Chapter 5 Control Charts For Variables

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82 Chapter 5. Control Charts For Variables (ATTENDANCE 4)1. Ice Cream Treat Weight, Raw DataIce cream treats are weighed (in ounces), four at a time (n = 4).sample x 1 x 2 x 3 x 41 7 9 12 142 9 5 5 123 7 10 11 74 8 9 5 145 7 8 11 126 12 11 9 107 16 9 10 78 6 5 11 39 8 7 10 1410 15 17 9 1411 7 12 13 1712 5 11 8 1213 16 10 13 1414 8 13 9 1315 11 8 11 1616 15 11 10 1417 10 9 11 1018 16 8 11 1219 8 7 10 1320 15 17 10 15SAS program: att4-5-2-icecream-xrchart(a) ¯x chart and R chartFrom SAS, both the ¯x chart and R chart for the ice cream weight is (chooseone) in / out of statistical control because there are no out-of-controlsignals, runs, trends, or cycles.(b) (LCL, UCL) for ¯x chart and R chartFrom the SAS graph the average of all averages is,¯x = (choose one) 10.45 / 10.55 / 10.65The upper control limit and the lower control limit for ¯x chart are,(choose one)i. (5.78, 15.32)ii. (5.68, 14.32)iii. (6.78, 15.32)¯x ± 3ˆσ/ √ n = (LCL, UCL) =
Section 2. Control Charts For ¯x and R (ATTENDANCE 4) 83Also, from SAS, ¯R = (choose one) 6.6 / 7.6 / 8.6The upper control limit and the lower control limit for the R chart are,(LCL, UCL) = (choose one)i. (5.5, 14.9)ii. (0, 14.9)iii. (−14.9, 14.9)(c) Natural tolerance limits, control limits and specification limitsUSLupper specification limits(predetermined)UNTLupper natural tolerance limitLCL = 15.32upper control limit10.55LNTLlower natural tolerance limitLSLlower specification limits(predetermined)individual xUCL = 5.78lower control limitaverage x,sample n = 4Figure 5.1 (Natural tolerance limits, control limits and specificationlimits)On the one hand, the control limits for the ¯x chart are,¯x ± 3ˆσ/ √ n = (LCL, UCL) = (5.78, 15.32),whereas, on the other hand, the natural tolerance limits for an individualx are(UNTL, LNTL) = ¯x ± 3ˆσ = 10.55 ± 3(3.18154) =(choose one 3 )i. (1.01, 20.09)ii. (0.68, 24.32)iii. (−1.02, 25.32)and the specification limits are (arbitrarily) predetermined limits set as“goals” to be achieved by the ice cream treat process in this case.(d) More process standard deviationIn addition to reading the process standard deviation ˆσ from SAS, wecould also use d 2 = 2.059 from Appendix VI, page 761 of the text, and sodetermine the process standard deviation to be(choose one) 3.18 / 4.34 / 5.66samplesˆσ = ¯R/d 2 ≈ 6.55/2.059 ≈3 The process standard deviation ˆσ can be found on the SAS printed output.
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Chapter 5 Control Charts For Variables

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