EXAMPLE Introduction Figure 1 Assumptions Analysis, results and findings Recommended corrective actions and improvements discussed Correlation, if any, between defects and x-bar and/or delta charts discussed (Information above will come from the questions asked in numbers 2 and 3.) Conclusion/Summary I went ahead and attached the pareto chart. Project Assignment 1. Read Case Study 10.2: Precise Molded Products, Inc. (Sower, pp. 274-278) below. The case study data with some of my comments and corrections is reproduced on the following pages for your convenience. Construct all charts and explain what is occurring in each chart. Answer all questions below. All charts have been filled in except for the pareto chart. 2. Construct and analyze x-bar and R charts for the length and width dimensions using data from exhibit A. The R charts should be analyzed first. Is the process out of control? If so, identify possible causes (hint: consider work shifts, whether different caliper sets are used, effect of temperature, repeatability and reliability of the caliper sets, etc.) and recommend corrective actions and improvements. You will need to state your assumptions. Also, suggest target values for the length and the width and construct and analyze a delta chart. Does the delta chart provide any additional information to support your corrective actions and improvements? 3. Construct and analyze a p-chart using data from exhibit B. Does the p-chart indicate the process is in or out of control? Support your answer. In addition, perform a Pareto analysis using exhibit B data and identify what is causing the majority of the quality issues. What if any correlation is there between defects such as inclusions, discoloration, warping, flash, etc. and the variations seen in the x-bar and/or delta charts? 4. The paper should be at least ten pages with double spacing. Please be sure to follow all APA requirements. A rubric for grading the project is below. Attached are all charts except the Pareto chart/analysis. Topic Area Introduction Description of Achievement Grasp of the issue demonstrated States what will be covered Chart Construction and Analysis Recommendation Summary, Structure, and Organization All charts constructed as directed Assumptions stated Analysis results and findings discussed Recommended corrective actions and improvements discussed Correlation, if any, between defects and x-bar and/or delta charts discussed Logical development of ideas Appropriate order; grammar, parallel structures, punctuation spelling Possible Points 5 45 20 30 Points Awarded APA formatting, proper citation and references Saint Leo core value of excellence and integrity is addressed Total Number of Points 100 Case Study 10.2 PRECISE MOLDED PRODUCTS, INC. 2003 Victor E. Sower, Ph.D., C.Q.E. You were just finishing an important report when, as you turned from your computer to your desk, you accidentally knocked over your half-full cup of coffee. As you raced to mop it up before your papers were ruined, Bob Thomas walked into your office. \"Did I catch you at a bad time?\" he asked. \"No, Bob,\" you lied. \"I'm just feeling a little stupid that I knocked over my coffee cup. I just finished a report about how everyone needs to be more careful to avoid accidents, and then I create a small accident myself while putting the report on my desk.\" Smiling, Bob says \"Well, I guess you didn't learn everything at State University. I thought they would have a class on avoiding spills.\" You both laugh. \"They only teach that to the basketball players,\" you reply. \"By the way, have you noticed how well they are doing this year? I'll have to take you to a game sometime.\" Bob only nodssomething is obviously on his mind. Bob is the Quality Manager at Precise Molded Products (PMP). In truth he is 25% of the entire Quality Department. He has an assistant and two inspectorsone on the day shift and one on the evening shift in his department. \"I'd like you to look at something,\" Bob begins while opening a folder. \"We just set up a new molding process to make the F-106B computer housing. Engineering and Maintenance have made sure that the machinery and process are in good shape. I double checked the quality of the raw materials and Gloria, the Production Manager, assigned her best operator to the job. I waited until the process stabilized then had my technicians collect data from the process during its two days of operation.\" [He hands you Exhibit A] \"We have two critical parameters we must maintain for our customer. These are Part Length and Part Width (see attached part drawing). We make these measurements with a set of calipers that are accurate to 0.001 inch. My technicians collect 4 parts each hour, measure both dimensions, and record the values in Exhibit A.\" \"Each part is also inspected by the operator for conformance to the other dimensional and cosmetic specifications. The operator records the number of rejected parts and the reason for the rejection on Exhibit B.