This document discusses statistical quality control and control charts. It defines statistical quality control as using statistics to monitor manufacturing processes and determine if variation is due to chance or assignable causes. The document outlines two types of control charts: variables control charts that measure continuous data like weight or temperature, and attributes control charts that count discrete data like defects. Specific variable charts discussed include X-bar and R charts, while attribute charts include P, C, U, and NP charts. Guidelines are provided on when and how to implement control charts to monitor processes and identify sources of variation.

1. A Concise Presentation
By
Mr. Deepak Sarangi M.Pharm
1

2. INTRODUCTION
TYPES OF CAUSES
TYPE OF CONTROL CHARTS
CONTROL CHARTS FOR VARIABLES
BSIC CONCEPTION
WHEN TO USE A CONTROL CHART
R- CHART
X BAR CHART
REFERENCES
2

3.  Statistical quality control:
 Statistics: The collection and analysis of large quantities of
information in the form of numericals.
 Quality Control: A system of maintaining standards in
manufactured products by testing a sample to see if it meets the
required standards.
 Statistical Quality Control: It may be used for monitoring at
various stages of production.
 Monitoring of process mean to determine whether major source
of observed variation is due to “chance variation”, which is
inevitable, during the process or it is due to “assignable cause”,
which can be detected and corrected with appropriate
measured.
3

4. Chance causes: These causes take place as per chance or
in a random fashion a a result of the cumulative effect of
multiplicity of several minor causes which cannot be
identified.
Assignable causes: It refers to those changes in the
quality of the products which can be assigned or
attribulted to any particular causes like defective
materials, defective labours, etc.
4

5. Types of the control charts
•Variables control charts
1. Variable data are measured on a continuous
scale. For example: time, weight, distance or
temperature can be measured in fractions or
decimals.
2. Applied to data with continuous distribution
•Attributes control charts
1. Attribute data are counted and cannot have
fractions or decimals. Attribute data arise when
you are determining only the presence or absence
of something: success or failure, accept or reject,
correct or not correct. For example, a report can
have four errors or five errors, but it cannot have
four and a half errors.
2. Applied to data following discrete distribution
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6.  VARIABLE CHARTS:
 X-bar charts: In this charts, the sample means are plotted in
order to control the mean value of a variable.
 R-Chart: In this chart, the sample ranges are plotted in order to
conrol the variability of variable.
 S chart: In this chart, the sample standard deviations are plotted
in order to control the variability of the variable.
 S**2 chart: In this chart, the sample variances are plotted in
order to control the variability of a variable.
 ATTRIBUTE CHARTS:
 C chart: In this chart , we plot the number of defecties (per day,
per batch, per machine)
 Uchart: In this chart, we plot the rate of defectives.
 Np chart: In this chart, we plot the number of defective and
sample size.
 P chart: In this chart,we plot the percent of defectives.
6

7.  Use x-bar charts to monitor the changes in the
mean of a process (central tendencies)
 Use R-bar charts to monitor the dispersion or
variability of the process
 System can show acceptable central tendencies
but unacceptable variability or
 System can show acceptable variability but
unacceptable central tendencies
7

8. What is a 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.
 Lines are determined from historical data. By comparing current data
to these lines, you can draw conclusions about whether the process
variation is consistent (in control) or is unpredictable (out of control,
affected by special causes of variation).
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9. When to use a control chart?
1. Controlling ongoing processes by finding and correcting
problems as they occur.
2. Predicting the expected range of outcomes from a
process.
3. Determining whether a process is stable (in statistical
control).
4. Analyzing patterns of process variation from special
causes (non-routine events) or common causes (built into
the process).
5. Determining whether the quality improvement project
should aim to prevent specific problems or to make
fundamental changes to the process.
9

10.  Always look at the Range chart first. The control
limits on the X-bar chart are derived from the
average range, so if the Range chart is out of
control, then the control limits on the X-bar chart
are meaningless.
 Look for out of control points. If there are any,
then the special causes must be eliminated..
 There should be more than five distinct values
plotted, and no one value should appear more than
25% of the time. If there are values repeated too
often, then you have inadequate resolution of your
measurements, which will adversely affect your
control limit calculations. In this case, you'll have
to look at how you measure the variable, and try to
measure it more precisely.
 Once the effect of the out of control points from
the Range chart is removed, look at the X-bar
Chart.
10

