Question

mail Address here are 8 problems on 6 pages plus 2 supplementary data pages (15 pts) A CNC lathes machines 3 different types of bearings with diameters of 100, 120, and 150 mm. Since part requirements are few, batch runs are small and expereive to do extensive sampling. Consoquently, halches are combined and measured as deviations tros mominal. A sample of 15, five for each part type, comsisting of 3 samples is given below You are lo calculale upper and kwer control limibs for both X-br and R chars Sample Par Number Type 0 033 3 0 4 0674 4 3 67 2 0 267 267 3 0.00 4 1.33 11 ? 2 0-10.33 3 4 Q.33 033

Answer 1

For sample size = 3, from control chart table for X and R,

Factor for LCL R chart = 0

Factor for UCL R chart = 2.574

Control factor for X chart = 1.023

Average X-bar = 0.69

Average R = 3.87

Lower control limit for X-bar = Average X-bar - (Control factor for X chart)*Average R

= 0.69 - 1.023*3.87

= -3.27

Upper control limit for X-bar = Average X-bar + (Control factor for X chart)*Average R

= 0.69 + 1.023*3.87

= 4.65

Lower control limit for R = Factor for LCL R chart*Average R

= 0*3.87

= 0

Upper control limit for R = Factor for UCL R chart*Average R

= 2.574*3.87

= 9.96