Control charts graphically represent measured characteristics over time to monitor processes for unusual variations. They depict changes in a process average or variability. Control charts determine whether a process is in control or out of control to ensure product quality and reduce scrap. Common types include X-bar and R charts. X-bar charts monitor the central tendency and are affected by variability changes. R charts control general variability. An example calculates control limits for an X-bar and R chart using sample data and constants.

1. CONTROL CHARTS
Cliya Jackson
S6 E2
Roll No 22

2. Definition
• Control chart is a graphical
representation of the collected
information.
• collected information – implies
measured characteristics of the
items or samples.
• Dynamic in nature – it is kept current
and up – to – date as per the changes
in processing conditions .

3. Purpose and advantages
• Depicts any change in the
characteristics of items since the
start of the production.
• It determines whether the process is
in control or out of control.
• It detects unusual variations taking
place in a process.
• It ensures product quality level.

4. Contd…..
• It warns in time and if the process is
rectified at that time , scrap or
percentage rejection can be reduced.
• It builds up the reputation of the
organization through customer’s
satisfaction.

5. Types of control charts
Control charts
Attribute Variables
p np C U X bar R σ

6. X chart
• Most commonly used variables chart.
• Chart for measure of central
tendency.
• Shows changes in process average
and is affected by changes in
process variability.

7. R chart
• Controls general variability of the
process
• Chart for measure of spread
• Use along with X chart

8. Example
Sample no. X R
1 7.0 2
2 7.5 3
3 8.5 2
4 10.0 2
5 9.5 3
6 11.0 4
7 11.5 3
8 4.0 2
9 3.5 3
10 4.0 2
∑ X =76 ∑ R = 26

9. • X and R Control
Chart Constants
n A 2
D 3
D 4
2 1.88 0 3.267
3 1.023 0 2.575
4 0.729 0 2.282
5 0.577 0 2.115
6 0.483 0 2.004
8 0.37 0.14 1.86
10 0.31 0.22 1.78
12 0.27 0.28 1.72

10. Control chart calculations
UCLR = D4 R UCL X = X + A2 R
= 2.11* 2.6 = 7.6 + (0.58 * 2.6)
5.48
= 9.11
CLR = R
CL X = X
= 2.6
= 7.6
LCLR = D3 R
= 0 * 2. 6 LCL X = X − A2 R
=0 = 7.6 − (0.58 * 2.6)
= 6.09

11. Plotting X chart

12. Plotting R chart