1. Statistical Quality Control
A Presentation BY
Aman Wadhawan 89

Namish Mishra
86

Rahul Chowdhry 67

Mohit Singh

88
Akshay Karnatak 70

2. 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

3. Categories Of SQC
Descriptive statistics
Statistical Process
Control
Acceptance Sampling

4. Causes Of Variation In Quality
Common Causes
Of Variation
Assignable Causes
Of Variation

5. Method Of SQC
Process Control
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

6. 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
the products.

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
process control.

7. Types Of Control Charts
 Control
Chart For Variables
X-Chart
R-Chart
 Control
Chart For
Attributes
P-Chart
NP-Chart
C-Chart

8. X-Chart

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.

9. 
To construct the upper and lower control limits of the chart, we use the following
formulas.

Upper control limit(UCL) =

Lower control limit (LCL) =

Where,
= 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
confidence)

10. Question
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.

11. Solution
= 15.95
The control limits are
UCL =
LCL =

12. 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.

13. 
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

18. 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
both mean.

20. C-CHART

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.

21. WHEN TO USE C-CHART?
Use
C-Charts for discrete
defects when there can be
more than one defect per
unit
Number
of flaws or stains
in a carpet sample cut
from a production run
Number
of complaints per
customer at a hotel

22. 
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:
UCL
c
c
z c
LCL
c
c
z c

23. C-CHART EXAMPLE

25. EXAMPLE USING SPREADSHEET

27. NP Chart
•
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

28. Example
Serial No.
Sample Size
No Of Defective Pens
1
100
2
2
121
2
3
81
0
4
100
1
5
121
2
Total
523
7

29. Solution

CL= np- bar

Np-bar= total no of defects/ total no
inspected samples

Np-bar= 7/5= 1.4

LCL = np − 3√np(1 − p),

1.4- 3√1.4(1-0.0133)=-2.13

UCL= np+3√np(1-p)

UCL= 4.93

P= proportion of defect/total units

30. SQC in Services

Service Organizations have lagged behind
manufacturers in the use of statistical quality control

Statistical measurements are required and it is more
difficult to measure the quality of a service



Services produce more intangible products
Perceptions of quality are highly subjective
A way to deal with service quality is to devise
quantifiable measurements of the service element

Check-in time at a hotel

Number of complaints received per month at a
restaurant

Number of telephone rings before a call is answered

Acceptable control limits can be developed and charted
© Wiley 2007

31. SQC Across the Organization

SQC requires input from other organizational
functions, influences their success, and are
actually used in designing and evaluating their
tasks




© Wiley 2007
Marketing – provides information on current and
future quality standards
Finance – responsible for placing financial values on
SQC efforts
Human resources – the role of workers change with
SQC implementation. Requires workers with right
skills
Information systems – makes SQC information
accessible for all.