Question

Question2 This table show the information on acid content in milliliters. Each test has 4 sample readings. Draw control charts (for X bar and R) and calculate values of the trial central line and limits. VARIABLES CONTROL CHART DEPTAREA CHARTID: Problemi CHARACTERISTIC: Acid Content PARTID: OPERATION ID: CHECK METHOD: NOMINAL VALUE: 0.70 ml TOLERANCE: 0.20 6 SAMPLE READINGS 12 7 89 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 857580 65.75 60 80 70 75 6080757065 85.80 70.70 65.65 55.75 80 65.65 20s as 80 75 70 75 76 60 65 70 75 85 70 70 75 76 as 60 es 60 soos es 60 70 .65 75 75 60 65 76.05.75 85 60 90 65 75 85 90 75 75 70 as .00 65.00 75 0570 4 70 as 70 80.70|75|75|80|80|50|es| 70 75 80 80 70 70 es 65 80 80 66.60.00

Answer 1

Drawing of control charts (for X bar and R) Number of tests conducted (m) = 25 Sample readings (n) = 4 “Xi” is the average of sample readings “Ri” is the difference between maximum and minimum sample reading in a test. Sample readings Average Tests Xi 0.7125 1 X1 0.85 0.75 0.8 0.65 X3 0.65 0.75 0.75 X4 0.7 0.85 0.7 Range Minimum value (22) 0.65 0.75 0.7 Maximum value (21) 0.85 0.85 0.8 0.75 Ri (21-22) 0.2 0.1 0.1 2 0.8 3 X2 0.65 0.85 0.8 0.75 0.7 0.75 0.75 0.7625 4 0.6 0.6 0.65 0.7 0.8 0.675 0.725 0.15 0.15 5 0.75 0.8 0.65 6 0.6 0.75 0.7 0.75 7 0.8 0.75 0.65 0.75 0.85 0.7 0.7375 0.7 0.8 0.6 0.65 0.6 0.75 0.15 0.15 0.15 0.1 8 0.6 0.75 0.8 0.75 0.85 9 0.85 0.8125 0.7 0.75 0.6 0.8 10 0.7 0.8 0.6 0.2 0.8 0.5 0.675 0.7375 11 0.75 0.9 0.5 0.4 0.6 0.9 0.85 0.75 0.75 0.85 12 13 0.85 0.7 0.7 0.7 0.65 اواد 0.65 0.7 0.75 0.65 0.7 0.65 0.2 0.05 14 15 0.75 0.85 0.8 0.75 0.85 0.8 0.8 0.75 0.85 0.85 0.8 0.85 0.7 0.2 0.1 0.05 16 0.75 0.8 0.75 0.75 0.7 0.6 17 0.7 0.75 0.7 0.15 0.85 0.6 18 0.7 0.7 0.7 0.1 19 0.65 0.65 0.8 0.8 20 0.775 0.7125 0.7375 0.8 0.775 0.75 0.675 0.7 0.625 0.625 0.7125 0.7125 0.625 0.6625 0.717 0.2 0.05 0.3 0.15 0.5 0.65 0.65 0.85 0.65 0.6 0.6 0.55 0.65 0.75 0.65 0.65 0.8 0.65 0.75 0.65 0.6 0.65 0.65 0.7 0.7 Final average of Xi 21 22 23 24 0.85 0.65 0.65 0.6 0.8 0.5 0.8 0.65 0.8 0.65 0.65 0.6 0.7 0.6 Final average of Ri 0.65 0.6 0.15 0.05 25 0.6 0.1 0.148

= 0.717 m ΣR R = 0.148 m X bar chart (central limits calculation) For sample readings n= 4; A2 = 0.729 (X bar Control chart constants) Central limit (X)=0.717 Upper control limit (UCL) = 7 + (A2 X R)=0.717 + (0.729 X 0.148)=0.8248 Lower control limit (LCL)= Ž - (A2 X R) =0.717 - (0.729 X 0.148)=0.6091 + X-bar chart 0.9 0.8 A 0.7 0.6 0.5 Sample reading average Series1 0.4 CL 0.3 UCL 0.2 LCL 0.1 0 0 5 10 15 20 25 Number of tests

R bar chart (central limits calculation) For sample readings n= 4; D3=0, D4= 2.282 (R bar Control chart constants) Central limit (R) = 0.148 Upper control limit (UCL) = D4 X Ř= 2.282 X 0.148 = 0.3377 Lower control limit (LCL) = D3 X R=0 X 0.148 = 0 R-bar chart 0.45 0.4 0.35 0.3 0.25 Sample range values CL 0.2 UCL 0.15 LCL 0.1 Ri 0.05 0 0 5 10 15 20 25 Number of tests