearn 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 dothis 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 news.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 this point.)4. Using the resolution matrix found in your online textbook, what is the resolution for the design you’re recommending?5. Based on your new recommendation, what will the confounding pattern be in your results?”I’m lost”Data:FactorDepthTempPressureR.P.M.Time(-)85140850440030(+)1501552500480045I try to enter + or – and it does not work.Trial1234567891011121314151617181920212223242526272829303132Factor 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 ECABDE++++Entering ++or – does++not work+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++Be sure to review the week 9 and 10 virtual classes on DOE for more information before you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 11 or earlierDO NOT SUBMIT THE DESIGNED EXPERIMENT!!Project:Manufacturing 2013 LAJDeliverable:DOE Design ChoiceStudent last name:Your last name here1. 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)+ or – ?III, IV, V or Full?3. Given the teams goals and budget, what isyour recommendation for the final design of Type your SPECIFIC recommendation here and use thecorrect notation for the design you recommend.this experiment? BE SPECIFIC AND USE THECORRECT DESIGN NOTATION AND/ORTERMINOLOGY!!4. What would the new resolution be under yourrecommendation in #3 above? (III, IV, or V) :::5. What will the generic confoundingpattern be for your final design?(NOT the design generators or aliassets!)III, IV, or V?Describe the GENERIC confounding pattern for thisdesign resolution. HINT: We do not want the alias setsor design generators.DO NOT SUBMIT THE DESIGNED EXPERIMENTTo send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – DOE” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.”I’m lost”HINT!HINT!HINT!HINT!Objective:Lovell Levelers just reported that Specific Motors is a satisfied customer. The leveler platequality 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 notcrop up again. The team is one step ahead of her and explained that the thickness of theleveler 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 thecontrol chart by hand, or you may use a charting function in Excel. There are blank forms in theback of your notebook .Control Charts in Excel 2003Control Charts in Excel 20071.2.3.4.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 ideaabout this one””I have no ideaabout this one”Data:Thickness data for XMR control chart0.5510.5461a. Calculate R-bar0.5470.548Self check0.5470.5471b. Calculate the0.538upper control limit0.546for the range0.542″How do I do that?”0.543Self check0.5450.5472 & 3. Calculate the0.543control limits for the0.548individuals0.545″How do I do that?”0.554Self check0.5490.5460.5450.5530.5490.5410.5420.5450.5460.5520.5460.5460.5450.5470.5480.5470.5450.540.545Calculating R-bar in Excel 2003Calculating R-bar in Excel 2007Be sure to review the week 11 virtual class for more information on SPC and measurement discrimination before you submit this!Target Assignment Submission Date – Submit in Week 13 or earlierYOU DO NOT NEED TO SUBMIT THE XmR CHARTProject:Manufacturing 2013 LAJDeliverable:XmR ChartStudent last name:Your last name hereCalculated R-Bar:Upper control limit for the range:Upper control limit for the individuals:Lower control limit for the individuals:Type in R-barType in UCL-RType in UCL-xType in LCL-xIs there adequate discrimination? Explain youranswer: Which chart did you use and exactly howmany strata are there on that chart? How manyshould there be?ROUND YOURFINAL RESULTS TO4 DECIMALPLACES.Type your answer here. Include whichchart you used and how many stratathere are on that chart.Is the Moving Range chart stable? Justify your answer using ALL of the tests for stabilitycovered in the online textbook and virtual class on SPC. NOTE: IF YOU SAY THE CHART ISUNSTABLE, SPECIFY WHICH TEST(S) IT FAILS AND WHERE ON THE CHART IT FAILS BYREFERENCING THE SPECIFIC DATA POINTS THAT FAIL BY NUMBER (NOT VALUE).CheckCheckCheckCheckHelpHelpType your answer here. If you say the chart is unstable, specify which test(s) it fails andwhere on the chart by referencing the specific data point numbers.Is the Individuals chart stable? Justify your answer using ALL of the tests for stabilitycovered in the online textbook and virtual class on SPC. NOTE: IF YOU SAY THE CHART ISUNSTABLE, SPECIFY WHICH TEST(S) IT FAILS AND WHERE ON THE CHART IT FAILS BYREFERENCING THE SPECIFIC DATA POINTS THAT FAIL BY NUMBER (NOT VALUE).HelpType your answer here. If you say the chart