\" \"Here's where I need your help. I need a way to analyze these data to determine how well the process is performing. In addition, I would like a way to monitor the process to be sure it continues to work right in the future. I am particularly concerned about the rise in the number of rejects. We have had many days where the number of rejects is low and then some when it is high. I have been spending a lot of time trying to find out what we are doing differently on the good and bad daysso far with no luck.\" \"I know that they have a great quality management course at State University that you completed just before we hired you last fall. We talked about that course during your interview trip and I was very impressed by how much you knew about my field, quality. Can you take these data and perform some statistical mumbo jumbo and give me a report that makes sense?\" \"No problem,\" you reply. \"My professor told me to keep my quality management book and I did. Let me spend a little time with it and your data and I think I can come up with something that will meet your needs.\" \"Thanks,\" replies Bob. \"I know that we hired you as a management trainee and this falls outside your normal responsibility, but your work since you joined the company has really impressed a lot of people. Just between the two of us, Bill Otis, the Plant Manager, doesn't put a lot of emphasis on the Quality Department. It sometimes seems that he thinks my job is to stop Production from shipping product on time. Anyway, I think if you produce the report he will be more likely to pay attention to it than if I did it myself. And to be honest, I never really understood that statistics stuff. My girlfriend helped me get through that course in college 10 years ago. I took my C- and ran never thinking I would ever actually need to use statistics. I have spent the 5 years that I have had this job trying to teach myself what I should have learned in that course. I wish I could go back in time. I would tell my younger self that you never know what course will be essential to your success. It pays to do your best in all of them.\" After Bob departs and you get your desk cleaned up, you begin the search for your quality management text. You find it in a box you haven't gotten around to unpacking yet, open it up and begin reading. \"Yeah, I remember this stuff. I can do this,\" you think to yourself. Exhibit A Precise Molded Products Date Time 1 2 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 Length Part 1 Part 2 20.10 20.00 20.10 19.94 20.08 20.06 20.11 20.06 19.88 20.03 19.88 19.87 20.01 19.92 19.96 20.05 19.95 19.99 20.09 20.00 20.08 20.00 20.05 19.97 20.11 20.06 20.09 20.08 20.10 20.03 20.09 19.94 20.01 20.01 19.97 19.97 20.01 20.00 20.02 20.09 20.10 19.98 20.11 20.06 20.13 20.06 Part 3 20.03 19.98 19.99 20.02 20.00 19.95 20.09 20.08 20.02 19.98 19.98 19.96 19.96 19.97 19.90 19.96 20.06 20.08 20.06 19.99 19.99 20.07 20.00 Part 4 20.05 20.09 20.03 20.01 20.12 20.05 20.00 20.00 19.96 19.92 19.96 19.99 19.89 19.97 19.90 20.00 20.07 20.06 20.05 20.00 20.05 20.06 20.09 Width Notes Part 1 Part 2 Part 3 Part 4 12.10 12.14 12.10 12.04 12.07 12.10 12.11 12.15 12.14 12.10 12.06 12.10 12.05 12.09 12.15 12.12 12.10 12.13 12.07 12.15 12.15 12.09 12.13 12.14 12.14 12.06 12.08 12.10 12.10 12.00 12.06 12.15 12.19 12.08 12.13 12.14 12.00 12.02 12.04 12.09 12.02 11.98 12.08 12.09 12.02 12.00 12.05 12.10 12.05 12.12 12.03 12.05 12.14 12.08 12.05 12.09 12.08 12.06 12.14 12.11 12.08 12.16 12.05 12.07 12.07 12.10 12.11 12.15 12.05 12.09 12.15 12.12 12.14 12.06 12.08 12.10 12.07 12.10 12.11 12.15 12.10 12.13 12.07 12.15 12.14 12.06 12.08 12.10 12.10 12.13 12.07 12.15 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 20.04 20.02 20.00 19.98 20.05 20.00 19.90 19.88 20.00 20.13 20.05 19.89 20.09 19.99 19.90 19.99 19.99 19.89 20.07 19.94 20.08 19.91 19.95 19.98 19.97 20.01 19.96 20.08 19.99 20.00 20.02 20.00 19.92 19.97 20.02 19.95 12.15 12.02 12.14 12.08 12.08 12.02 12.14 12.00 12.02 12.09 12.00 12.08 12.16 12.06 12.00 12.08 12.02 11.98 12.13 12.05 12.05 12.05 12.14 12.05 12.05 12.04 12.08 12.14 12.10 12.09 12.07 12.11 12.10 12.09 12.09 12.09 Exhibit B Precise Molded Products Date 1 Time 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 2 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Total Sample Rejected Size Parts 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 5 6 2 3 9 5 4 6 2 4 3 4 8 7 5 4 1 5 7 3 3 7 2 5 6 7 5 8 9 4 7 6 Sh. Shot Inclus. Discol. 