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2 Comments / Manufacturing Sampling Plans / By Wayne Taylor
Recent Posts
Dr. Wayne A. Taylor
Acceptance Sampling Standards
Mil-Std-105E indexes sampling plans by AQL, Levels of Inspection, and lot size. It is a
common misconception that 105E includes lot size because “larger lots require more samples
to obtain the same level of protection.” In actuality, 105E takes more samples from larger
lots in order to get better protection. Figure 1 shows the OC curves of several of the 1.0% AQL
sampling plans. Increasing lot size increases the sample size letter code which steepens the
OC curve resulting in better protection.
STAT-18: Statistical Techniques for Normality Testing and
Transformations
STAT-16: Statistical Techniques for Equivalence Testing
STAT-12: Veri cation/Validation Sampling Plans for
Proportion Nonconforming
STAT-04: Statistical Techniques for Design Veri cation
Categories
Audits and Effectiveness Checks
Design of Experiments
Design Validation (Clinical and User Testing)
Design Veri cation (Product Testing)

Manufacturing Sampling Plans
Normality Testing and Transformations
Process Validation (Process and Supplier Testing)
Spec Setting, Tolerance Analysis and Robust Design
Statistical Policy and General
Figure 1: AQL=1% OC Curves
Test Method Validation
Trending of Quality Data
Better protection for larger lots can be justi ed by the fact that for larger lots the costs of
rejecting good lots and the costs of accepting bad lots are higher. Since the consequences of
making wrong decisions are higher, it is logical to take more samples to lower the risk of
Validation Sampling Plans
making wrong decisions.
While this justi cation has merit when considering a single product, 105E is used to inspect a
Archives
variety of products. Should more samples be selected from a large lot of pencils or from a
September 2018
small lot of pace makers? To overcome this objection, different levels of inspection are
August 2018
provided. 105E states that these inspection levels are to be selected based on the
October 2017
“discrimination” required.
September 2017
The “discrimination” or protection provided by a sampling plan depends primarily on the
number of units inspected and the acceptance number. Lot size has only a minor effect limited
December 2004
to the case when 10% or more of the lot is inspected. As a result, the single sampling plan
August 2002
n=13 and a=0 provides the same protection regardless of whether the lot size is 50, 200, or
April 2000
200,000. Figure 2 shows OC curves for these different lot sizes. OC curves based on lot size,
are called Type-A OC curves (hypergeometric distribution). They are closely approximated by
May 1998
the Type-B OC curve which assumes an in nite lot size (binomial distribution). The Type-B OC
December 1997
Curve represents the worse case. It has the greatest chance of both accepting bad lots and
rejecting good lots.
October 1997
September 1997
May 1997
October 1996
May 1996
October 1995
February 1995
November 1994
September 1994
March 1994
November 1993
Figure 2: OC Curves of n=13, a=0
Since Type-B OC curves represent the worse case, sampling plans selected based on Type-B
OC curves can be used to inspect any lot regardless of size. When selecting statistically valid
sampling plans, it is not necessary to use different sampling plans for different lot sizes. A
better strategy is to select one sampling plan based on the protection it provides, i.e., its OC
curve. The OC curves of the 105E plans are given in Table X of 105E. Tables of sampling
plans indexed by their OC curves are given in my book.
Appeared in FDC Control, Food Drug & Cosmetic Division ASQC, No. 103, Sept. 1994, p. 6
Copyright © 1994 Taylor Enterprises, Inc.
Note:
All the OC curves shown in Mil=Std-105E are Type-B, so do not depend on lot size.
Another justi cation of selecting sampling plans independent of lot size is given on
pages 2-3 and 188 of the book Statistical Procedures for the Medical Device Industry.
When sampling plans are selected based on risk, the risk components Severity,
Occurrence, Detection, P1, P2 do not depend on lot size so the resulting sampling plans
should not depend on lot size.
Further information can be found in:
Book Guide to Acceptance Sampling
Software package Sampling Plan Analyzer
STAT-09, Manufacturing Acceptance Sampling Plans and Inspections, of the
book Statistical Procedures for the Medical Device Industry
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2 thoughts on “The E ect of Lot Size”
LEE SEUNG RYUL
SEPTEMBER 22, 2022 AT 6:51 PM
Dear. Dr. Wayne A. Taylor
My name is Lee Seung Ryul and I am a pharmaceutical company QA.
I saw your article, and I am very interested.
I also do not apply sample quantity based on lot size.
Currently, we have a xed quantity of 125 such that C=0 based on AQL Limit=0.1.
This basis was established using OC Curve, hypergeometric distribution, and customer risk.
However, we do not accept data on this during the audit.
Could you please help on this part?
You are the only person who can credibly support this.
Please help.
Reply
WAYNE TAYLOR
SEPTEMBER 28, 2022 AT 9:33 AM
The hypergeometric distribution is used for OC curves based on lot size. It is based on the lot
percent defective (X/N, X = number of defects, N = lot size) The binomial distribution is used
for OC curves independent of lot size. It is based on the process percent defective (p =
probability of a defect). I assume your statement about the hypergeometric is in error. The OC
curves in ANSI Z1.4 are based on the binomial distribution ass described in
Variation.com/the-effect-of-lot-size/.
The reason ANSI Z1.4 includes lot size as an index is not due to the effect of lot size on OC
curve. It is based on an economic model that states as lot size increases the costs of making
incorrect decisions increase so the OC curve should be tightened for larger lots. While there
is some validity to this statement, there is still the question of what should the relationship be
between lot size and the OC curve. This leads to multiple levels of inspection to choose
between affecting the RQL of the selected sampling plan.
An alternative is to select lot size independent sampling plans directly based on just the AQL
and RQL. This simpli es the process of selecting a sampling plan and aligns it with using a
risk-based approach. Pages 2, 133 and 188 of the book Statistical Procedures for the Medical
Device Industry justify this approach based on the fact that for a risk-based approach for
selecting sampling plans, the fact that risk is lot size independent means the resulting
sampling plans will be lot size independent.
Reply
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