Question

Given that the customer requirements for the process is (11.9, 12.1), using X bar and R chart, find Cp, Cpk and DPMO for the following samples (there are 16 samples). Assume the process is normally distributed.

Given that the customer requirements for the processis (11.9, 12.1), using X bar and R chart, find Cp, Cpk and DPMO for the following samples (there are 16 samples). Assume the process is ormally distributed. 1 Subgroup 111.945 2 12.03 3 12.01 4 11.97 12.0012.03 11.98 12.01 12.02 12.03 12.00 11.98 12.0011.97 11.98 12.00 11.9812.00 12.03 11.99 5 12.00 12.01 12.02 12.03 12.02 12.0412.00 12.01 11.99 12.0112.03 12.00 11.98 12.0112.04 12.00 12.02 12.02 11.96 12.00 11.98 12.0011.97 12.05 12.00 11.9811.99 11.96 11.97 11.9811.97 11.98 11.99 12.0112.02 12.01 11.99 12.0312.00 12.01 11.99 12.0112.02 12.00 12.01 11.9811.99 11.99 12.02 6 11.98 7 12.00 8 12.00 9 12.00 10 12.02 11 12.00 12 12.02 13 12.00 14 11.97 15 11.99 16 12.00

Answer 1

Compute X and R for each sample X is computed as average of the observations for each sample R is computed by subtracting the minimum value from the maximum value of each sample Plot control charts using Xbar, R and control limits CL LCL UCL CLR LCLR UCLR R-chartx-chart 12.00 | 11.97 | 12.03 | 0.05 | 0.00 | 0.11 | TRUE | TRUE 12.0011.9712.03 0.05 0.00 0.11 TRUE TRUE 12.0011.9712.03 0.05 0.00 0.11 TRUE TRUE 12.00 11.97 12.030.05 0.00 0.11 TRUE TRUE 12.00 11.97 12.030.05 0.00 0.11 TRUE TRUE 12.00 11.9712.030.050.000.11TRUE TRUE 12.00 11.97 12.030.050.000.11 TRUE TRUE 12.00 | 11.97 | 12.03 | 0.05 | 0.00 | 0.11 | TRUE | TRUE 12.00 | 11.97 | 12.03 | 0.05 | 0.00 | 0.11 | TRUE | TRUE 12.0011.9712.03 0.05 0.00 0.11 TRUE TRUE 12.00 11.9712.03 0.05 0.00 0.11 TRUE TRUE 12.00 11.97 12.030.05 0.00 0.11 TRUE TRUE 12.00 11.9712.030.050.000.11TRUE TRUE 12.00 11.9712.030.050.000.11TRUE TRUE 12.00 11.9712.030.050.000.11TRUE TRUE 12.00 11.9712.03 0.05 0.00 0.11 TRUE TRUE Sample 1 2 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 # 13 #14 #15 # 16 | 11.95 | 12.00 | 12.03 | 11.98 | 12.01 | 11.99 | 0.08 | 12.03 | 12.02 | 12.03 | 12.00 | 11.98 | 12.01 | 0.05 | 12.01 | 12.00 | 11.97 | 11.98 | 12.00 | 11.99 | 0.04 11.97 11.98 12.00 12.03 11.99 11.99 0.06 | 12.00 | 12.01 | 12.02 | 12.03 | 12.02 | 12.02 | 0.03 | 11.98 | 12.04 | 12.00 | 12.01 | 11.99 | 12.00 | 0.06 | 12.00 | 12.01 | 12.03 | 12.00 | 11.98 | 12.00 | 0.05 | 12.00 | 12.01 | 12.04 | 12.00 | 12.02 | 12.01 | 0.04 | 12.00 | 12.02 | 11.96 | 12.00 | 11.98 | 11.99 | 0.06 | 12.02 | 12.00 | 11.97 | 12.05 | 12.00 | 12.01 | 0.08 | 12.00 | 11.98 | 11.99 | 11.96 | 11.97 | 11.98 | 0.04 | 12.02 | 11.98 | 11.97 | 11.98 | 11.99 | 11.99 | 0.05 | 12.00 | 12.01 | 12.02 | 12.01 | 11.99 | 12.01 | 0.03 | 11.97 | 12.03 | 12.00 | 12.01 | 11.99 | 12.00 | 0.06 | 11.99 | 12.01 | 12.02 | 12.00 | 12.01 | 12.01 | 0.03 | 12.00 | 11.98 | 11.99 | 11.99 | 12.02 | 12.00 | 0.04 Average12.000 0.050 | Determine X and R R-Chart 0.12 X- 12.000 R R R0.os0 0.06 Control chart constants corresponding to sample size N 0.04 Sample size, N5 0.02 2.114 0.577 D4 1 2 3 45 6 7 8 9 10 11 12 13 14 15 16 A2 Control limits for X-chart Control limits for R-chart X-Chart 12.04 2.03 0.106 1202 12.02 12.01 12.00 11.99 11.98 11.97 11.96 11.95 11.94 = 11.972 LCLx=又一A, Comment about process control 0 X-value lie outside of control limits. Therefore based on X-chart, the process is In Control 0 R-value lie outside of control limits. 1 2 3 45 6 7 89 10 11 12 13 14 15 16 Therefore based on R-chart, the process is In Control

For subgroup size, n = 5, value of control chart constant, d2 = 2.326 (from table of control chart constants)

Standard deviation = Rbar / d2 = 0.050/2.326 = 0.021

LSL = 11.9

USL = 12.1

mean (m) = Xdblbar = 12.000

Cp = (USL-LSL)/6s = (12.1-11.9)/(6*0.021) = 1.5873

Cpk = MIN((USL-m)/3s, (m-LSL)/3s)

= MIN((12.1-12.0)/(3*0.021), (12.0-11.9)/(3*0.021)) = 1.5873

For LSL, z value = (11.9-12.0)/0.021 = -4.76, F(z) = NORMDIST(-4.76) = 0.00000096

For USL, z value = (12.1-12.0)/0.021 = 4.76, F(z) = NORMDIST(4.76) = 0.99999904

Proportion defective = (1-0.99999904)+0.00000096 = 0.00000192

DPMO = 1.92 ~ 2