1 1 2 1 3 1 1 1 2 1 1 2 1 1 CAUSES Warp. Stain Scuff Burr Flash 1 2 1 2 3 1 2 1 1 2 1 1 2 1 1 2 1 2 2 1 1 2 1 2 1 1 1 1 1 1 1 2 1 2 1 2 2 1 1 1 1 2 1 1 2 2 1 3 2 2 1 2 4 3 2 3 6 2 1 2 1 1 2 2 1 1 3 3 4 2 3 2 3 1 1 1 2 1 1 2 3 3 1 \fn A2 A3 c4 B3 B4 D3 D4 d2 2 3 4 5 6 7 1.8800 2.6590 0.7979 0.0000 3.2670 0.0000 3.2670 1.1280 1.0230 1.9510 0.8862 0.0000 2.5680 0.0000 2.5750 1.6930 0.7290 1.6280 0.9213 0.0000 2.2660 0.0000 2.2820 2.0590 0.5770 1.4270 0.9400 0.0000 2.0890 0.0000 2.1150 2.3260 0.4830 1.2870 0.9515 0.0300 1.9700 0.0000 2.0040 2.5340 8 0.4190 0.3730 1.1820 1.0990 0.9594 0.9650 0.1180 0.1850 1.8820 1.8150 0.0760 0.1360 1.9240 1.8640 2.7040 2.8470 9 0.3370 1.0320 0.9693 0.2390 1.7610 0.1840 1.8160 2.9700 10 0.3080 0.9750 0.9727 0.2S4 1.7160 0.2230 1.7770 3.0780 11 0.2850 0.9270 0.9754 0.3210 1.6790 0.2560 1.7440 3.1730 12 0.2660 0.8860 0.9776 0.3540 1.6460 0.2840 1.7160 3.2580 13 0.2490 0.8500 0.9794 0.3820 1.6180 0.3080 1.6920 3.3360 14 0.2350 0.8170 0.9810 0.4060 1.5940 0.3290 1.6710 3.4070 15 0.2230 0.7890 0.9823 0.4280 1.5720 0.3480 1.6520 3.4720 16 0.2120 0.7630 0.9835 0.4480 1.5520 0,364 1.6360 3.5320 17 0.2030 0.7390 0.9845 0.4660 1.5340 0.3790 1.6210 3.5880 18 0.1940 0.7180 0.9854 0.4820 1.5180 0.3920 1.6080 3.6400 19 0.1870 0.6980 0.9862 0.4970 1.5030 0.4040 1.5960 3.6890 20 0.1800 0.6800 0.9869 0.5100 1.4900 0.4140 1.5860 3.7350 21 0.1730 0.6630 0.9876 0.5230 1.4770 0.4250 1.5750 3.7780 X-bar x CL A2 0.729 UCL LCL 20.09611 19.92342 R CL D4 2.282 UCL 0.270274 20.0098 R-bar 0.118 D3 0 LCL 0 0.300 R ch art UC L LCL CL 0.250 0.200 0.150 0.100 0.050 0.000 0 5 10 15 20 25 30 35 20.1500 20.1000 Xbar UC L LCL CL 20.0500 20.0000 19.9500 19.9000 19.8500 19.8000 0 5 10 15 20 25 30 35 Samples (k) 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 1 20.100 20.000 20.100 19.940 20.080 20.060 20.110 20.060 19.880 20.030 19.880 19.870 20.010 19.920 19.960 20.050 19.950 19.990 20.090 20.000 20.080 20.000 20.050 20.040 20.020 20.000 19.980 20.050 20.000 19.900 19.880 20.000 Observations (n) 2 3 19.970 20.030 20.110 19.980 20.060 19.990 20.090 20.020 20.080 20.000 20.100 19.950 20.030 20.090 20.090 20.080 19.940 20.020 20.010 19.980 20.010 19.980 19.970 19.960 19.970 19.960 20.010 19.970 20.000 19.900 20.020 19.960 20.090 20.060 20.100 20.080 19.980 20.060 20.110 19.990 20.060 19.990 20.130 20.070 20.060 20.000 20.130 20.070 20.050 19.940 19.890 20.080 20.090 19.910 19.990 19.950 19.900 19.980 19.990 19.970 19.990 20.010 19.890 19.960 n= 4 20.050 20.090 20.030 20.010 20.120 20.050 20.000 20.000 19.960 19.920 19.960 19.990 19.890 19.970 19.900 20.000 20.070 20.060 20.050 20.000 20.050 20.060 20.090 20.080 19.990 20.000 20.020 20.000 19.920 19.970 20.020 19.950 x 20.0375 20.0450 20.0450 20.0150 20.0700 20.0400 20.0575 20.0575 19.9500 19.9850 19.9575 19.9475 19.9575 19.9675 19.9400 20.0075 20.0425 20.0575 20.0450 20.0250 20.0450 20.0650 20.0500 20.0800 20.0000 19.9925 20.0000 19.9975 19.9500 19.9575 19.9750 19.9500 4 Range 0.130 0.130 0.110 0.150 0.120 0.150 0.110 0.090 0.140 0.110 0.130 0.120 0.120 0.090 0.100 0.090 0.140 0.110 0.110 0.120 0.090 0.130 0.090 0.090 0.110 0.190 0.180 0.100 0.100 0.090 0.140 0.110 X-bar x CL A2 0.729 UCL LCL 12.15426 12.02121 R CL D4 2.282 UCL 0.208233 12.0877 R-bar 0.091 D3 0 LCL 0 0.250 R ch art UC L LCL CL 0.200 0.150 0.100 0.050 0.000 0 5 10 15 20 25 30 35 12.2000 Xbar UC L LCL CL 12.1500 12.1000 12.0500 12.0000 11.9500 0 5 10 15 20 25 30 35 Samples (k) 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 1 12.100 12.070 12.140 12.050 12.100 12.150 12.140 12.100 12.190 12.000 12.020 12.020 12.050 12.140 12.080 12.080 12.070 12.050 12.140 12.070 12.100 12.140 12.100 12.150 12.020 12.140 12.080 12.080 12.020 12.140 12.000 12.020 Observations (n) 2 3 12.140 12.100 12.100 12.110 12.100 12.060 12.090 12.150 12.130 12.070 12.090 12.130 12.060 12.080 12.000 12.060 12.080 12.130 12.020 12.040 11.980 12.080 12.000 12.050 12.120 12.030 12.080 12.050 12.060 12.140 12.160 12.050 12.100 12.110 12.090 12.150 12.060 12.080 12.100 12.110 12.130 12.070 12.060 12.080 12.130 12.070 12.090 12.130 12.000 12.050 12.080 12.050 12.160 12.050 12.060 12.140 12.000 12.050 12.080 12.050 12.020 12.040 11.980 12.080 n= 4 12.040 12.150 12.100 12.120 12.150 12.140 12.100 12.150 12.140 12.090 12.090 12.100 12.050 12.090 12.110 12.070 12.150 12.120 12.100 12.150 12.150 12.100 12.150 12.140 12.100 12.090 12.070 12.110 12.100 12.090 12.090 12.090 x 12.0950 12.1075 12.1000 12.1025 12.1125 12.1275 12.0950 12.0775 12.1350 12.0375 12.0425 12.0425 12.0625 12.0900 12.0975 12.0900 12.1075 12.1025 12.0950 12.1075 12.1125 12.0950 12.1125 12.1275 12.0425 12.0900 12.0900 12.0975 12.0425 12.0900 12.0375 12.0425 4 Range 0.100 0.080 0.080 0.100 0.080 0.060 0.080 0.150 0.110 0.090 0.110 0.100 0.090 0.090 0.080 0.110 0.080 0.100 0.080 0.080 0.080 0.080 0.080 0.060 0.100 0.090 0.110 0.080 0.100 0.090 0.090 0.110 delta-bar R-bar CL 0.0000 A2 0.729 UCL LCL 0.076431 -0.076431 R CL D4 2.282 UCL 0.239253 0.105 D3 0 LCL 0 0.300 0.250 R ch art UC L LCL CL 0.200 0.150 0.100 0.050 0.000 0 10 20 30 20 30 40 50 60 70 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 -0.0200 -0.0400 -0.0600 -0.0800 -0.1000 0 10 40 50 60 70 deltabar UCL LCL CL Samples (k) 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 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1 20.100 20.000 20.100 19.940 20.080 20.060 20.110 20.060 19.880 20.030 19.880 19.870 20.010 19.920 19.960 20.050 19.950 19.990 20.090 20.000 20.080 20.000 20.050 20.040 20.020 20.000 19.980 20.050 20.000 19.900 19.880 20.000 12.100 12.070 12.140 12.050 12.100 12.150 12.140 12.100 12.190 12.000 12.020 12.020 Observations (n) 2 3 19.970 20.030 20.110 19.980 