Question

A new process is started, and the sum of the sample standard deviation, ∑s, for 25 rows of measurement, each of subgroup size 4, is 750. If the specifications are 700 ± 80 and the process center, X_bar-bar = 720, compute (to 3 decimal places) the Process Capability Index C_pk. (Please show all work)

Answer 1

C_pl = (Mean – LSL)/3*
C_pu = (USL – Mean)/3*

Process Capability Index C_pk = Min (C_pl, C_pu)

LSL = 700 - 80 = 620

USL = 700 + 80 = 780

Mean – LSL = 720 - 620 = 100

USL – Mean = 780 - 720 = 60

Thus,

Process Capability Index C_pk = 60 / 3*

Process standard deviation, = / c₄

= / 25 = 750 / 25 = 30

c₄ for subgroup size 4 is 0.9213

Process standard deviation, = 30 / 0.9213 = 32.56268

Process Capability Index C_pk = 60 / (3*32.56268) = 0.614