1. Please answer below

Consider a production line producing three different types of bearings with the short productions runs. The nominal values (in millimeters) of inside diameters of three types of bearings are 47mm, 53 mm and 17 mm. The subgroup sample size is 3 for all three types of bearings. To simplify the monitoring process, we would like to use one set of charts to monitor this production line. The nominal values and average ranges are given in the table below. Bearing type Nominal value Average range Type A 47 mm 0.53 nnn Type B 53 mm 1.28 mm Type C 17 mm 0.13 mm (a) What are the UCL, LCL, and Centerline of the appropriate control charts, assuming the standard deviation of three types are different? (6 Points) (b) For the three samples of size 3 given below, is the process statistically in control? (10 Points) Sample Type Mean Range 1 A 46.6 mm 0.96 mm 2 B 55.5 mm 3.02 mm 3 C 17.1 mm 0.51 mm