Statistical Quality Control
A Presentation BY
Aman Wadhawan 89
Rahul Chowdhry 67
Akshay Karnatak 70
Meaning Of Statistical Quality Control
Statistical quality control can be simply defined
as an economic & effective system of
maintaining & improving the quality of outputs
throughout the whole operating process of
specification, production & inspection based on
continuous testing with random samples
Categories Of SQC
Causes Of Variation In Quality
Method Of SQC
It extend the use of descriptive statistics to monitor the
quality of the product and process
Under this the quality of the products is controlled while
the products are in the process of production.
It is secured with the technique of control charts
PURPOSE & USES OF CONTROL CHARTS
A control chart (also called process chart or
quality control chart) is a graph that shows
whether a sample of data falls within the
common or normal range of variation.
Helps in determining the quality standard of
Helps in detecting the chance & assignable
variations in the quality standards by setting
two control limits
Indicates whether the production process is in
control or not.
Ensures less inspection cost & time in the
Types Of Control Charts
Chart For Variables
A mean control chart is often referred to
as an x-bar chart. It is used to monitor
changes in the mean of a process.
To construct a mean chart we first need
to construct the center line of the chart.
To construct the upper and lower control limits of the chart, we use the following
Upper control limit(UCL) =
Lower control limit (LCL) =
= the average sample means
Z = standard normal variable (2 for 95.44% confidence, 3 for 99.74%
= standard deviation of the distributed sample means, computed as
= population (process) standard deviation
N = sample size
A quality control inspector at the Cocoa Fizz soft drink company has taken 5 samples with
four observations each of the volume of bottles ﬁlled. The data and the computed
means are shown in the table. If the standard deviation of the bottling operation is
0.14 ounces, use this information to develop control limits of three standard deviations
for the bottling operation.
The control limits are
RANGE - CHART
Range (R) charts are another type of
control chart for variables.
Whereas x-bar charts measure shift in the
central tendency of the process, range
charts monitor the dispersion or variability
of the process.
The method for developing and using Rcharts is the same as that for x-bar charts.
The center line of the control chart is the
average range, and the upper and lower
control limits are computed as follows.
CL = R
UCL = D4. R
LCL = D3. R
Where as , CL =central line
UCL = upper control limit
LCL = lower control limit
D3 and D4 are factors of r chart
Using Mean and Range Charts Together
You can see that mean and range
charts are used to monitor different
variables. The mean or x-bar chart
measures the central tendency of
the process, whereas the range
chart measures the dispersion or
variance of the process. Since both
variables are important, it makes
sense to monitor a process using
A control chart used to monitor the number
of defects per unit.
Examples are the number of returned
meals in a restaurant, the number of trucks
that exceed their weight limit in a
month, and the number of bacteria in a
milliliter of water.
WHEN TO USE C-CHART?
C-Charts for discrete
defects when there can be
more than one defect per
of flaws or stains
in a carpet sample cut
from a production run
of complaints per
customer at a hotel
Note that the types of units of measurement we are considering are a period
of time, a surface area, or a volume of liquid.
The average number of defects, is the center line of the control chart. The
upper and lower control limits are computed as follows:
Sometimes it is necessary (or
convenient) to look at the number
of defective items rather than the
proportion of defective items.
we use np - charts instead of p – charts
Difference between p - charts and
np - charts is that in the later case
y-axis represents the number of
defective items in a subgroup
No Of Defective Pens
CL= np- bar
Np-bar= total no of defects/ total no
Np-bar= 7/5= 1.4
LCL = np − 3√np(1 − p),
P= proportion of defect/total units