1. 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

2. 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.

3. 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

5. 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.

6. 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.

7. LTPD Tables

8. Limitations of Tables LTPD values restricted to only those listed.
There are finite ranges of sample sizes and acceptance numbers.

9. 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?

10. 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.

11. Graphical Techniques*
*Applied Reliability, 2nd ed., P. Tobias and D. Trindade

12. 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.

13. EXCEL Solution (Add-In)

14. Find LTPD for Given Sampling Plan

15. Find LTPD for a Given sampling Plan: Output

16. Find Alternative LTPD Sampling Plan

17. Find Alternative Sampling Plan: Output

18. Find Sample Size for Given c

19. Find Sample Size for Given c: Output

20. Final Comments Description and theory presented in paper.
LTPD add-in and paper available for download from
Questions to:
(VB programming)