Control charts consist of three horizontal lines: a central line showing the process average, an upper control limit, and a lower control limit. Variables are quality characteristics that can be measured and expressed quantitatively. An R chart plots sample ranges to control variability within subgroups. To set up an R chart, sample ranges are plotted against sample number, with upper, central, and lower control limits calculated using constants D3 and D4 that depend on sample size.

1. Control Charts
International Institute Of Population Science
Source : Fundamentals Of Applied Statistics
By
Smruti Mokal &
Tejal Lakhan

2. Structure of Control Chart
• Consist of Three horizontal lines
1. A central line – shows where the process average is
centered
2.Upper Control Limit
3.Lower Control Limit
• Upper control limit (UCL) and Lower control
limit (LCL)
– describes the process spread

4. Variables
• Variables are those quality characteristic of a
product which are measurable and can be
expressed in specific units of measurements
• Eg Diameter of a radio tube which can be
measured and expressed in cms

5. R chart
– In this chart, the sample ranges are plotted in
order to control the variability of a variable.
– used to detect changes in variation within
subgroups

6. How to set up R chart
• We plot the sample range against the sample number
• Control limit for R chart is given as follows
• UCL = D4*R
• CL = R
• LCL = D3*R
• D3 and D4 are constants depending on sample size n

7. • The x and R chart plots the mean value for the
quality characteristic across all units in the
sample, plus the range of the quality
characteristic across all units in the sample as
follows:
• R = xmax - xmin.