Control charts are graphs used to study how a process changes over time by plotting data points in time order. A control chart contains a central line for the average, and upper and lower control limits determined from historical data. There are variable control charts that measure things like weight, and attribute control charts that count outcomes like defects. Control charts help determine whether a process is stable or experiencing unusual variations so quality can be ensured. While useful, control charts have been criticized for how they model processes and compare performance.

1. Control charts
Rashmi.k.awal- 05
Nikita awale- 06
Sumitted to- Prof.Anurag.S

2. What is control chart?
The control chart is a graph used to study how a process
changes over time. Data are plotted in time order. A control
chart always has a central line for the average, an upper
line for the upper control limit and a lower line for the lower
control limit. These lines are determined from historical
data.

3. Control Charts -
Statistically based control chart is a
device intended to be used -
- at the point of operation
- by the operator of that process
- to asses the current situation
- by taking sample and plotting sample result
- To enable the operator to decide about the process.

4. History of control chart-
Mr. Shewart, an American, has been credited with the
invention of control charts for variable and attribute data in
the 1920s, at the Bell Telephone Industries. The term
‘Shewart Control Charts’ is in common use.

5. Elements of control chart-
 There are three main elements of a control chart as
shown in Figure -
1. A control chart begins with a time series graph.
2. A central line (X) is added as a visual reference for
detecting shifts or trends – this is also referred to as the
process location.
3. Upper and lower control limits (UCL and LCL) are
computed from available data and placed equidistant
from the central line. This is also referred to as process
dispersion.

7. Controlled variations -
Controlled variation is characterized by a stable and consistent
pattern of variation over time, and is associated with common
causes. A process operating with controlled variation has an
outcome that is predictable within the bounds of the control limits.

8. Uncontrolled variation -
Uncontrolled variation is characterized by variation that changes
over time and is associated with special causes. The outcomes of
this process are unpredictable; a customer may be satisfied or
unsatisfied given this unpredictability.

9. Types of control charts-

10. Variable Control Charts -
Deal with items that can be measured .
 Examples
1) Weight
2) Height
3) Speed
4) Volume .

11. Types of Variable Control Charts -
 X chart
o Most commonly used variables chart.
o Chart for measure of central tendency.
o Shows changes in process average and is affected by
changes in process variability.

12. Continue ..
 R chart
o Controls general variability of the process
o Chart for measure of spread
o Use along with X chart.

13. Attribute control chart -
Attribute control charts can be used to monitor the stability of
systems where any count or percentage is accumulated
 p charts
For discrete attribute data, use the p chart. Recall that discrete
attribute data results when you categorize or bucket each
instance you are measuring.
For example - you might track defective and non-defective
components in a manufacturing process. This chart plots the
proportion ("p") of the data falling into the relevant category over
time

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 c charts
The c chart is similar to the np chart, in that it requires equal
sample sizes for each data point.
For example - in evaluating errors on loan applications, you would
use this chart if you sampled the same number of applications
each week. But instead of plotting the proportion of data in a
certain category, as does the np chart, the c chart plots count
data, such as number of errors. As with the other control charts,
special cause tests check for outliers and process shifts.

15. Continue ..
 np charts
When each data point is based on the same sample size, a special
version of the p chart can be used. The np chart follows the same
principle as the p chart, but actually plots the number of instances
in a category over time rather than the proportion in the category.
The name "np" derives from the convention of using "n" to refer to
sample size. By multiplying sample size by proportion (n x p) you
get the actual number in a category.

17. Comparison of variable and
attribute charts.
1. Variable charts involve the measurement of the job
dimensions whereas an attribute chart only differentiates
between a defective item and a non-defective item.
2. Variable charts are more detailed and contain more
information as compared to attribute charts.
3. Attribute charts is based on ‘GO and NO GO’ data require
comparatively bigger sample size.
4. Variables charts are expensive.

18. 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
 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

19. Criticism -
 Several authors have criticised the control chart on the grounds
that it violates the likelihood principle. However, the principle is
itself controversial and supporters of control charts further
argue that, in general, it is impossible to specify a likelihood
function for a process not in statistical control, especially
where knowledge about the cause system of the process is
weak.
 Some authors have criticised the use of average run lengths
(ARLs) for comparing control chart performance, because that
average usually follows a geometric distribution, which has high
variability and difficulties.
 Some authors have criticized that most control charts focus on
numeric data. Nowadays, process data can be much more
complex, e.g. non-Gaussian, mix numerical and categorical,
missing-valued