Question

The diameter of a casting used in a gas turbine jet aircraft engine is an important quality characteristic. A coordinating measuring machine is used to measure the diameter of each casting at four different locations. Data for ten castings are shown in the accompanying table. 4 Casting 2 34 11.711 11.783 11.749 11.497 2 11.798 11.889 11.849 11.746 3 11.914 11.761 11.736 11.707 11.726 11.733 11.742 11.757 5 11.836 11.802 11.798 11.987 6 11.707 11.711 11.745 11.729 7 11.712 11.798 11.429 11.716 8 11.802 11.827 11.897 11.798 11.776 11.773 11.754 11.732 10 11.758 11.626 | 11.753 11.787 Suppose # and R charts are used for this process assuming the measurements on each casting from a rational subgroup. Suppose also that 2.75 sigma control limits are used for both x and R charts. Find the number of points that are out of the control limits for x chart. 9 a. 0 b. 1 c. 2 d.3

Answer 1

sample mean x̅ =			11.759
average range R̅ =			0.1567
sample size n   =			4
sample size n=4, criitcal value of A2=			0.729
control line (CL) = x̅=			11.75878
upper control limit =x̅+3*A2R̅ =			11.87
lower control limit =x̅-3*A2R̅ =			11.64

since all the points are within control limits

option A is correct