Suppose the LCL for a control chart is 2, the UCL is 10, and the CL is 6. Which of the following sequences, if plotted on this control chart, would be "out of control"? Check Il that apply. ach set of points are listed in order of oldest to newest. 0, 2, 6, 4, 5, 4 3, 4, 5, 6, 7, 8 7765432
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- Which of the following is NOT usually part of a control chart a. Centre line b. Lower control limit c. Out of control line d. Upper control limitwe have seen various methods to set control limits for control charts. Which method would you prefer and why?Northshore hospital surgeon, Bill, wants to build 3-sigma x- bar control limits for the open heart surgery. The target value for the mean of the process (x-bar) is 10 units, and the standard deviation of the process is 8. If samples of size 16 are to be taken, what will be the upper and lower control limits, respectively? Question 33 options: 8 and 12 16 and 4 -8 and 28 18 and 6 16 and 4
- Problem 10-4 (Static) Software upgrade times (in minutes) are being evaluated. Samples of five observations each have been taken, and the results are as listed. 1 79.2 78.8 80.0 78.4 81.0 Number of Observations in Subgroup, n 2 4 5 6 7 8 9 Click here for the Excel Data File Factors for three-sigma control limits for and Rcharts 10 11 13 12 13 14 SAMPLE 2 4 3 80.5 79.6 78.9 78.7 81.0 80.4 79.7 79.6 79.4 80.4 79.4 80.1 80.6 15 16 17 18 19 20 80.3 80.8 Factor for I Chart, A2 1.88 1.02 0.73 0.58 0.48 0.42 5 6 80.5 79.7 79.6 80.6 80.4 80.5 80.8 80.0 78.8 81.1 0.37 0.34 0.31 0.29 0.27 0.25 0.24 0.22 0.21 0.20 0.19 0.19 0.18 FACTORS FOR R CHARTS Lower Upper Control Limit, D3 Control Linit, D4 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.60 1.59 0 8 0 0 0 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 0.38 0.39 0.40 0.41Control charts for X-bar and R, using a subgroup size of 5, are to be applied to control thecritical dimension of a certain manufacturing process. Specifications call for a nominal dimension of1,250.000 + 0.050 mm. The process is believed to have a σ of 0.015 mm Determine appropriate control limits for the X-bar and R charts. a) After 12 subgroups have been drawn and X-bar and R plotted on the charts, a computation of X-double bar give 1,250.015. b1) What is the probability that a value of X-bar will fall within the limits if this is the true value of the mean setting? b2) What is the probability that all 12values fall within the control limits? b) Make the necessary calculations to determine if the process can meet specifications by solvingfor Cp, Cpu, CpL, Cpk . Assume a normal distribution of product output. Illustrate how the processwould look like relative to the result of the computations of the process capability analysis.Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed: Sample Mean Range 1 3.06 .42 2 3.15 .50 3 3.11 .41 4 3.13 .46 5 3.06 .46 6 3.09 .45 Using the factors in Table 10.3 , determine upper and lower limits for mean and range charts. Is the process in control?
- 26. Discuss the following pro and con positions on using optimization models to design control charts: Con: “These models are useless to me because I don’t feel I can accurately estimate the values of the required inputs." Pro: “The choice of specific values of n and k in the construction of X bar charts means that you are assuming values for the various system costs and parameters. You might as well take the bull by the horns and obtain the best estimates you can and use those to design the X bar chart."Steps to monitor using the control charts: Now monitor the process. An additional ten days of data have been collected, see table labeled “1st 10 Days of Monitoring Reservation Processing Time” in the Data File. Develop Xbar and R charts for the 1st 10 days of monitoring. Plot the data for the 1st 10 days on the Xbar and R charts. Is the process in control? If the control chart indicates an out-of-control process, note which days, the pattern, and whether it is the Xbar or R chart. Now that we have set up the control charts using enough data from a stable process, the 30 days of data, we will monitor the process. While monitoring the process, what will we use as the upper control limit for the X-bar Chart to compare against our new x-bar values? Enter your response to three decimal places. You do not need to include the units (minutes), ONLY the numeric value. USE DATA TO GET UPPER CONTROL LIMIT4. For a certain drilling machine of the Putnam Manufacturing Company, control limits foran x−Chart have been determined as: UCLx = 86.8 and LCLx = 83.3 (a) Sample averages for the most recent six samples, in sequential order, are 83.2, 83.9,84.7, 85.4, 85.9, and 86.7. What should be concluded about the process average?Should some action be taken? Why or why not? (b) What would you conclude (and why) about the process average if the sample averagesfor the most recent six samples, in sequential order, were 85.6, 84.9, 86.2, 85.2, 85.5,and 85.1?
- 56. The construction of the p chart described in this chapter requires specification of both UCL and LCL levels. Is the LCL meaningful in this context? In particular, what does it mean when an observed value of p is less than the LCL? If only the UCL is used to signal an out-of-control condition, should the calculation of the UCL be modified in any way? (Hint: The definition of the Type 1 error probability, a, will be different. The hypothesis test for determining if the process is in control is one-sided rather than two-sided.)5 Sample data: Mean (Microns) (N=4) Minimum Maximum3.821 3.764 3.9993.946 3.804 4.2514.049 4.039 4.4543.793 3.779 3.9233.635 3.534 4.0684.046 3.578 4.5043.569 2.974 3.9084.084 3.779 5.6673.414 2.806 4.2565.319 5.168 6.3464.096 4.092 4.2234.108 3.957 4.3084.037 3.982 4.3933.789 3.691 3.8534.066 4.023 4.269 Sample Size N A2 D3 D4 2 1.88 0 3.27 3 1.02 0 2.57 4 0.73 0 2.28 5 0.58 0 2.11 6 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.725-4 Sample data:Mean (Microns) (N=4) Minimum Maximum3.821 3.764 3.9993.946 3.804 4.2514.049 4.039 4.4543.793 3.779 3.9233.635 3.534 4.0684.046 3.578 4.5043.569 2.974 3.9084.084 3.779 5.6673.414 2.806 4.2565.319 5.168 6.3464.096 4.092 4.2234.108 3.957 4.3084.037 3.982 4.3933.789 3.691 3.8534.066 4.023 4.269 Constants: Sample Size N A2 D3 D4 2 1.88 0 3.27 3 1.02 0 2.57 4 0.73 0 2.28 5 0.58 0 2.11 6 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72