20.060 19.990 20.090 20.020 20.080 20.000 20.100 19.950 20.030 20.090 20.090 20.080 19.940 20.020 20.010 19.980 20.010 19.980 19.970 19.960 19.970 19.960 20.010 19.970 20.000 19.900 20.020 19.960 20.090 20.060 20.100 20.080 19.980 20.060 20.110 19.990 20.060 19.990 20.130 20.070 20.060 20.000 20.130 20.070 20.050 19.940 19.890 20.080 20.090 19.910 19.990 19.950 19.900 19.980 19.990 19.970 19.990 20.010 19.890 19.960 12.140 12.100 12.100 12.110 12.100 12.060 12.090 12.150 12.130 12.070 12.090 12.130 12.060 12.080 12.000 12.060 12.080 12.130 12.020 12.040 11.980 12.080 12.000 12.050 4 20.050 20.090 20.030 20.010 20.120 20.050 20.000 20.000 19.960 19.920 19.960 19.990 19.890 19.970 19.900 20.000 20.070 20.060 20.050 20.000 20.050 20.060 20.090 20.080 19.990 20.000 20.020 20.000 19.920 19.970 20.020 19.950 12.040 12.150 12.100 12.120 12.150 12.140 12.100 12.150 12.140 12.090 12.090 12.100 Nominal Value 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 Samples (k) 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 33 34 35 36 37 38 39 40 41 42 43 44 1 0.09 -0.01 0.09 -0.07 0.07 0.05 0.10 0.05 -0.13 0.02 -0.13 -0.14 0.00 -0.09 -0.05 0.04 -0.06 -0.02 0.08 -0.01 0.07 -0.01 0.04 0.03 0.01 -0.01 -0.03 0.04 -0.01 -0.11 -0.13 -0.01 0.01 -0.02 0.05 -0.04 0.01 0.06 0.05 0.01 0.10 -0.09 -0.07 -0.07 Delta Observations (n) 2 -0.04 0.10 0.05 0.08 0.07 0.09 0.02 0.08 -0.07 0.00 0.00 -0.04 -0.04 0.00 -0.01 0.01 0.08 0.09 -0.03 0.10 0.05 0.12 0.05 0.12 0.04 -0.12 0.08 -0.02 -0.11 -0.02 -0.02 -0.12 0.05 0.01 0.01 0.00 0.04 0.00 -0.03 -0.09 -0.01 -0.07 -0.11 -0.09 12.050 12.140 12.080 12.080 12.070 12.050 12.140 12.070 12.100 12.140 12.100 12.150 12.020 12.140 12.080 12.080 12.020 12.140 12.000 12.020 12.120 12.080 12.060 12.160 12.100 12.090 12.060 12.100 12.130 12.060 12.130 12.090 12.000 12.080 12.160 12.060 12.000 12.080 12.020 11.980 12.030 12.050 12.140 12.050 12.110 12.150 12.080 12.110 12.070 12.080 12.070 12.130 12.050 12.050 12.050 12.140 12.050 12.050 12.040 12.080 12.050 12.090 12.110 12.070 12.150 12.120 12.100 12.150 12.150 12.100 12.150 12.140 12.100 12.090 12.070 12.110 12.100 12.090 12.090 12.090 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 -0.04 0.05 -0.01 -0.01 -0.02 -0.04 0.05 -0.02 0.01 0.05 0.01 0.06 -0.07 0.05 -0.01 -0.01 -0.07 0.05 -0.09 -0.07 0.03 -0.01 -0.03 0.07 0.01 0.00 -0.03 0.01 0.04 -0.03 0.04 0.00 -0.09 -0.01 0.07 -0.03 -0.09 -0.01 -0.07 -0.11 elta Observations (n) 3 0.02 -0.03 -0.02 0.01 -0.01 -0.06 0.08 0.07 0.01 -0.03 -0.03 -0.05 -0.05 -0.04 -0.11 -0.05 0.05 0.07 0.05 -0.02 -0.02 0.06 -0.01 0.06 -0.07 0.07 -0.10 -0.06 -0.03 -0.04 0.00 -0.05 0.01 0.02 -0.03 0.06 -0.02 0.04 -0.01 -0.03 0.04 -0.05 -0.01 -0.04 4 0.04 0.08 0.02 0.00 0.11 0.04 -0.01 -0.01 -0.05 -0.09 -0.05 -0.02 -0.12 -0.04 -0.11 -0.01 0.06 0.05 0.04 -0.01 0.04 0.05 0.08 0.07 -0.02 -0.01 0.01 -0.01 -0.09 -0.04 0.01 -0.06 -0.05 0.06 0.01 0.03 0.06 0.05 0.01 0.06 0.05 0.00 0.00 0.01 n= delta bar 0.0277 0.0352 0.0352 0.0052 0.0602 0.0302 0.0477 0.0477 -0.0598 -0.0248 -0.0523 -0.0623 -0.0523 -0.0423 -0.0698 -0.0023 0.0327 0.0477 0.0352 0.0152 0.0352 0.0552 0.0402 0.0702 -0.0098 -0.0173 -0.0098 -0.0123 -0.0598 -0.0523 -0.0348 -0.0598 0.0073 0.0198 0.0123 0.0148 0.0248 0.0398 0.0073 -0.0102 0.0473 -0.0502 -0.0452 -0.0452 4 Range 0.130 0.130 0.110 0.150 0.120 0.150 0.110 0.090 0.140 0.110 0.130 0.120 0.120 0.090 0.100 0.090 0.140 0.110 0.110 0.120 0.090 0.130 0.090 0.090 0.110 0.190 0.180 0.100 0.100 0.090 0.140 0.110 0.100 0.080 0.080 0.100 0.080 0.060 0.080 0.150 0.110 0.090 0.110 0.100 -0.06 -0.04 0.05 -0.04 0.02 0.06 -0.01 0.02 -0.02 -0.01 -0.02 0.04 -0.04 -0.04 -0.04 0.05 -0.04 -0.04 -0.05 -0.01 -0.04 0.00 0.02 -0.02 0.06 0.03 0.01 0.06 0.06 0.01 0.06 0.05 0.01 0.00 -0.02 0.02 0.01 0.00 0.00 0.00 -0.0252 0.0023 0.0098 0.0023 0.0198 0.0148 0.0073 0.0198 0.0248 0.0073 0.0248 0.0398 -0.0452 0.0023 0.0023 0.0098 -0.0452 0.0023 -0.0502 -0.0452 0.090 0.090 0.080 0.110 0.080 0.100 0.080 0.080 0.080 0.080 0.080 0.060 0.100 0.090 0.110 0.080 0.100 0.090 0.090 0.110 7.00% 6.00% p 5.00% UCL LCL use 4.00% CL 3.00% 2.00% 1.00% 0.00% 1 4 7 10 13 16 19 22 25 28 31 Samples (k) 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 No. defective 5 6 2 3 9 5 4 6 2 4 3 4 8 7 5 4 1 5 7 3 3 7 2 5 6 7 5 8 9 4 7 6 * p-bar = (sum of No. defective)/(sum of observations) Observ. (n) p UCL LCL calc 200 2.50% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 200 1.00% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 4.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 200 1.00% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 4.00% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 0.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 1.00% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 4.00% 0.058633 -0.008008 200 4.