Question

Consider the piston ring data in the following Table. 1. Using formulas in chapter 6, find the trial centerline and upper and lower control limit for Xbar and R. Clearly mention what values from tables you have used. 131 126.4 2- Using Minitab (or if you prefer, manually), draw the two charts of Xtar and R and insert it here first. Then if there are outliers, assume you know the assignable cause of them, so remove them in second step and draw the revised plots and find the centerline, UCL and LCL and insert your new plots again. day XXXXX 1 138. 9 135.3 131.5 137.9 2 1 139.7 127. 3 130.5 129 3 135. 2 132.8 136.1 131 4 124.6 128.8 137.5 131.6 S 138.2 124.4 137.1 127.5 6 132.8 124 135 135 135.8 7 1 30.4 133.3 124.8 128.5 129.3 8 132.7 131. 1 134133.9 125.1 9 136.4 136. 2 134.7 137.1 173.2 10135125.4 139.1 138.3 130.4 111 39.6 137.9 131.1 133.7 120.5 12 138.3 130.2 130.4 132.4 135.1 13 138.7 121.8 139.5 123.3 131.8 14 138.6 139131. 9 130.2 131.1 15138.1 120.8 138. 7 137.4 138.4 16139.3 132. 1 135134 124.3 17 125,9 135.6 134. 2 135127.4 18108.5 106.5 100.2 102.6 102.2 19 138.2 133,8 127.1 132.4 150.9 20 120.1 124.6 135.1 123.8 139.6 21 135.2 121 134.6 130.2 127.3 22 134.8 138.3 129.6 151.8 132.7 131.5 133.1 128.5 133.2 24 139.8 148.3 164 158.1 193.1 25 133. 4 120131.6 138.4 134.2 3- Based on the result of revised control lines, estimate the potential and actual process capability assuming that specifications are 130.0 20.0 mm. 23 131.6

Answer 1

WAT for R chart CLR = R = is 25 E 'N 25 py uri va = R + 3 To are * o - od 3 dr TR = Roda cua xo = R + 3 Rd3 = DOR Lahe = R-3Rdz = D₂R Dy = 1 + 3ds Dg a max ( de Contret chant constant table n=5 dr - 303 dar DA = 2.114 15.82 .. uae La - (15.82) (2.114) = 33.4435 =0 - For X-ban 25 Chart x = { Xi - x S iN225 X L-IN (Ucz, Lax) = x + 3T

Xbar-R Chart of X1, ..., X5 Sample Mean UCL=142.00 X=132.88 LCL=123.75 i 3 5 1 9 11 15 17 19 21 23 25 13 Sample UCL=3345 Sample Range R=15.82 LCL=0 3 5 7 9 11 15 17 19 21 23 25 13 Sample

Below are tests for which an outlier were being decided.

Xbar-R Chart: Options Parameters | Estimate Limits Tests Stages Box-Cox Display Storage Perform selected tests for special causes 1 point > K standard deviations from center line K points in a row on same side of center line k points in a row, all increasing or all decreasing k points in a row, alternating up and down

Below is the revised control chart - eliminating - 9, 24, and 18 th value.

Xbar-R Chart of X1_2, ..., X5_2 UCL=140.19 Sample Mean X=132.44 LCL=124.70 1 3 5 7 9 13 15 17 19 21 11 Sample UCL=28.39 Sample Range R=1343 LCl=0 79 13 15 17 19 21 11 Sample

So, Now process is in control.