# A General EXCEL Solution for LTPD Type Sampling Plans by ciq80626

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```									  A General EXCEL Solution for
LTPD Type Sampling Plans
David C. Trindade, Ph.D.
Sun Microsystems
AMD

1999 Joint Statistical Meetings          Baltimore, MD
Lot Acceptance Sampling
• Assume single random sample of size n
from a process or a very large lot.
• Binomial distribution is appropriate.
• Refer to as type B sampling.
Sampling Plan
• Specifies
– the sample size n
– the acceptance number c
• An operating characteristic (OC) curve
shows the probability of lot acceptance for a
given level of incoming lot percent
defective p
OC Curve
1.00                       n = 50    c =3
0.90
Probability of Acceptance

0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0%   2%   4%   6%     8%     10% 12% 14% 16% 18% 20%
Lot Percent Defective
LTPD Plans
• The quality level at 10% probability of acceptance
(consumer’s risk) is called the LTPD.
• This rejectable quality level (RQL) is highest
percent defective (poorest quality) tolerable in a
small percentage of product.
• Borderline of distinction between a satisfactory lot
and an unsatisfactory one.
• LTPD plans are used for many product
qualification plans to assure consumer protection.
Common Sampling Problem in
Industry
• There are constraints on sample size based
on limited time, money, or other resources.
• There is often the need to adjust sample size
and corresponding acceptance number
while holding LTPD constant.
LTPD Tables
Limitations of Tables
• LTPD values restricted to only those listed.
• There are finite ranges of sample sizes and
acceptance numbers.
Example Case
• Reliability qualification plan for integrated circuits
calls for stressing a sample of 300 units for 1000
hours. Pass requirement is no more than three
failures.
• Early samples are precious, costing approximately
\$10,000 each and are needed for other evaluations.
• How can the engineer reduce the sample size and
allowed failures while holding the LTPD
constant?
Approaches by Engineer
• First, the LTPD value must be determined.
• Then, LTPD tables may be consulted to see
if n = 300 and c = 3 are tabulated.
• Approximation may be necessary:
– Checking LTPD table, we see n = 333 and c = 3
for LTPD = 2%.
– For c = 1, LTPD = 2%, we need n = 195.
Graphical Techniques*

*Applied Reliability, 2nd ed., P. Tobias and D. Trindade
Graphical Results
• For n = 300, c = 3, LTPD = 2.2%.
• For LTPD = 2.2%, c = 1, n ~ 180.

There is a limitation in these graphs to
only c = 0, 1, 2, or 3.
Find LTPD for Given Sampling Plan
Find LTPD for a Given sampling
Plan: Output
Find Alternative LTPD Sampling Plan
Find Alternative Sampling Plan: Output
Find Sample Size for Given c
Find Sample Size for Given c: Output