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Introduction to
SAMPLING PLAN
• References Used for preparing this presentation:
• Introduction to Statistical Quality Control, 6th
Edition by Douglas C. Montgomery.
• http://dl4a.org/uploads/pdf/581SPC.pdf
• Reference Used is Chapter 11:
– Reading: (Handout) E.L Grant and R.S.
Leavenworth, Statistical Quality Control 7th Edition,
pp. 444-448, 451-454
– Problems: 11.6, 11.7, p. 458
SAMPLING PLAN
DOUBLE SAMPLING PLAN
OBJECTIVES
• To collect samples that are representative and
then to ensure that changes in composition do
not take place between collection and
analysis.
• Understand the role of acceptance sampling in
modern quality control system
• Understand the advantages & disadvantages
of sampling plan
INTRODUCTION
• A double sampling plan is more difficult to construct and more difficult to implement than a single sampling plan. However, it has the following advantages:
– A double sampling plan may give similar
levels of the consumer’s and the producer’s
risk but require less sampling in the long run
than a single sampling plan
Double Sampling Plan
• In an effort to reduce the amount of inspection
double (or multiple) sampling is used. Whether
or not the sampling effort will be reduced
depends on the defective proportions of
incoming lots. Typically, four parameters are
specified:
n1= number of units in the first sample
c1 = acceptance number for the first sample
n2= number of units in the second sample
c2 = acceptance number for both samples
First Random
sample
Lot
C1 r1
First sample inconclusive,
take second sampleReject LotAccept Lot
Compare number of defective found in the first random sample to C1
and r1 and make appropriate decision.
Double Sampling Plan
C2
Reject LotAccept Lot
Compare the total number of defective in both lots to C2 and make
the appropriate decision
Lot First Random sample
Second Random sample
Double Sampling Plan
PROCEDURE
• A double sampling plan proceeds as follows:
A random sample of size n1 is drawn from the lot.
If the number of defective units (say d1 ) ≤ c1 the lot is accepted.
If d1> c2 the lot is rejected.
If neither of these conditions are satisfied a second sample of size n2 is drawn from the lot.
If the number of defectives in the combined samples (d1 + d2) > c2 the lot is rejected. If not the lot is accepted.
Double Sampling Plan Example
• A double sampling plan is associated with four
numbers:
• The interpretation of the numbers is shown by
an example:
• 1. Inspect a sample of size 20
• 2. If the sample contains 3 or less defectives,
accept the lot
• 3. If the sample contains more than 5 defectives,
reject the lot.
531020 2121 ==== ccnn ,,, Let
2121 ccnn and ,,
• If the sample contains more than 3 and less than or
equal to 5 defectives (i.e., 4 or 5 defectives), then
inspect a second sample of size 10
• 5. If the cumulative number of defectives in the
combined sample of 30 is not more than 5, then accept
the lot.
• 6. Reject the lot if there are more than 5 defectives in the combined lot of 30
Double Sampling Plan
Finding Probability of Acceptance • Example: Assume that a lot contains 2% defectives.
If the double sampling plan with
• is used, what is the probability that the lot will be
accepted? Assume that the lot size is large enough for
Table G to be applicable.
Solution: The solution to the above problem takes a tree
structure that is shown next. Computing probabilities at
all the branches and nodes, the probability of
acceptance is:
531020 2121 ==== ccnn ,,,
r=0
Sam
ple 1
r=4
r=5
Sample 2
Sample 2
Accept lot
Reject lot
0≤r≤
3
r≥6
r=4
r=5
Accept lot
Accept lot
Reject lot
Reject lot
r=0
r≤1
r≥2
r≥1
Chapter 15
Introduction to Statistical Quality Control, 6th Edition by Douglas C.
Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.17
Objectives
�Explain the purpose of acceptance
sampling
�Contrast acceptance sampling and
process control
�Compare and contrast single- and
multiple-sampling plans
COMPARISON Sr.No. FACTOR SINGLE DOUBLE SEQUENTIAL
1 No. of sample One Two Small group
2 Sample size Large First sample size is half
of the single sample
size
1 unit or 1 group
at a time
3 Decision for
acceptance or
rejection
Based on
result in
sample
inspection
Base on result of 1st as
well as2nd inspection
combine
Based on the no.
of defective
relative to
acceptance or
rejection lines
4 Inspection cost High Less Much lower
5 Inspection load
variation
Inspection
load is
constant
Depend on he result of
1st sample
Highly variable
6 Data handling
analysis load
Least Higher Maximum
7 Average sample
size
High intermediate Low