# X-Chart and P-Chart

Topics: 3, Integers, Duodecimal Pages: 6 (933 words) Published: April 8, 2011
PROBLEMS
2. 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 limits.

|SUBGROUP NUMBER |Xbar |R |SUBGROUP NUMBER |Xbar |R | | |20.35 |0.34 | 14. |20.41 |0.36 | | |20.40 |0.36 | 15. |20.45 |0.34 | | |20.36 |0.32 |16. |20.34 |0.36 | | |20.65 |0.36 |17. |20.36 |0.37 | | |20.20 |0.36 |18. |20.42 |0.73 | | |20.40 |0.35 |19. |20.50 |0.38 | | |20.43 |0.31 |20. |20.31 |0.35 | | |20.37 |0.34 |21. |20.39 |0.38 | | |20.48 |0.30 |22. |20.39 |0.33 | | |20.42 |0.37 |23. |20.40 |0.32 | | |20.39 |0.29 |24. |20.41 |0.34 | | |20.38 |0.30 |25. |20.40 |0.30 | | |20.40 |0.33 | | | |

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[pic] = 510.01R = 8.89
25 25
= 20.40mm = 0.3556mm

From Table B in the appendix, the values for the factors for 6 subgroup size (n) of r are A2 = 0.483, D4 = 2.004, D3 = 0. Trial control limits for the X chart are

UCLxbar = 20.40 + A2R bar LCLxbar = 20.40 - A2R bar
= 20.40+ (0.483) (0.3556) = 20.40- (0.483) (0.3556)
= 20.57mm = 20.23mm

Trial control limits for the R chart are

UCLR = D4R LCL R = D3R
= (2.004) (0.3556) = (0) (0.3556)
= 0.71 mm = 0 mm

Revise the central line and limits:
a) One of point is outside control limit (mean of subgroup number 4 (20.65mm) above UCL x-chart (20.57mm) / range of subgroup number 18 (0.73mm) above UCL R-chart (0.71mm). This is showed that this process is out of control. The special cause variation exists in this x-chart.

Assume assignable causes are machine technical problem or bad material. 3. 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. Of any points are out of control, assume assignable causes and calculate revised limits and central line.

|SUBGROUP NUMBER |Xbar |R |SUBGROUP NUMBER |Xbar |R | | |476 |32 | 14. |482 |22 | | |466 |24 | 15. |506 |23 | | |484...