INTRODUCTION TO ENGINEERING ECONOMICS Chapter 1: Engineering Decision Making

1
Double and Multiple Sampling Plan

• Outline
• Double Sampling Plan
• Multiple Sampling Plan

2
Double Sampling Plan

• 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 consumers and the producers risk but
  require less sampling in the long run than a
  single sampling plan

3
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.

4
Double Sampling Plan Example
4. 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
5
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
6
(No Transcript)
7
Multiple Sampling Plan Finding Probability of
Acceptance

• Double sampling plans may be extended to triple
  sampling plans, which may also be extended to
  higher order plans. The logical conclusion of
  this process is the multiple or sequential
  sampling plan.
• Multiple sampling and sequential sampling are
  very similar. Usually, in a multiple sampling
  plan the decisions (regarding accept/reject/contin
  ue) are made after each lot is sampled. On the
  other hand, in a sequential sampling plan, the
  decisions are made after each item is sampled. In
  a multiple sampling 3 or more samples are taken.
  A sequential sampling may not have any limit on
  the number of items inspected.

8
Text Problem 11.6 (modified) A multiple sampling
plan is as follows Sample Individual
Combined Acceptance Rejection Number Sample
Size Sample Size Number Number 1
5 5
-- 2 2 5
10 0
2 3 5 15
1 3 4
5 20 2
3 Assuming that lot size is large
enough for Table G to be applicable, compute the
probability of acceptance of a 10 defective lot.

9
(No Transcript)