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AN ANALYSIS OF THE LONG RANGE OPERATING CHARACTERISTICS 
OF THE MIL-STD-105D SAMPLING SCHEME AND SOME SUG- 
GESTED MODIFICATIONS 


Gerald G. Brown 

Naval Postgraduate School, 
Monterey, California 

and 

Herbert C. Rutemiller 
California State University, Fullerton 


ABSTRACT 

An integral part of the MIL-STD-105D scheme for sampling inspection by attributes is 
the transfer from normal inspection to reduced or tightened inspection when the historical 
record of inspected lots suggests unusually good or bad quality. The switching rules in 
MIL-STD-105D have been cridcized, especially by Japanese manufacturers, as being too 
severe when what is defined as acceptable quality material is submitted. This paper examines 
the long range fraction of lots rejected for several MIL-STD-105D sampling plans by using 
the MIL-STD-105D switching rules, using a modification suggested by the Japanese 
Standards Association, and by using a second modification developed by the authors. 

The Japanese Standards Association switching rules are more complex than those in 
MIL-STD-105D. It is demonstrated that they lead to improved long-range properties for 
Normal-Tightened-Reduced schemes, but to poorer properties for Normal-Tightened 
schemes. 

A simplified set of switching rules is suggested, wherein the “limit numbers" in MIL— 
STD-105D are eliminated. In comparison to MIL-STD-105D, the simpler rules lead to a 
lower probability of rejection for good lots and a comparable probability of rejection for 
bad lots. 


1. INTRODUCTION 

The sampling scheme designated as MIL-STD-105D [4] has been widely adopted throughout 
the western world for lot-by-lot sampling inspection by attributes. The sampling plans in this document 
are indexed by lot size and by a number called the acceptable quabty level (AQL). The AQL is specified 
by the consumer. The AQL is a designated percentage defective which, ifTnet by the supplier, will 
lead to acceptance of the great majority of lots [4, sec. 4.3]. MIL-STD-lOfiD provides two parameters 
for each sampling plan, a sample size, n, and acceptance number, c. If c or fewer defectives are found 
in a random sample of size n, the lot is accepted. 

Fundamental to the MIL-STD-105D scheme is the concept of “normal” and “tightened” inspec¬ 
tion. Sampling' inspection begins with the normal plan, and the user is required to maintain an historical 
record of the results for each lot inspected. If two out of any five consecutive lots are rejected, a switch 
to tightened inspection is required. Under tightened inspection, n is usually the same as for normal 
inspection, but c is reduced, decreasing the probability of acceptance for all incoming quality levels. 
Normal inspection may be resumed if five consecutive lots are accepted. If tightened inspection 
continues for 10 consecutive lots, then sampling inspection must be discontinued. 

667 



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1. REPORT DATE 

1975 


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4. TITLE AND SUBTITLE 

An Analysis of the Long Range Operating Characteristics of the 
Mil-Std-105D Sampling Scheme and Some Suggeted Modifications 

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Naval Postgraduate School,Monterey,CA,93943 

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00-00-1975 to 00-00-1975 

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Approved for public release; distrihution unlimited 

13. SUPPLEMENTARY NOTES 

Naval Research Logistics Quarterly, 22, pp. 667-679 

14. ABSTRACT 

An integral part of the MIL-STD-105D scheme for sampling inspection hy attributes is the transfer from 
normal inspection to reduced or tightened inspection when the historical record of inspected lots suggests 
unusually good or bad quality. The switching rules in MIL-STD-105D have been criticized, especially by 
Japanese manufacturers, as being too severe when what is defined as acceptable quality materialis 
submitted. This paper examines the long range fraction of lots rejected for several hfIL-STD-lOSD 
sampling plans by using the MIL-STD-105D switching rules, using a modification suggested by the 
Japanese Standards Association, and by using a second modification developed by the authors. The 
Japanese Standards Association switching des are more complex than those in MILSTD-105D. It is 
demonstrated that they lead to improved long-range properties for Normal-Tightened-Reduced schemes, 
but to poorer properties for Normal-Tightened schemes. A simplified set of switching rules is suggested, 
wherein the ’’limit numbers" in MILSTD- 105D are eliminated. In comparison to MIL-STD-IOSD, the 
simpler rules lead to a lower probability of rejection for good lots and a comparable probability of 
rejection for bad lots. 

