various QC techniques for operators

1. STATISTICAL
QUALITY
CONTROL
(S.Q.C.)

2. Contents-:
Meaning…………….
Definitions …………
Characteristics………
Causes of variations……….
Methods of S.Q.C………..
Process Control-:
Control Chart………..
Purpose & uses of control charts……….
Types of control charts………
Control charts for variables-:
Chart……
R Chart ……
σ Chart………

3. Control chart for attributes-:
p-chart…………
np-chart…......
C-Chart…………
Product Control/Acceptance Sampling-:
Meaning…………..
Definition………….
Risks in Acceptance Sampling-:
Producer’s Risk……….
Consumer’s Risk……….
Types of Sampling Inspection plans-:
Single Sampling plan………
Double Sampling Plan……..
Multiple Sampling Plan…….
Advantages of S.Q.C……………
Limitations of S.Q.C…………….

5. MEANING-:
 manufactured Refers to the use of
statistical techniques in controlling the
quality of goods.
 Means of establishing & achieving
quality specification, which requires use
of tools & techniques of statistics.

6. DEFINATION-:
“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.”
By-:
YA LUN CHOU

7. Definition-:
“Statistical quality control should be
viewed as a kit of tools which may
influence decisions to the functions of
specification, production or inspection.
By-:
EUGENE L. GRANT

8. CHARACTERISTICS OF S.Q.C.-:
 Designed to control quality standard of goods
produced for marketing.
 Exercise by the producers during production to
assess the quality of goods.
 Carried out with the help of certain statistical tools
like Mean Chart, Range Chart, P-Chart, C-Chart etc.
 Designed to determine the variations in quality of the
goods & limits of tolerance.

9. CAUSES OF VARIATIONS IN
QUALITY-:
1. ASSIGNABLE CAUSES-: It refers to those
changes in the quality of the products which
can be assigned or attributed to any
particular causes like defective materials,
defective labour, etc.
2. CHANCE CAUSES-: These causes take place
as per chance or in a random fashion as a
result of the cumulative effect of a
multiplicity of several minor causes which
cannot be identified. These causes are
inherent in every type of production.

10. METHODS OF S.Q.C.-:
1. PROCESS CONTROL-: Under this the
quality of the products is controlled while
the products are in the process of
production.
The process control is secured with the
technique of control charts. Control charts
are also used in the field of advertising,
packing etc. They ensures that whether the
products confirm to the specified quality
standard or not.

11. A control chart is a time plot of a statistic, such as a sample mean, range,
standard deviation, or proportion, with a center line and upper and lower
control limits. The limits give the desired range of values for the statistic.
When the statistic is outside the bounds, or when its time plot reveals certain
patterns, the process may be out of control.
A process is considered in statistical control if it has no assignable causes,
only natural variation.
UCL
LCL
Center
Line
Time
Value
This point is out of the control limits
3
3
Control Chart

12. PURPOSE & USES OF CONTROL
CHARTS
1. Helps in determining the quality standard of
the products.
2. Helps in detecting the chance & assignable
variations in the quality standards by setting
two control limits.
3. Reveals variations in the quality standards of
the products from the desired level.
4. Indicates whether the production process is
in control or not.
5. Ensures less inspection cost & time in the
process control.

13. Types-:
Types of
Control
Charts
Control
Charts
for
Variables
Chart
Control
Charts for
Attributes
R-Chart σ-Chart p-Chart np-Chart C-Chart

14. CONTROL CHATS FOR
VARIABLES
 CHART/ MEAN CHART-: This chart is
constructed for controlling the variations in
the average quality standard of the products
in a production process.
 R-CHART-: This chart is constructed for
controlling the variations in the dispersion or
variability of the quality standards of the
products in a production process.

15. EXAMPLE-:
Sample No. Weights
1
2
3
4
5
20 15 10 11 14
12 18 10 8 22
21 19 17 10 13
15 12 19 14 20
20 19 26 12 23
Conversion factors for n=5, A2 =0.577, D3 =0,
D4=2.115

16. Solution-:
Sample
no.
Weights (X) Total
Weights
(ΣX)
=(ΣX/5)
Range
R=(L-S)
1
2
3
4
5
K=5
20 15 10 11 14
12 18 10 8 22
21 19 17 10 13
15 12 19 14 20
20 19 26 12 23
70
70
80
80
100
14
14
16
16
20
Σ =80
10
14
11
8
14
ΣR=57

17. Grand = Σ /K = 80/5=16
Grand Chart
Grand = 16 (Central line)
Control limits-:
UCL = Grand + A2
= 16 + 0.577 x 11.4
= 22.577
LCL = Grand - A2
= 16 – 0.577 x 11.4
= 9.423

18. = ΣR/K = 57/5 = 11.4
Range Chart
= 11.4 (Central line)
Control limits-:
UCL = D4.
= 2.115 x 11.4
= 24.09
LCL = D3.
= 0 x 11.4
= 0

19. σ Chart-: This chart is constructed to get a better picture of
the variations in the quality standard in a process than that is
obtained from the range chart provided the standard deviation(σ)
of the various samples are readily available.
Example-: Quality control is maintained in a factory with
the help of standard deviation chart. Ten items are chosen in
every sample. 18 samples in all were chosen whose ΣS was
8.28. Determine the three sigma limits of σ- chart. You may use
the following-:
n = 10, B3 = 0.28, B4 = 1.72, K = 18.
Solution-: = ΣS/K = 8.28/18 = 0.46
UCL = B4. LCL = B3.
= 1.72 x 0.46 = 0.28 x 0.46
= 0.7912 = 0.1288

20. Control Charts for Attributes-:
 p-chart-: This chart is constructed for controlling
the quality standard in the average fraction defective
of the products in a process when the observed
sample items are classified into defectives & non-
defectives.
 np-chart-: This chart is constructed for controlling
the quality standard of attributes in a process where
the sample size is equal & it is required to plot the no.
of defectives (np) in samples instead of fraction
defectives (p).

