Control Charts
 Control Charts allow a company’s
performance over time to be analyzed by
combining performance data, average,
range and standard deviation. Control
charts usually used to analyze a process the
company performs.
Data
 The data used in the control charts we
Data
will discuss (X bar and R Charts) are
samples of a population
 From Gillette example 15 hours become 15
subgroups representing the total population
of razor blades and each subgroup will have
5 data values n = 5.
Table of Data from Gillette
Example
5 measurements for
each subgroup
Subgroups
Calculations for the Data
 Find the mean (X) and the range for each
subgroup
1. X = ( Σ xi ) / n
2. R = Max (xi) – Min (xi)
 Find the mean of the X and Range
1. X = ( Σ X i ) / (#of sub groups )
2. R = ( Σ Ri ) / (# of sub groups )
Data with Calculated figures
Create Control Charts
Limits to our Control charts
 Upper and lower control limits represent 3
standard deviations above and 3 standard
deviations below the mean line respectfully.
 Instead of calculating the standard deviation
for all of the sample data we use these
simple equations
Control Limit Equations
 X (UCLx) = X + A2*R
 X (LCLx) = X - A2*R
Where A2 can be found on page 237 of your Intro to IE
textbook
 R (UCLR) = D4*R
 R (LCLR) = D3*R
Where D4 and D3 can be found on page 237 of your Intro to
IE textbook.
Finished Control Charts
Control Chart Analysis
 To analyze the control charts it is important
to remember that the data is represented
over six standard deviations, there are three
standard deviations from the mean line to
the upper control limit and three from the
mean to the lower control limit. To help
analyze the charts, it is important to divide
the chart area into six sections A, B, and C
representing the standard deviations.
Example of Different Zones
Interpreting the Control Chart
 To interpret the data we first look at the R
chart. The R chart represents the variety in
the data and if the variety is to great than
there is no need to look at the X control
chart.
 The chart is out of control if one or a
combination of the following four examples
occur:
Process out of Control
1.
If one point falls outside of the 3 sigma
control limits (beyond zone A)
Process out of Control
2. If two out of any three successive points
fall in zone A of the same side
Process out of Control
3. If four out of any five successive points
fall in or beyond zone B of the same side
Process out of Control
4. If eight successive points fall in or beyond
zone C of the same side
How does the Co-ops Control
Charts Look?