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