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 * p-bar LCL use 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CL 2.53% EXAMPLE Introduction Figure 1 Assumptions Analysis, results and findings Recommended corrective actions and improvements discussed Correlation, if any, between defects and x-bar and/or delta charts discussed (Information above will come from the questions asked in numbers 2 and 3.) Conclusion/Summary I went ahead and attached the pareto chart. Project Assignment 1. Read Case Study 10.2: Precise Molded Products, Inc. (Sower, pp. 274-278) below. The case study data with some of my comments and corrections is reproduced on the following pages for your convenience. Construct all charts and explain what is occurring in each chart. Answer all questions below. All charts have been filled in except for the pareto chart. 2. Construct and analyze x-bar and R charts for the length and width dimensions using data from exhibit A. The R charts should be analyzed first. Is the process out of control? If so, identify possible causes (hint: consider work shifts, whether different caliper sets are used, effect of temperature, repeatability and reliability of the caliper sets, etc.) and recommend corrective actions and improvements. You will need to state your assumptions. Also, suggest target values for the length and the width and construct and analyze a delta chart. Does the delta chart provide any additional information to support your corrective actions and improvements? 3. Construct and analyze a p-chart using data from exhibit B. Does the p-chart indicate the process is in or out of control? Support your answer. In addition, perform a Pareto analysis using exhibit B data and identify what is causing the majority of the quality issues. What if any correlation is there between defects such as inclusions, discoloration, warping, flash, etc. and the variations seen in the x-bar and/or delta charts? 4. The paper should be at least ten pages with double spacing. Please be sure to follow all APA requirements. A rubric for grading the project is below. Attached are all charts except the Pareto chart/analysis. Topic Area Introduction Description of Achievement Grasp of the issue demonstrated States what will be covered Chart Construction and Analysis Recommendation Summary, Structure, and Organization All charts constructed as directed Assumptions stated Analysis results and findings discussed Recommended corrective actions and improvements discussed Correlation, if any, between defects and x-bar and/or delta charts discussed Logical development of ideas Appropriate order; grammar, parallel structures, punctuation spelling Possible Points 5 45 20 30 Points Awarded APA formatting, proper citation and references Saint Leo core value of excellence and integrity is addressed Total Number of Points 100 Case Study 10.2 PRECISE MOLDED PRODUCTS, INC. 2003 Victor E. Sower, Ph.D., C.Q.E. You were just finishing an important report when, as you turned from your computer to your desk, you accidentally knocked over your half-full cup of coffee. As you raced to mop it up before your papers were ruined, Bob Thomas walked into your office. \"Did I catch you at a bad time?\" he asked. \"No, Bob,\" you lied. \"I'm just feeling a little stupid that I knocked over my coffee cup. I just finished a report about how everyone needs to be more careful to avoid accidents, and then I create a small accident myself while putting the report on my desk.\" Smiling, Bob says \"Well, I guess you didn't learn everything at State University. I thought they would have a class on avoiding spills.\" You both laugh. \"They only teach that to the basketball players,\" you reply. \"By the way, have you noticed how well they are doing this year? I'll have to take you to a game sometime.\" Bob only nodssomething is obviously on his mind. Bob is the Quality Manager at Precise Molded Products (PMP). In truth he is 25% of the entire Quality Department. He has an assistant and two inspectorsone on the day shift and one on the evening shift in his department. \"I'd like you to look at something,\" Bob begins while opening a folder. \"We just set up a new molding process to make the F-106B computer housing. Engineering and Maintenance have made sure that the machinery and process are in good shape. I double checked the quality of the raw materials and Gloria, the Production Manager, assigned her best operator to the job. I waited until the process stabilized then had my technicians collect data from the process during its two days of operation.\" [He hands you Exhibit A] \"We have two critical parameters we must maintain for our customer. These are Part Length and Part Width (see attached part drawing). We make these measurements with a set of calipers that are accurate to 0.001 inch. My technicians collect 4 parts each hour, measure both dimensions, and record the values in Exhibit A.\" \"Each part is also inspected by the operator for conformance to the other dimensional and cosmetic specifications. The operator records the number of rejected parts and the reason for the rejection on Exhibit B.