6.2.3.1. Choosing a Sampling Plan: MIL
Standard 105D
The AQL or
Acceptable
Quality
Level is the
baseline
requirement
Sampling plans are typically set up with reference to an
acceptable quality level, or AQL . The AQL is the base line
requirement for the quality of the producer's product. The
producer would like to design a sampling plan such that the
OC curve yields a high probability of acceptance at the AQL.
On the other side of the OC curve, the consumer wishes to be
protected from accepting poor quality from the producer. So
the consumer establishes a criterion, the lot tolerance percent
defective or LTPD . Here the idea is to only accept poor
quality product with a very low probability. Mil. Std. plans
have been used for over 50 years to achieve these goals.
The U.S. Department of Defense Military Standard 105E
Military
Standard
105E
sampling
plan
Standard military sampling procedures for inspection by
attributes were developed during World War II. Army
Ordnance tables and procedures were generated in the early
1940's and these grew into the Army Service Forces tables. At
the end of the war, the Navy also worked on a set of tables. In
the meanwhile, the Statistical Research Group at Columbia
University performed research and outputted many
outstanding results on attribute sampling plans.
These three streams combined in 1950 into a standard called
Mil. Std. 105A. It has since been modified from time to time
and issued as 105B, 195C and 105D. Mil. Std. 105D was
issued by the U.S. government in 1963. It was adopted in
1971 by the American National Standards Institute as ANSI
Standard Z1.4 and in 1974 it was adopted (with minor
changes) by the International Organization for Standardization
as ISO Std. 2859. The latest revision is Mil. Std 105E and was
issued in 1989.
These three similar standards are continuously being updated
and revised, but the basic tables remain the same. Thus the
discussion that follows of the germane aspects of Mil. Std.
105E also applies to the other two standards.
Description of Mil. Std. 105D
Military
Standard
105D
sampling
This document is essentially a set of individual plans,
organized in a system of sampling schemes. A sampling
scheme consists of a combination of a normal sampling plan,
a tightened sampling plan, and a reduced sampling plan plus
plan
rules for switching from one to the other.
AQL is
foundation
of standard
The foundation of the Standard is the acceptable quality level
or AQL. In the following scenario, a certain military agency,
called the Consumer from here on, wants to purchase a
particular product from a supplier, called the Producer from
here on.
In applying the Mil. Std. 105D it is expected that there is
perfect agreement between Producer and Consumer regarding
what the AQL is for a given product characteristic. It is
understood by both parties that the Producer will be
submitting for inspection a number of lots whose quality level
is typically as good as specified by the Consumer. Continued
quality is assured by the acceptance or rejection of lots
following a particular sampling plan and also by providing for
a shift to another, tighter sampling plan, when there is
evidence that the Producer's product does not meet the agreedupon AQL.
Standard
offers 3
types of
sampling
plans
Mil. Std. 105E offers three types of sampling plans: single,
double and multiple plans. The choice is, in general, up to the
inspectors.
Inspection
level
In addition to an initial decision on an AQL it is also necessary
to decide on an "inspection level". This determines the
relationship between the lot size and the sample size. The
standard offers three general and four special levels.
Steps in the
standard
The steps in the use of the standard can be summarized as
follows:
Because of the three possible selections, the standard does not
give a sample size, but rather a sample code letter. This,
together with the decision of the type of plan yields the
specific sampling plan to be used.
1.
2.
3.
4.
5.
6.
7.
Decide on the AQL.
Decide on the inspection level.
Determine the lot size.
Enter the table to find sample size code letter.
Decide on type of sampling to be used.
Enter proper table to find the plan to be used.
Begin with normal inspection, follow the switching
rules and the rule for stopping the inspection (if
needed).
Additional
information
There is much more that can be said about Mil. Std. 105E,
(and 105D). The interested reader is referred to references
such as (Montgomery (2000), Schilling, tables 11-2 to 11-17,
and Duncan, pages 214 - 248).
There is also (currently) a web site developed by Galit
Shmueli that will develop sampling plans interactively with
the user, according to Military Standard 105E (ANSI/ASQC
Z1.4, ISO 2859) Tables.