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S 6.6) sampling four pieces of precision-cut wire(to be used in computer assembly) every hour for the past 24 hour has produced the following results:

a) What is the process standard deviation o? What is of? b) If z = 3. what are the control limits for the mean chart? IS c) What are the control limits for the range chart? d) Is the process in control? PX . . . $6.11 Twelve samples, each containing five parts, were ta from a process that produces steel rods. The length of each rodIs the process st ons produced ed a) Wh been as follows ... $6.10 A process that is considered to be in control measures an ingredient in grams. Below are the last 10 samples (each of size use " =5) taken. The population standard deviation is 1.36. b) Wh Range (mm) c) Wh 4.2 Samples d) Wh 4.6 2 3 4 5 6 7 8 9 10 e) Wh 4.1 10 9 13 10 12 10 10 13 8 10 f) Ex 5.0 9 9 9 10 10 10 11 10 8 12 . . S 4.5 10 11 10 11 9 8 10 8 12 9 system 9 11 10 10 1I 12 8 10 12 8 Co. T 12 10 9 10 10 take a 9 9 8 9 12 and lo. . $6.7 Auto pistons at Yongpin Zhou's plant in Shanghai art produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows Day Mean (mm) Range (mm) Un A W N - 156.9 4.2 153.2 4.6 153.6 4.1 155.5 5.0 156.6 4.5 a) What is the value of X? b) What is the value of R?population 8.12 - 8.01 8.01 - 7.88 minimum of (3)(0.03) (3)(0.03) 0.11 0.13 0.09 - 1.22 0.09 = 1.44 tions and has an implied error rate of less than 2700 defects per million. ed to contain .. $6.6 Sampling four pieces of precision-cut wire (to be us p the 3-sigma in computer assembly) every hour for the past 24 hours has pro- duced the following results: a) Est are attempt- Hour R Hour the X iation is 1.72. 0.71 cm 13 R ead of mean chart, if 1 3.25 cm 3.11 em 0.85 cm 3.10 1.18 14 2.83 b) If 3 3.22 1.43 15 1.31 3.12 val 1.06 4 3.39 1.26 16 2.84 0.50 .. S taken from a 5 3.07 1.17 17 2.86 ensure 1.43 have t 6 2.86 0.32 18 2.74 1.29 proces the x-chart, 7 3.05 0.53 19 3.41 1.61 LCL; 8 2.65 1.13 20 2.89 1.09 they h the R-chart, 9 3.02 0.71 21 2.65 1.08 found 10 2.85 1.33 22 3.28 0.46 en with 30% 11 2.83 1.17 23 2.94 1.58 Sar ess for "lite" 12 2.97 hicken breast 0.40 24 2.64 0.97 loric content Develop appropriate control charts and determine whether there is any cause for concern in the cutting process. Plot the information doric content and look for patterns. PX be chosen at .. $6.7 Auto pistons at Yongpin Zhou's plant in Shanghai art produced in a forging process, and the diameter is a critical factor that Is the n the target? chart if these must be controlled. From sample sizes of 10 pistons produced each ns from the day, the mean and the range of this diameter have been as follows ...S Day an ing a filling pro- Mean (mm) Range (mm) n =5 1 range is 6 cc. 156.9 4.2 ower control 153.2 4.6 A 153.6 4.1 10 155.5 5.0 Windows 156.6 4.5 a) What is the value of X? b) What is the value of R?") What are the UCL, and LCL, using 30? d) What are the UCLR and LCLR using 30? as con- e) If the true diameter mean should be 155 mm and you want this as 3.0 and your centre (nominal) line, what are the new UCL, and LCL;? PX d) 0.04) ]. $6.8 Bill Kime's bowling ball factory makes bowling balls ly The standard deviation in the weight from