\" \"Here's where I need your help. I need a way to analyze these data to determine how well the process is performing. In addition, I would like a way to monitor the process to be sure it continues to work right in the future. I am particularly concerned about the rise in the number of rejects. We have had many days where the number of rejects is low and then some when it is high. I have been spending a lot of time trying to find out what we are doing differently on the good and bad daysso far with no luck.\" \"I know that they have a great quality management course at State University that you completed just before we hired you last fall. We talked about that course during your interview trip and I was very impressed by how much you knew about my field, quality. Can you take these data and perform some statistical mumbo jumbo and give me a report that makes sense?\" \"No problem,\" you reply. \"My professor told me to keep my quality management book and I did. Let me spend a little time with it and your data and I think I can come up with something that will meet your needs.\" \"Thanks,\" replies Bob. \"I know that we hired you as a management trainee and this falls outside your normal responsibility, but your work since you joined the company has really impressed a lot of people. Just between the two of us, Bill Otis, the Plant Manager, doesn't put a lot of emphasis on the Quality Department. It sometimes seems that he thinks my job is to stop Production from shipping product on time. Anyway, I think if you produce the report he will be more likely to pay attention to it than if I did it myself. And to be honest, I never really understood that statistics stuff. My girlfriend helped me get through that course in college 10 years ago. I took my C- and ran never thinking I would ever actually need to use statistics. I have spent the 5 years that I have had this job trying to teach myself what I should have learned in that course. I wish I could go back in time. I would tell my younger self that you never know what course will be essential to your success. It pays to do your best in all of them.\" After Bob departs and you get your desk cleaned up, you begin the search for your quality management text. You find it in a box you haven't gotten around to unpacking yet, open it up and begin reading. \"Yeah, I remember this stuff. I can do this,\" you think to yourself. Exhibit A Precise Molded Products Date Time 1 2 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 Length Part 1 Part 2 20.10 20.00 20.10 19.94 20.08 20.06 20.11 20.06 19.88 20.03 19.88 19.87 20.01 19.92 19.96 20.05 19.95 19.99 20.09 20.00 20.08 20.00 20.05 19.97 20.11 20.06 20.09 20.08 20.10 20.03 20.09 19.94 20.01 20.01 19.97 19.97 20.01 20.00 20.02 20.09 20.10 19.98 20.11 20.06 20.13 20.06 Part 3 20.03 19.98 19.99 20.02 20.00 19.95 20.09 20.08 20.02 19.98 19.98 19.96 19.96 19.97 19.90 19.96 20.06 20.08 20.06 19.99 19.99 20.07 20.00 Part 4 20.05 20.09 20.03 20.01 20.12 20.05 20.00 20.00 19.96 19.92 19.96 19.99 19.89 19.97 19.90 20.00 20.07 20.06 20.05 20.00 20.05 20.06 20.09 Width Notes Part 1 Part 2 Part 3 Part 4 12.10 12.14 12.10 12.04 12.07 12.10 12.11 12.15 12.14 12.10 12.06 12.10 12.05 12.09 12.15 12.12 12.10 12.13 12.07 12.15 12.15 12.09 12.13 12.14 12.14 12.06 12.08 12.10 12.10 12.00 12.06 12.15 12.19 12.08 12.13 12.14 12.00 12.02 12.04 12.09 12.02 11.98 12.08 12.09 12.02 12.00 12.05 12.10 12.05 12.12 12.03 12.05 12.14 12.08 12.05 12.09 12.08 12.06 12.14 12.11 12.08 12.16 12.05 12.07 12.07 12.10 12.11 12.15 12.05 12.09 12.15 12.12 12.14 12.06 12.08 12.10 12.07 12.10 12.11 12.15 12.10 12.13 12.07 12.15 12.14 12.06 12.08 12.10 12.10 12.13 12.07 12.15 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 20.04 20.02 20.00 19.98 20.05 20.00 19.90 19.88 20.00 20.13 20.05 19.89 20.09 19.99 19.90 19.99 19.99 19.89 20.07 19.94 20.08 19.91 19.95 19.98 19.97 20.01 19.96 20.08 19.99 20.00 20.02 20.00 19.92 19.97 20.02 19.95 12.15 12.02 12.14 12.08 12.08 12.02 12.14 12.00 12.02 12.09 12.00 12.08 12.16 12.06 12.00 12.08 12.02 11.98 12.13 12.05 12.05 12.05 12.14 12.05 12.05 12.04 12.08 12.14 12.10 12.09 12.07 12.11 12.10 12.09 12.09 12.09 Exhibit B Precise Molded Products Date 1 Time 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 2 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:05 17:00 18:00 19:00 20:00 21:00 22:00 23:00 Total Sample Rejected Size Parts 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 5 6 2 3 9 5 4 6 2 4 3 4 8 7 5 4 1 5 7 3 3 7 2 5 6 7 5 8 9 4 7 6 Sh. Shot Inclus. Discol. 