is unstable, specify which test(s) it fails andwhere on the chart by referencing the specific data point numbers.Based upon what the control chart is telling you, what would you do next?HelpType your answer here.How to submit an AssignmentTo send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – XmR Chart” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.CheckObjective:So far, so good. The process has been in control for the past four months. Phyllis isn’tas well versed in Six Sigma as the team is, and it is her nature to question everything.So she has asked for a capability study to be performed on the 7 key process factors thataffect leveler 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 youcalculate Pp and Ppk for each of the 7 factors. Is Phyllis going to be happy or is shegoing 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 correctlyAND MAKE ALL OF THECORRECTIONS REQUIRED ON THE PREVIOUS ASSIGNMENTSand 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: Thefirst 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 specificationsare 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 SpecsLower SpecsThickness0.5480.5500.5520.5540.5520.5470.5470.5520.5490.5480.5490.5490.5500.5510.5490.5500.5510.5500.5500.5530.5480.5520.5510.5500.5490.5510.5510.5500.5510.5500.5490.5500.5510.5490.550Time115115115115115115115115115115115115115115115115115115115115115115115115115115115115115115115115115115115Temp Pressure145130014614001461500147150014815001481500148150014914001491800149160015016001501600150160015016001501600150160015016001501600151160015118001511800151140015114001531700149170015217001481700147170015017001511700151180015118001521900152190015419000.125 dim.0.1210.1220.1220.1230.1230.1240.1240.1240.1250.1250.1250.1250.1250.1280.1280.1250.1290.1260.1260.1260.1260.1260.1260.1260.1270.1270.1270.1270.1270.1270.1270.1280.1280.1290.1300.23 dim.0.2290.2300.2300.2310.2310.2310.2310.2310.2310.2310.2310.2310.2300.2300.2340.2330.2350.2290.2340.2320.2320.2320.2320.2320.2320.2320.2320.2320.2330.2330.2330.2330.2340.2340.235R.P.M.44004400440044004450445044504450445044504450445044504500450045004550460046504650465047004700470047004700470047004700470047004750475047504800HBThickness0.56000.5400Time140100Temp1601400.125 dim.0.13500.11500.23 dim.0.24000.2200R.P.M.80002000HB500300Press2600900400402404404406406406408408408410410410410410411410410409409410412412412412412412412412414414414414416418Be sure to review the week 3 and 12 virtual classes for more information on judging normality and Process Capability & Performancebefore you submit this!How to submit an AssignmentTarget Assignment Submission Date – Submit in Week 14 or earlierYOU DO NOT NEED TO CREATE CONTROL CHARTS TO COMPLETE THIS ASSIGNMENT!!DO NOT SEND THE ACTUAL HISTOGRAMS UNLESS YOUR INSTRUCTOR ASKS YOU TO.Project:Manufacturing 2013 LAJDeliverable:Pp PpkStudent last name:Your LAST name hereINSTRUCTIONS: (1) IF YOU SAY THE DISTRIBUTION IS NOT APPROXIMATELY NORMAL, GIVE THECORRECT NAME FOR THE PATTERN YOU SEE IN YOUR HISTOGRAM. (2) BASE YOUR DECISION ONACCEPTABILITY ON THE ASSUMPTIONS AND CRITERIA FOR Pp and Ppk DISCUSSED IN THE RECORDEDLECTURES AND VIRTUAL CLASSES ON CAPABILITY. YOU DO NOT NEED TO CREATE CONTROLHINT!CHARTS FOR THIS ASSIGNMENT!!ThicknessTimeTempPressure0.125 dim0.230 dimR.P.M.HB tempPpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?PpPpkApproximately Normal?If not normal, what is the shape?Acceptable?Why is it acceptable or not acceptable?CheckYes or NoYes or NoROUND YOUR Pp and PpkFINAL RESULTS TO 2DECIMAL PLACES.CheckYes or NoYes or NoYes or NoYes or NoIF YOU ANSWER “NO” TOCheckANY QUESTIONS ABOUTNORMALITY, DESCRIBETHE SHAPE YOU SEE USINGTHE CORRECTTERMINOLOGY.CheckYes or NoYes or NoHINT: REMEMBER THATTWO ASSUMPTIONSMUST BE MET IN ORDER TOUSE THESE FORMULASCheckCORRECTLY.Yes or NoYes or NoCheckYes or NoYes or NoCheckYes or NoYes or NoCheckYes or NoYes or NoTo send each assignment to your instructor:Click-and-hold the LEFT mouse button at the TOP-LEFT corner of thepeach-colored box, then while holding down on that button, drag tothe LOWER-RIGHT corner of the box. This will highlight the entirepeach-colored box. Release the mouse button. Do a CTRL-C. This willcopy what has been highlighted.Go to your Villanova website and follow this sequence:1. COMMUNICATE2. CLASS ROSTER3. Click on your instructor’s email envelope icon4. Type “Check My Work – Pp, Ppk” in the SUBJECT box.5. Click once inside of the message box6. 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 ofalignment. 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% correctis 7 days prior to the end of the course.