21. Example-:
Sample No. Size of sample
(n)
No. of
defectives (d)
Fraction
defectives (d/n)
1
2
3
4
5
6
7
8
9
10
100
100
100
100
100
100
100
100
100
100
5
3
3
6
5
6
8
10
10
4
0.05
0.03
0.03
0.06
0.05
0.06
0.08
0.1
0.1
0.04
K = 10 Σd = 60

22. = Total no. of defectives/Total no. of units =
60/1000 = 0.06
»q̅ = 1- = 1- 0.06 = 0.94
= 0.06 (central line)
UCL = + 3√ . q̅/n
= 0.06 + 3√0.06x0.94/100
= 0.1311
LCL = - 3 √ . q̅/n
= 0.06 - 3 √ 0.06x0.94/100
= -0.0111 = 0

24. Example-:
An inspection of 10 samples of size 400 each from 10 lots reveal
the following number of defectives:
17, 15, 14, 26, 9, 4, 19, 12, 9, 15
Calculate control limits for the no. of defective units.
Solution-: n = 400, k (No. of samples) = 10, Σd (total no. of
defectives) = 140
n = Σd/k = 140/10 = 14
Now, = n /n = 14/400 = 0.035,
»q̅ = 1- = 1- 0.035 = 0.965
n = 14 (central line)
UCL= n + 3√ n q̅ LCL= n - 3√ n q
̅ = 14 + 3√400x0.035x0.965 = 14 - 3√400x0.035x0.965
= 25.025 = 2.975

26.  C-Chart-: This chart is used
for the control of no. of
defects per unit say a piece
of cloth/glass/paper/bottle
which may contain more than
one defect. The inspection
unit in this chart will be a
single unit of product. The
probability of occurrence of
each defect tends to remain
very small.

27. USES-:
The following are the field of application
of C-Chart-:
 Number of defects of all kinds of
aircraft final assembly.
 Number of defects counted in a roll of
coated paper, sheet of photographic
film, bale of cloth etc.

28. ACCEPTANCE SAMPLING
Meaning-:
Another major area of S.Q.C. is “Product
Control” or “Acceptance Sampling”. It is
concerned with the inspection of
manufactured products. The items are
inspected to know whether to accept a
lot of items conforming to standards of
quality or reject a lot as non-
conforming.

29. DEFINITION-:
“ Acceptance Sampling is concerned with the
decision to accept a mass of manufactured
items as conforming to standards of quality or
to reject the mass as non-conforming to
quality. The decision is reached through
sampling.”
By-:
SIMPSON AND KAFKA

30. Risks in Acceptance sampling
1. Producer’s risk-: Sometimes inspite of good
quality, the sample taken may show defective
units as such the lot will be rejected, such
type of risk is known as producer’s risk.
2. Consumer’s Risk-: Sometimes the quality of
the lot is not good but the sample results
show good quality units as such the consumer
has to accept a defective lot, such a risk is
known as consumer’s risk.

31. Types of Sampling Inspection Plan
Single Sampling Plan-: Under single
sampling plan, a sample of ‘n’ items is
first chosen at random from a lot of N
items. If the sample contains, say, ‘c’ or
few defectives, the lot is accepted,
while if it contains more than ‘c’
defectives, the lot is rejected (‘c’ is
known as ‘acceptance number’).

32. Single Sampling Plan
Count the no. of defectives,
‘d’ in the sample of size ‘n’
Is ‘d’ ≤ ‘c’
If yes, than accept the lot If no, then reject the lot

33. Double Sampling Plan-:
Under this sampling plan, a sample of ‘n1’ items is
first chosen at random from the lot of size
‘N’. If the sample contains, say, ‘c1’ or few
defectives, the lot is accepted; if it contains
more than ‘c2’ defectives, the lot is rejected.
If however, the number of defectives in the
sample exceeds ‘c1’, but is not more than ‘c2’, a
second sample of ‘n2’ items is take from the
same lot. If now, the total no. of defectives in
the two samples together does not exceed
‘c2’, the lot is accepted; otherwise it is
rejected. (‘c1’ is known as acceptance no. for
the first sample & ‘c2’ is the acceptance no. of
both the samples taken together)

34. Double Sampling Plan-:
Count the no. of defectives,
d1in the first sample of size n1
Is d1 ≤ c1 ?
Draw another sample of
size n2
If No, then check
If c1 ≤ d1 ≥ c2 ?
Count the no. of defectives d2 in
this sample
Is d1 + d2 ≤ c2
If No, reject the lot
If yes, accept the lot
If yes, then accept
the lot.

35. Multiple Sampling Plan-:
Under this sampling plan, a decision to
accept or reject a lot is taken after
inspecting more than two samples of
small size each. In this plan, units are
examined one at a time & after
examining each unit decision is taken.
“However, such plan are very
complicated & hence rarely used in
practice.”

36. ADVANTAGES OF S.Q.C.-:
 Helpful in controlling quality of a
product
 Eliminate Assignable causes of variation
 Better quality at lower inspection cost
 Useful to both consumers & producers
 It makes workers quality conscious
 Helps in earn goodwill

37. LIMITATIONS-:
 Does not serve as a ‘PANACEA’ for all
quality evils.
 It cannot be used to all production
process.
 It involves mathematical & statistical
problems in the process of analysis &
interpretation of variations in quality.
 Provides only an information services.

38. THE
END