1 1 2 1 3 1 1 1 2 1 1 2 1 1 CAUSES Warp. Stain Scuff Burr Flash 1 2 1 2 3 1 2 1 1 2 1 1 2 1 1 2 1 2 2 1 1 2 1 2 1 1 1 1 1 1 1 2 1 2 1 2 2 1 1 1 1 2 1 1 2 2 1 3 2 2 1 2 4 3 2 3 6 2 1 2 1 1 2 2 1 1 3 3 4 2 3 2 3 1 1 1 2 1 1 2 3 3 1 \fn A2 A3 c4 B3 B4 D3 D4 d2 2 3 4 5 6 7 1.8800 2.6590 0.7979 0.0000 3.2670 0.0000 3.2670 1.1280 1.0230 1.9510 0.8862 0.0000 2.5680 0.0000 2.5750 1.6930 0.7290 1.6280 0.9213 0.0000 2.2660 0.0000 2.2820 2.0590 0.5770 1.4270 0.9400 0.0000 2.0890 0.0000 2.1150 2.3260 0.4830 1.2870 0.9515 0.0300 1.9700 0.0000 2.0040 2.5340 8 0.4190 0.3730 1.1820 1.0990 0.9594 0.9650 0.1180 0.1850 1.8820 1.8150 0.0760 0.1360 1.9240 1.8640 2.7040 2.8470 9 0.3370 1.0320 0.9693 0.2390 1.7610 0.1840 1.8160 2.9700 10 0.3080 0.9750 0.9727 0.2S4 1.7160 0.2230 1.7770 3.0780 11 0.2850 0.9270 0.9754 0.3210 1.6790 0.2560 1.7440 3.1730 12 0.2660 0.8860 0.9776 0.3540 1.6460 0.2840 1.7160 3.2580 13 0.2490 0.8500 0.9794 0.3820 1.6180 0.3080 1.6920 3.3360 14 0.2350 0.8170 0.9810 0.4060 1.5940 0.3290 1.6710 3.4070 15 0.2230 0.7890 0.9823 0.4280 1.5720 0.3480 1.6520 3.4720 16 0.2120 0.7630 0.9835 0.4480 1.5520 0,364 1.6360 3.5320 17 0.2030 0.7390 0.9845 0.4660 1.5340 0.3790 1.6210 3.5880 18 0.1940 0.7180 0.9854 0.4820 1.5180 0.3920 1.6080 3.6400 19 0.1870 0.6980 0.9862 0.4970 1.5030 0.4040 1.5960 3.6890 20 0.1800 0.6800 0.9869 0.5100 1.4900 0.4140 1.5860 3.7350 21 0.1730 0.6630 0.9876 0.5230 1.4770 0.4250 1.5750 3.7780 X-bar x CL A2 0.729 UCL LCL 20.09611 19.92342 R CL D4 2.282 UCL 0.270274 20.0098 R-bar 0.118 D3 0 LCL 0 0.300 R ch art UC L LCL CL 0.250 0.200 0.150 0.100 0.050 0.000 0 5 10 15 20 25 30 35 20.1500 20.1000 Xbar UC L LCL CL 20.0500 20.0000 19.9500 19.9000 19.8500 19.8000 0 5 10 15 20 25 30 35 Samples (k) 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 1 20.100 20.000 20.100 19.940 20.080 20.060 20.110 20.060 19.880 20.030 19.880 19.870 20.010 19.920 19.960 20.050 19.950 19.990 20.090 20.000 20.080 20.000 20.050 20.040 20.020 20.000 19.980 20.050 20.000 19.900 19.880 20.000 Observations (n) 2 3 19.970 20.030 20.110 19.980 20.060 19.990 20.090 20.020 20.080 20.000 20.100 19.950 20.030 20.090 20.090 20.080 19.940 20.020 20.010 19.980 20.010 19.980 19.970 19.960 19.970 19.960 20.010 19.970 20.000 19.900 20.020 19.960 20.090 20.060 20.100 20.080 19.980 20.060 20.110 19.990 20.060 19.990 20.130 20.070 20.060 20.000 20.130 20.070 20.050 19.940 19.890 20.080 20.090 19.910 19.990 19.950 19.900 19.980 19.990 19.970 19.990 20.010 19.890 19.960 n= 4 20.050 20.090 20.030 20.010 20.120 20.050 20.000 20.000 19.960 19.920 19.960 19.990 19.890 19.970 19.900 20.000 20.070 20.060 20.050 20.000 20.050 20.060 20.090 20.080 19.990 20.000 20.020 20.000 19.920 19.970 20.020 19.950 x 20.0375 20.0450 20.0450 20.0150 20.0700 20.0400 20.0575 20.0575 19.9500 19.9850 19.9575 19.9475 19.9575 19.9675 19.9400 20.0075 20.0425 20.0575 20.0450 20.0250 20.0450 20.0650 20.0500 20.0800 20.0000 19.9925 20.0000 19.9975 19.9500 19.9575 19.9750 19.9500 4 Range 0.130 0.130 0.110 0.150 0.120 0.150 0.110 0.090 0.140 0.110 0.130 0.120 0.120 0.090 0.100 0.090 0.140 0.110 0.110 0.120 0.090 0.130 0.090 0.090 0.110 0.190 0.180 0.100 0.100 0.090 0.140 0.110 X-bar x CL A2 0.729 UCL LCL 12.15426 12.02121 R CL D4 2.282 UCL 0.208233 12.0877 R-bar 0.091 D3 0 LCL 0 0.250 R ch art UC L LCL CL 0.200 0.150 0.100 0.050 0.000 0 5 10 15 20 25 30 35 12.2000 Xbar UC L LCL CL 12.1500 12.1000 12.0500 12.0000 11.9500 0 5 10 15 20 25 30 35 Samples (k) 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 1 12.100 12.070 12.140 12.050 12.100 12.150 12.140 12.100 12.190 12.000 12.020 12.020 12.050 12.140 12.080 12.080 12.070 12.050 12.140 12.070 12.100 12.140 12.100 12.150 12.020 12.140 12.080 12.080 12.020 12.140 12.000 12.020 Observations (n) 2 3 12.140 12.100 12.100 12.110 12.100 12.060 12.090 12.150 12.130 12.070 12.090 12.130 12.060 12.080 12.000 12.060 12.080 12.130 12.020 12.040 11.980 12.080 12.000 12.050 12.120 12.030 12.080 12.050 12.060 12.140 12.160 12.050 12.100 12.110 12.090 12.150 12.060 12.080 12.100 12.110 12.130 12.070 12.060 12.080 12.130 12.070 12.090 12.130 12.000 12.050 12.080 12.050 12.160 12.050 12.060 12.140 12.000 12.050 12.080 12.050 12.020 12.040 11.980 12.080 n= 4 12.040 12.150 12.100 12.120 12.150 12.140 12.100 12.150 12.140 12.090 12.090 12.100 12.050 12.090 12.110 12.070 12.150 12.120 12.100 12.150 12.150 12.100 12.150 12.140 12.100 12.090 12.070 12.110 12.100 12.090 12.090 12.090 x 12.0950 12.1075 12.1000 12.1025 12.1125 12.1275 12.0950 12.0775 12.1350 12.0375 12.0425 12.0425 12.0625 12.0900 12.0975 12.0900 12.1075 12.1025 12.0950 12.1075 12.1125 12.0950 12.1125 12.1275 12.0425 12.0900 12.0900 12.0975 12.0425 12.0900 12.0375 12.0425 4 Range 0.100 0.080 0.080 0.100 0.080 0.060 0.080 0.150 0.110 0.090 0.110 0.100 0.090 0.090 0.080 0.110 0.080 0.100 0.080 0.080 0.080 0.080 0.080 0.060 0.100 0.090 0.110 0.080 0.100 0.090 0.090 0.110 delta-bar R-bar CL 0.0000 A2 0.729 UCL LCL 0.076431 -0.076431 R CL D4 2.282 UCL 0.239253 0.105 D3 0 LCL 0 0.300 0.250 R ch art UC L LCL CL 0.200 0.150 0.100 0.050 0.000 0 10 20 30 20 30 40 50 60 70 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 -0.0200 -0.0400 -0.0600 -0.0800 -0.1000 0 10 40 50 60 70 deltabar UCL LCL CL Samples (k) 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 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 1 20.100 20.000 20.100 19.940 20.080 20.060 20.110 20.060 19.880 20.030 19.880 19.870 20.010 19.920 19.960 20.050 19.950 19.990 20.090 20.000 20.080 20.000 20.050 20.040 20.020 20.000 19.980 20.050 20.000 19.900 19.880 20.000 12.100 12.070 12.140 12.050 12.100 12.150 12.140 12.100 12.190 12.000 12.020 12.020 Observations (n) 2 3 19.970 20.030 20.110 19.980 20.060 19.990 20.090 20.020 20.080 20.000 20.100 19.950 20.030 20.090 20.090 20.080 19.940 20.020 20.010 19.980 