Statistical process control (SPC) uses statistical tools like control charts to monitor and control processes and ensure continuous quality improvement. Control charts, also called Shewhart charts, are tools used in SPC to determine if a process is statistically in control. The document presents data from samples of digital watches tested over eight periods. X-bar and R charts are constructed from the data and show that the process is in a state of statistical control.

1. STATISTICAL PROCESS CONTROL

2. STATISTICAL PROCESS CONTROL (SPC)
• Statistical process control (SPC) is a method of quality control
which uses statistical tools
• SPC is applied in order to monitor and control a process
• SPC can be applied to any process where the "conforming
product" (product meeting specifications) output can be
measured
• It is used to ensure the continuous improvement in quality of
the products, services and productivity in the workforce

3. CONTROL CHARTS :
• Control charts are also known as Shewhart charts (after Walter A.
Shewhart) or process-behavior charts
• Control charts are the
tools in SPC, used to determine if a
manufacturing or business process is in a state of statistical control.

4. Question :
A manufacturer produces digital watches. Every 2 hours ,a sample of six
watches is selected randomly to be tested. Each watch is run for exactly
15 minutes and is timed by an accurate , precise timing device. Because
of the variation among watches, they do not all run the same. Shown
here are the data from eight different samples given in minutes. Use
these data to construct
chart and R chart. Observe the results and
comment on whether the process is in control

5. Sample 1
Sample 2
Sample 3
Sample 4
15.01
15.03
14.96
15
14.99
14.96
14.97
15.01
14.99
15.01
14.96
14.97
15.00
15.02
14.99
15.01
14.98
14.97
15.01
14.99
14.99
15.01
14.98
14.96
Sample 5
Sample 6
Sample 7
Sample 8
15.02
15.02
15.03
14.96
15.03
15.01
15.04
14.99
14.99
14.97
15.03
15.02
15.01
15.00
15.00
15.01
15.02
15.01
15.01
14.98
15.01
14.99
14.99
15.02

6. Formulas used:

7. Calculation :
Sample 1
Sample 2
Sample 3
Sample 4
15.01
15.03
14.96
15
14.99
14.96
14.97
15.01
14.99
15.01
14.96
14.97
15.00
15.02
14.99
15.01
14.98
14.97
15.01
14.99
14.99
15.01
14.98
14.96
Mean
14.99
15.00
14.98
14.99
Range
0.03
0.07
0.05
0.05

8. Contd..
Sample 5
Sample 6
Sample 7
Sample 8
15.02
15.02
15.03
14.96
15.03
15.01
15.04
14.99
14.99
14.97
15.03
15.02
15.01
15.00
15.00
15.01
15.02
15.01
15.01
14.98
15.01
14.99
14.99
15.02
Mean
15.01
15.00
15.02
15.00
Range
0.04
0.05
0.05
0.06

12. Control Charts : Interpretation
X bar chart
15.03
15.02
Sample Mean
15.01
15
14.99
14.98
14.97
14.96
1
2
3
4
5
sample
6
7
8

13. R chart
0.08
0.07
0.06
Range
0.05
0.04
0.03
0.02
0.01
0
1
2
3
4
5
Sample
6
7
8

14. THANK YOU