A General EXCEL Solution for
LTPD Type Sampling Plans
David C. Trindade, Ph.D.
Sun Microsystems
David Meade
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
n = 50
Probability of Acceptance
1.00
c =3
0.90
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.
EXCEL Solution (Add-In)
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
Final Comments
• Description and theory presented in paper.
• LTPD add-in and paper available for
download from
www.trindade.com/LTPD.html
• Questions to:
– david.trindade@eng.sun.com
– david.meade@amd.com (VB programming)