11.  The X-bar chart monitors the process location over time, based on the average
of a series of observations, called a subgroup.
 X-bar / Range charts are used when you can rationally collect
measurements in groups (subgroups) of between two and ten observations.
Each subgroup represents a "snapshot" of the process at a given point in time.
The charts' x-axes are time based, so that the charts show a history of the
process. For this reason, data should be time-ordered; that is, entered in the
sequence from which it was generated. If this is not the case, then trends or
shifts in the process may not be detected, but instead attributed to random
(common cause) variation.
 For subgroup sizes greater than ten, use X-bar / Sigma charts, since the
range statistic is a poor estimator of process sigma for large subgroups. In fact,
the subgroup sigma is always a better estimate of subgroup variation than
subgroup range. The popularity of the Range chart is only due to its ease of
calculation, dating to its use before the advent of computers.
 For subgroup sizes equal to one, an Individual-X / Moving Range chart can be
used, as well as EWMA or CuSum charts.
 X-bar Charts are efficient at detecting relatively large shifts in the process
average, typically shifts of +-1.5 sigma or larger. The larger the subgroup, the
more sensitive the chart will be to shifts, providing a Rational Subgroup can be
formed. For more sensitivity to smaller process shifts, use an EWMA or CuSum
chart.
)
11
andRchartxforRA
andSchartxsAxLCL
andSchartxsAxUCL
2
3
3
)(
)(
−=
+=

12.  Descriptive Statistics include
 The Mean- measure of central
tendency
 The Range- difference between
largest/smallest observations in a set
of data
 Standard Deviation measures the
amount of data dispersion around
mean
 Distribution of Data shape
 Normal or bell shaped or
 Skewed
n
x
x
n
1i
i∑=
=
( )
1n
Xx
σ
n
1i
2
i
−
−
=
∑=
12

13. xx
xx
n21
zσxLCL
zσxUCL
sampleeachw/innsobservatioof#theis
(n)andmeanssampleof#theis)(where
n
σ
σ,
...xxx
x x
−=
+=
=
++
=
k
k
 Center line and
control limit formulas
Time 1 Time 2 Time 3
Observation 1 15.8 16.1 16.0
Observation 2 16.0 16.0 15.9
Observation 3 15.8 15.8 15.9
Observation 4 15.9 15.9 15.8
Sample means
(X-bar)
15.875 15.975 15.9
Sample ranges
(R)
0.2 0.3 0.2
13

14.  Center line (x-double bar):
 Control limits for±3σ limits:
15.92
3
15.915.97515.875
x =
++
=
15.62
4
.2
315.92zσxLCL
16.22
4
.2
315.92zσxUCL
xx
xx
=





−=−=
=





+=+=
14

15. 15

16.  Center Line and Control Limit
formulas:
 Factors for three sigma control limits
0.00.0(.233)RDLCL
.532.28(.233)RDUCL
.233
3
0.20.30.2
R
3
4
R
R
===
===
=
++
=
Factor for x-Chart
A2 D3 D4
2 1.88 0.00 3.27
3 1.02 0.00 2.57
4 0.73 0.00 2.28
5 0.58 0.00 2.11
6 0.48 0.00 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86
9 0.34 0.18 1.82
10 0.31 0.22 1.78
11 0.29 0.26 1.74
12 0.27 0.28 1.72
13 0.25 0.31 1.69
14 0.24 0.33 1.67
15 0.22 0.35 1.65
Factors for R-Chart
Sample Size
(n)
16

17. 17

18.  Use this method when sigma for the process
distribution is not know
 Control limits solution:
( )
( ) 15.75.2330.7315.92RAxLCL
16.09.2330.7315.92RAxUCL
.233
3
0.20.30.2
R
2x
2x
=−=−=
=+=+=
=
++
=
18

19. CH. NARASIMHA RAO, A TEXT BOOK OF
BIOSTASTICS.
REMINGTON, PRAMACEUTICAL PRACTICE, 19TH
EDITION.
19

20. 20
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