I I l IMEPRO3 Case 1 Problem 1: Engineers at a manufacturing plant have just been to a course to learn the basics of SPC. They have decided tc, set up their first charting application on a CNC turnjng center where a motor shaft is being ma<:hined. The quality characteristic that they wish to monitor is the outside diameter, which as ia nominal value of 2.1250 inches t 0.0010 inch. Recently, however, they have been feeling pressure from the company to which they are supplying the parts to improve the consistency of the part dimension in question, and the engineers feel that methods of SPC may be able to assist them in reducing variability. lnitially, they collect data on the outside diameter in subgroulps of 4 consecutive parts at intervals of approximalely lz hour, with the results shown in the table. The measurements were made in inches to the nearest ten thousandth of an inch (e g , 2.1248 and 2.1259 inches, etc.). The data are coded using the last two digits Sample X X, X. Xt Sample Xr X, Xs Xa 1 4ti 59 42 40 21 58 52 57 tt4 2 4ti 52 51 50 22 50 56 44 44 3 50 49 60 44 23 47 53 42 40 4 50 41 48 43 24 56 55 44 li8 5 5 49 60 60 25 39 54 44 54 6 4tl 47 54 45 26 40 43 59 36 7 50 57 53 48 27 48 4B 34 43 I 4ei 63 63 41 28 36 45 43 32 o 54 53 53 46 29 51 48 24 55 10 54 46 55 58 30 43 50 40 53 11 5 56 53 37 31 43 43 49 31 12 5 49 67 50 32 29 42 43 42 13 4 2l 47 48 39 33 36 43 43 48 14 43i 50 44 38 34 48 42 43 39 15 41 54 59 53 35 45 51 43 39 16 6q 45 52 46 4 17 4El 50 45 40 18 4ti 39 43 61 -r.i 19 32 54 45 20 a. az,. 50 47 57 Can we assume that the outside diameter is normally distributed? Use the normal b. probability plot in answering this question. Using all 35 samples, construct the appropriate control charVs. d. Plot the points in the oontrol chart. Apply all appropriate rules to interpret the charts, indicating every inciderrce of an out-of-control condition, and identifying the rule that is violated in each case. What can you say about the stability of the process? c. IMT?ROS Case t ?age t been found that Sirppose that after the preliminary results from the 35 samples, it has proper edge preparation, the cutting tools being used from one of t'he suppliers did not have the verified, the control causing a more rapid'tool vvear condition. Once this was determined and it was proposed to charting, the chart seemed to exhibit go,rd statistical control. To continue were collected, samples use control limits determined from the first 25 samples. Fifteen more again at roughly half-hour intervals, with the resulting data shown below' Sample 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Xt X2 Xs Xa 51 45 53 47 56 56 48 54 50 48 50 47 50 54 60 54 46 55 40 44 46 39 52 49 61 51 57 51 46 54 54 54 51 46 49 45 45 49 51 54 45 49 44 49 57 49 48 55 44 54 54 51 39 51 54 57 51 53 55 47 25 samples from the Determine the new coni:rol limits for the control chart/s using the first control' original data. Plot the ptlints and verify if the process is in statistical about the process? you comment can f. Plot the new set of data (samples 36 to 50). what g Given the final control lirnits, what is the percentage nonconforming? would happen to the percentage h. lf the process ,u"irg., suddenly shifts to 52, what nonconforming? -operating characteristic curve for this process. construct the i. following the shift? j What is the probaOility"of detecting a shift to 52 on the first sample in (h) is detected? k How many samples woulld be allowed to pass before the shift 6 h Problem 2: Nofe: Please trse Average Sample Size for items a to of del'ective parts it is number for the monitored An injection molding process-is beini produ cino. SamPles are tak.en from 15 shifts and the data are as fgllows: Count of shift Output Units 80 1 72 2 68 3 4 81 5 75 70 82 6 7 8 IN4E?ROS 64 Case t ?age z Congtruct the appropriate control chart, Plot the points on the control charts and evaluate the stability of the process c. Supposing that out of control points are detected and its cause/s have been identified so the point may be removed, what are the final control limits? d. What is the probability that if the process average shifts to 6%, it will not be detected? a. b. / It was suggested that perhaps data on the count of nonconformities would be more appropriate. The data on the nonconfornrities of the 15 shifts are given below: l--sirn It a2 ls a4 ls l6 ltls le I to ) tt Itz Its I tt Itq e. f. g h Scrafches Deformities Discoloration 6 6 7 3 8 3 4 9 3 5 3 I 8 5 6 5 3 3 1 4 3 5 10 b 2 4 5 4 1 3 2 3 5 6 7 8 4 3 0 3 6 b 11 5 7 Construct the appropriate chart/s for this new set of data. Analyze the chart/s and comment on the statistical signals. Construct a Pareto diagram of the nonconformities and suggest where problem-solving efforts should concentrate. Explain your reasoning. Suppose that the average number of scratches shifts to 7. What is the probability that this would only be detected on the Sth sample following the shift? NOTE: Answers to the problems must be typewritten on a bond paper, Times New Roman 12. Show all pertinent solutions charts and graphs. I-MT?TIOS Case t ?age 3