The bolded name(s) within the question refer to the Excel sheet that needs to be used.
Mica Thickness Review the data from Ott on Mica Thickness measurements. The data shows samples of five from 40 batches of shipments. a) Show a histogram of the population. b) Show a histogram of sample averages. c) Discuss the data arrangement, what type variation has been considered? d) Approximate that . Funnel Experiment Considering the funnel experiment literature and class experiment, Funnel data shows the results of such experiment. Discuss the four rules using XmR chart of each rule and related variation. It is helpful to produce the charts in sequence (side by side) to observe the impact of rules. Regression Control Chart A classic paper by Mandel studied mail processing at the United States postal service (Mandel). The data represents pieces of mail processed (independent variable) and labor hours (dependent variable) required. Develop a regression control chart and discuss your findings. If a location uses 162 million pieces of mail, how would you explain labor hours to the management? Understanding Variation and Performance Appraisal The table below shows the quarterly production for ten marketing staff at a company. At the end of each year the company first ranks the staff and based on the ranking awards cash bonuses. Tap into understanding Variation (Wheeler, Tribus, etc.) to support your discussion. a) Develop a control chart of total production and discuss your findings. b) How would you rank the staff and assign cash bonuses? Staff QI QII QIII QIV Total FH 12 10 10 9 41 PF 12 12 10 10 44 HM 13 7 10 10 40 PM 10 10 11 7 38 GS 8 9 11 12 40 MC 9 9 12 10 40 JG 11 9 10 11 41 SW 8 10 11 13 42 NY 12 11 8 6 37 SF 9 11 13 10 43 Occupational Asthma In a research study, workers suspected of having asthma are asked to record their lung function at work and away from work for a period of at least two weeks. The aim is to determine if the worker’s asthma is work – related. The lung function test used in this research is peak expiratory flow (PEF) which is expressed in milliliter per second (mL/s). A worker who was suspected of having occupational asthma was asked to record his daily PEF four time daily (n) for a period of at least two weeks (14 days) while away from work (vacation). Here the sample size (n) is 4 and there are 14 subgroups. The data set is shown below. a) Discuss the data arrangement, that is, group and subgroup, type of variation? b) Considering our class discussion, review of Wheeler Chapter 3, Papers on understanding variation, develop a control chart and discuss your findings. Away Day Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 7:00-8:00 400 420 380 380 400 430 400 450 420 420 430 450 420 420 11:00-13:00 430 430 450 410 400 440 490 450 420 470 410 440 440 470 16:00-17:00 420 425 440 420 410 430 440 410 440 440 455 440 460 450 21:00-22:00 435 430 430 460 410 410 440 420 410 430 430 420 420 425 The worker returns to work and continues monitoring his lung function. The data set for the first 5 days after returning to work is shown below. Work Time 1 2 3 4 5 7:00-8:00 285 350 340 350 350 11:00-13:00 400 200 400 230 230 16:00-17:00 310 290 400 360 240 21:00-22:00 350 410 400 250 250 c) Plot the daily average and range for these five work days on away period control chart. Discuss your observations now. What is the state of the worker’s asthma at work? Food Processing A food processing operation consists of mixing ingredients, forming and cooking. Figure below shows the cooking process where the formed material travels through a cooking oven on a conveyer belt. The raw material is subject to shrinkage due to the cooking process. The specification limits for shrinkage is between 5% and 9%. There are two machines operating two shifts daily. A technician selects samples before and after cooking process and calculates percent shrinkage. Table below shows the data set for several cooked samples taken from the upper and lower machines. The weight is in pounds. Using quality control chart to evaluate data homogeneity, compare lower vs. upper machine. Is the supervisor’s claim that both machines are the same correct? Discuss. Upper Cooked Lower Cooked 1.020 1.024 1.034 1.018 1.034 0.974 1.016 1.032 1.028 1.034 1.012 1.012 0.998 0.998 1.016 1.000 1.018 1.016 1.018 1.020 1.028 0.974 Understanding Variation – Sales Data In a management meeting attended by senior managers of your company, you will hear from the CEO about flat sales in the last several months. That, unless the company reaches the target goal of $4 million sales in the next couple of months, the bonuses will be reduced, possibly reduce the sales budget and may even resort to sales force reduction. To support her decision, the CEO presents the sales data for the last several months as shown below. Month Sales ($) Sep 2,786,210 Oct 1,886,760 Nov 1,506,500 Dec 1,618,430 Jan 1,531,590 Feb 1,118,880 Mar 1,279,610 Apr 2,122,580 May 2,559,010 Jun 2,615,360 Jul 1,459,910 Aug 1,346,550 Sep 2,019,880 Oct 2,678,670 Nov 2,182,690 Dec 2,121,660 Jan 1,532,330 Feb 1,865,280 Mar 1,884,350 Apr 1,674,640 May 1,928,160 Jun 2,359,180 a) Develop an XmR chart, educate the CEO on understanding variation/ b) How would you suggest to use the control chart for forecasting purpose? c) What are your suggestions about the demand for $4M in sales? How can this be achieved? Please be sure to have a substantive discussion. 1 Mica Thickness Batch Sample12345678910111213141516171819202122232425262728293031323334353637383940 18.012.512.514.013.512.014.012.010.014.58.013.015.09.512.515.013.512.011.011.013.010.011.08.510.57.010.012.012.010.513.08.010.09.013.015.010.013.511.57.5 210.010.58.015.09.013.011.010.014.011.011.511.510.012.59.013.011.516.010.59.013.510.510.57.58.012.510.514.512.08.011.07.07.515.513.015.511.510.59.59.5 312.010.513.511.512.015.514.07.511.511.09.514.510.05.013.57.511.09.010.514.011.08.011.510.08.510.512.010.511.010.510.57.010.012.59.510.010.012.08.510.0 412.012.015.513.512.517.08.011.011.517.09.513.59.08.012.512.09.510.07.510.514.513.08.511.013.58.511.011.010.012.59.59.512.57.09.512.010.010.08.512.0 511.59.09.511.512.514.011.513.013.015.010.512.514.513.012.512.013.08.510.510.512.07.08.013.513.06.010.010.012.014.511.511.58.010.514.58.510.012.512.511.0 Mandel PiecesManhours 154569 157572 157564 160605 161570 164599 164573 168645 169599 172650 175670 179640 179665 180675 180637 183645 184671 184656 184655 186645 188667 191700 193710 Occupational Asthma Away Day Time1234567891011121314 7:00-8:00400420380380400430400450420420430450420420 11:00-13:00430430450410400440490450420470410440440470 16:00-17:00420425440420410430440410440440455440460450 21:00-22:00435430430460410410440420410430430420420425 Work Time12345 7:00-8:00285350340350350 11:00-13:00400200400230230 16:00-17:00310290400360240 21:00-22:00350410400250250 Performance Appraisal StaffQIQIIQIIIQIVTotal FH121010941 PF1212101044 HM137101040 PM101011738 GS89111240 MC99121040 JG119101141 SW810111342 NY12118637 SF911131043 Food Processing Upper CookedLower Cooked 1.021.024 1.0341.018 1.0340.974 1.0161.032 1.0281.034 1.0121.012 0.9980.998 1.0161 1.0181.016 1.0181.02 1.0280.974 Funnel DropRule 1Rule 2Rule 3Rule 4 151494648 250535447 352484850 450505251 550494750 650535347 750454648 849525746 952504346 1047505549 1151484449 1252545351 1352475153 1451494855 1548485560 1650514458 1748475358 1852555156 1951475057 2048515154 2149494856 2250515354 2348494453 2451525856 2549504455