Chapter_4_Control_Charts_Eng_Abobakr_Alsufyani.pptx

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1. Chapter 4: Control Charts for Variables By: Eng. Abobakr Alsufyani Based on Montgomery’s Statistical Quality Control

2. Overview Control charts are tools used to monitor process stability over time. Two main charts for variable data: 1. X̄ Chart – monitors process mean. 2. R Chart – monitors process variability. Goal: Detect assignable causes and maintain statistical control.

3. Concept of Control Charts Control charts distinguish between: • Common causes – natural variation in the process. • Special causes – due to specific problems (machine, operator, materials). If points are within limits, the process is in control. If points fall outside limits → investigation required.

4. Example 1: Basic X̄ and R Chart A manufacturing process produces shafts. Samples of size n=4 are taken. Measurements (mm): Sample 1: 10.1, 10.3, 10.2, 10.4 Sample 2: 10.2, 10.5, 10.3, 10.4 Sample 3: 10.3, 10.4, 10.2, 10.5 Sample 4: 10.1, 10.2, 10.2, 10.3 Sample 5: 10.4, 10.3, 10.5, 10.4

5. Example 1: X̄ Chart Process averages with control limits:

6. Example 1: R Chart Process ranges with control limits:

7. Example 2: Out-of-Control Situation A metal part process is monitored (n=5, k=6 samples): Sample means: 10.22, 10.36, 10.08, 10.46, 10.22, 10.68 Sample ranges: 0.2, 0.3, 0.2, 0.3, 0.2, 0.2 Goal: Identify any points outside control limits and interpret.

8. Example 2: X̄ Chart Note samples 3 and 6 are outside control limits (special causes).

9. Example 2: R Chart All ranges are within limits – variability is stable.

10. Interpretation and Actions Example 1: All points within limits → Process is in control. Example 2: Samples 3 and 6 out of control → Assignable causes exist. Possible reasons: • Machine misalignment • Tool wear or change • Operator error • Material variation Actions: Identify, correct, and prevent reoccurrence.

11. Summary • Control charts monitor process stability. • X̄ chart tracks process mean; R chart tracks variability. • If points are outside control limits → special cause. • Stable process → predictable quality. By: Eng. Abobakr Alsufyani