20.010 19.980 19.970 19.960 19.970 19.960 20.010 19.970 20.000 19.900 20.020 19.960 20.090 20.060 20.100 20.080 19.980 20.060 20.110 19.990 20.060 19.990 20.130 20.070 20.060 20.000 20.130 20.070 20.050 19.940 19.890 20.080 20.090 19.910 19.990 19.950 19.900 19.980 19.990 19.970 19.990 20.010 19.890 19.960 12.140 12.100 12.100 12.110 12.100 12.060 12.090 12.150 12.130 12.070 12.090 12.130 12.060 12.080 12.000 12.060 12.080 12.130 12.020 12.040 11.980 12.080 12.000 12.050 4 20.050 20.090 20.030 20.010 20.120 20.050 20.000 20.000 19.960 19.920 19.960 19.990 19.890 19.970 19.900 20.000 20.070 20.060 20.050 20.000 20.050 20.060 20.090 20.080 19.990 20.000 20.020 20.000 19.920 19.970 20.020 19.950 12.040 12.150 12.100 12.120 12.150 12.140 12.100 12.150 12.140 12.090 12.090 12.100 Nominal Value 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 20.010 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 Samples (k) 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 33 34 35 36 37 38 39 40 41 42 43 44 1 0.09 -0.01 0.09 -0.07 0.07 0.05 0.10 0.05 -0.13 0.02 -0.13 -0.14 0.00 -0.09 -0.05 0.04 -0.06 -0.02 0.08 -0.01 0.07 -0.01 0.04 0.03 0.01 -0.01 -0.03 0.04 -0.01 -0.11 -0.13 -0.01 0.01 -0.02 0.05 -0.04 0.01 0.06 0.05 0.01 0.10 -0.09 -0.07 -0.07 Delta Observations (n) 2 -0.04 0.10 0.05 0.08 0.07 0.09 0.02 0.08 -0.07 0.00 0.00 -0.04 -0.04 0.00 -0.01 0.01 0.08 0.09 -0.03 0.10 0.05 0.12 0.05 0.12 0.04 -0.12 0.08 -0.02 -0.11 -0.02 -0.02 -0.12 0.05 0.01 0.01 0.00 0.04 0.00 -0.03 -0.09 -0.01 -0.07 -0.11 -0.09 12.050 12.140 12.080 12.080 12.070 12.050 12.140 12.070 12.100 12.140 12.100 12.150 12.020 12.140 12.080 12.080 12.020 12.140 12.000 12.020 12.120 12.080 12.060 12.160 12.100 12.090 12.060 12.100 12.130 12.060 12.130 12.090 12.000 12.080 12.160 12.060 12.000 12.080 12.020 11.980 12.030 12.050 12.140 12.050 12.110 12.150 12.080 12.110 12.070 12.080 12.070 12.130 12.050 12.050 12.050 12.140 12.050 12.050 12.040 12.080 12.050 12.090 12.110 12.070 12.150 12.120 12.100 12.150 12.150 12.100 12.150 12.140 12.100 12.090 12.070 12.110 12.100 12.090 12.090 12.090 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 12.088 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 -0.04 0.05 -0.01 -0.01 -0.02 -0.04 0.05 -0.02 0.01 0.05 0.01 0.06 -0.07 0.05 -0.01 -0.01 -0.07 0.05 -0.09 -0.07 0.03 -0.01 -0.03 0.07 0.01 0.00 -0.03 0.01 0.04 -0.03 0.04 0.00 -0.09 -0.01 0.07 -0.03 -0.09 -0.01 -0.07 -0.11 elta Observations (n) 3 0.02 -0.03 -0.02 0.01 -0.01 -0.06 0.08 0.07 0.01 -0.03 -0.03 -0.05 -0.05 -0.04 -0.11 -0.05 0.05 0.07 0.05 -0.02 -0.02 0.06 -0.01 0.06 -0.07 0.07 -0.10 -0.06 -0.03 -0.04 0.00 -0.05 0.01 0.02 -0.03 0.06 -0.02 0.04 -0.01 -0.03 0.04 -0.05 -0.01 -0.04 4 0.04 0.08 0.02 0.00 0.11 0.04 -0.01 -0.01 -0.05 -0.09 -0.05 -0.02 -0.12 -0.04 -0.11 -0.01 0.06 0.05 0.04 -0.01 0.04 0.05 0.08 0.07 -0.02 -0.01 0.01 -0.01 -0.09 -0.04 0.01 -0.06 -0.05 0.06 0.01 0.03 0.06 0.05 0.01 0.06 0.05 0.00 0.00 0.01 n= delta bar 0.0277 0.0352 0.0352 0.0052 0.0602 0.0302 0.0477 0.0477 -0.0598 -0.0248 -0.0523 -0.0623 -0.0523 -0.0423 -0.0698 -0.0023 0.0327 0.0477 0.0352 0.0152 0.0352 0.0552 0.0402 0.0702 -0.0098 -0.0173 -0.0098 -0.0123 -0.0598 -0.0523 -0.0348 -0.0598 0.0073 0.0198 0.0123 0.0148 0.0248 0.0398 0.0073 -0.0102 0.0473 -0.0502 -0.0452 -0.0452 4 Range 0.130 0.130 0.110 0.150 0.120 0.150 0.110 0.090 0.140 0.110 0.130 0.120 0.120 0.090 0.100 0.090 0.140 0.110 0.110 0.120 0.090 0.130 0.090 0.090 0.110 0.190 0.180 0.100 0.100 0.090 0.140 0.110 0.100 0.080 0.080 0.100 0.080 0.060 0.080 0.150 0.110 0.090 0.110 0.100 -0.06 -0.04 0.05 -0.04 0.02 0.06 -0.01 0.02 -0.02 -0.01 -0.02 0.04 -0.04 -0.04 -0.04 0.05 -0.04 -0.04 -0.05 -0.01 -0.04 0.00 0.02 -0.02 0.06 0.03 0.01 0.06 0.06 0.01 0.06 0.05 0.01 0.00 -0.02 0.02 0.01 0.00 0.00 0.00 -0.0252 0.0023 0.0098 0.0023 0.0198 0.0148 0.0073 0.0198 0.0248 0.0073 0.0248 0.0398 -0.0452 0.0023 0.0023 0.0098 -0.0452 0.0023 -0.0502 -0.0452 0.090 0.090 0.080 0.110 0.080 0.100 0.080 0.080 0.080 0.080 0.080 0.060 0.100 0.090 0.110 0.080 0.100 0.090 0.090 0.110 7.00% 6.00% p 5.00% UCL LCL use 4.00% CL 3.00% 2.00% 1.00% 0.00% 1 4 7 10 13 16 19 22 25 28 31 Samples (k) 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 No. defective 5 6 2 3 9 5 4 6 2 4 3 4 8 7 5 4 1 5 7 3 3 7 2 5 6 7 5 8 9 4 7 6 * p-bar = (sum of No. defective)/(sum of observations) Observ. (n) p UCL LCL calc 200 2.50% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 200 1.00% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 4.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 200 1.00% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 4.00% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 0.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 1.50% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 1.00% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 2.50% 0.058633 -0.008008 200 4.00% 0.058633 -0.008008 200 4.50% 0.058633 -0.008008 200 2.00% 0.058633 -0.008008 200 3.50% 0.058633 -0.008008 200 3.00% 0.058633 -0.008008 * p-bar LCL use 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CL 2.53%