Question X-Chart and P-Chart

CONTROL CHARTS FOR VARIABLES

TUTORIAL 4 : CONTROL CHARTS FOR VARIABLES
1. Control charts for X and R are to be established on a certain dimension part, measured in millimeters. Data were collected in subgroup sizes of 6 and are given below. Determine the trial central line and control limits. Assume assignable causes and revise the central line and control limits. SUBGROUP NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13

X
20.35 20.40 20.36 20.65 20.20 20.40 20.43 20.37 20.48 20.42 20.39 20.38 20.40

R 0.34 0.36 0.32 0.36 0.36 0.35 0.31 0.34 0.30 0.37 0.29 0.30 0.33

SUBGROUP NUMBER 14 15 16 17 18 19 20 21 22 23 24 25

X
20.41 20.45 20.34 20.36 20.42 20.50 20.31 20.39 20.39 20.40 20.41 20.40

R 0.36 0.34 0.36 0.37 0.73 0.38 0.35 0.38 0.33 0.32 0.34 0.30

2. The following table gives the average and range in kilograms for tensile tests on an improved plastic cord. The subgroup size is 4. Determine the trial central line and control limits. If any points are out of control, assume assignable causes and calculate revised limits and central line. SUBGROUP NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13

X
476 466 484 466 470 494 486 496 488 482 498 464 484

R 32 24 32 26 24 24 28 23 24 26 25 24 24

SUBGROUP NUMBER 14 15 16 17 18 19 20 21 22 23 24 25

X
482 506 496 478 484 506 476 485 490 463 469 474

R 22 23 23 25 24 23 25 29 25 22 27 22

QUALITY CONTROL

1

DMFD 3583

CONTROL CHARTS FOR VARIABLES

3. Table 1 shows the average and range dimension of rods (in millimeters) in subgroup size of 7. By using the data given in Table 1, (i) (ii) (iii) Determine the trial central line and control limits for X and R control chart. Construct the control charts and identify the out of control subgroup. Assume assignable causes and revise the central limit and control limits. Table 1: Average and Range Dimension of Rods (in millimeters). Subgroup No 1 2 3 4 5 6 7 8 9 10 11

X
23.87 23.56 23.40 23.60 23.50 23.33 23.34 23.54 23.69 23.99 23.44

R 0.53 0.42 0.4