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
                      David Meade

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
Probability of Acceptance

                                   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
• 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
• 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
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
• Questions to:
  – david.trindade@eng.sun.com
  – david.meade@amd.com (VB programming)

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