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668 


G. G. BROWN AND H. C. RUTEMILLER 


An optional feature of MIL-STD-105D is the provision for “reduced” inspection when the histor¬ 
ical quality record is unusually good. A move from normal to reduced inspection requires that the 
previous 10 lots have been accepted and that the total number of defectives in the 10 lots does not 
exceed a set of “limit numbers.” Some examples are shown in Table 1.* Under reduced inspection, 
n is substantially decreased, and two numbers, c and r (> c) are supplied. Lots are accepted if the 
number of defectives is less than r, but normal inspection must be resumed if the number of defectives 
is more than c. 

It is the contention of many critics of MIL-STD-105D that the switching rules are too severe 
when incoming quahty is in the vicinity of the AQL. Furthermore, the switching rules are difficult to 
learn and administer, especially with respect to the transfer from normal to reduced inspection. The 
purpose of this paper is to examine some long-range operating characteristics of MIL-STD-105D 
and two alternative schemes which provide some modifications in the switching rules. 

2. THE COIVCEPT OF “LONG RANGE” O.C. CURVES 

It is clear that tightened, normal, and reduced inspection wUl each have a different probability of 
acceptance for a given incoming lot quality. Hence, the long-range proportion of lots accepted will 
be dependent on the proportion of lots inspected under each plan. 

It is traditional in the literature of quality control to examine the performance of an attributes 
sampling plan under the assumption that, when the process is “in control,” a stream of product is being 
produced with a fixed probability, p, that each item is defective (see Duncan [2, p. 147] or Grant and 
Leavenworth [3, p. 364]). The value of p for a specific manufacturing process is often well established. 
We may think of p as a parameter of the in-control process. Even if fraction defective is not a constant 
from lot to lot in a particular process, the long-range O.C. curve is of considerable value. For example, 
the vendor may be able to set a value of p as an upper bound of fraction defective for his process, 
whereupon the long-range O.C. curve provides an upper bound for fraction of lots rejected. 

3. METHODS AND ASSUMPTIONS 

In a previous paper [1], we have described the theoretical basis for development of a long-range 
O.C. curve for the MIL-STD-105D scheme. Tightened and reduced inspection are treated as Markov 
chains, and normal inspection as a semi-Markov chain. If the process percent defective is nonzero, the 
MIL-STD-105D scheme leads to repeated visits to tightened inspection, and eventually to tightened 
inspection of 10 consecutive lots and the discontinuation of sampling inspection. We assume that, when 
this occurs, the next 10 lots will be treated as reyectedlots and subjecte4to 100 percent inspection, after 
which normal sampling inspection may be resumed. 

4. PROPOSED MODIFICATIONS 

Ohmae [5] described some changes in the switching rules which were claimed to lead to a high 
probability of acceptance for AQL quality lots with a smaller probability than MIL-STD-I05D of 
invoking tightened inspection for such lots. The Ohmae modifications eventually led to a new set of 
switching rules, which have been adopted by the Japanese Standtuds Association. These changes are 
shown in Table 2. 


'See tables at end of paper. 



MIL-STD-105D SAMPLING ANALYSIS 


669 


It is apparent that the Ohmae proposals make the switching rules for transfer from normal to 
tightened inspection more complicated than the original MIL-STD-105D scheme through the intro¬ 
duction of another set of limit numbers, and that the principal effect will be to alter the probability of a 
transfer to tightened inspection for all quality levels, and to decrease the probability of discontinuing 
sampling inspection when tightened inspection is adopted. 

We suggest a different modification, also shown in Table 2. Limit numbers for transfer to reduced 
or tightened inspection are completely eliminated. Lots are viewed as a series of discrete subsets of five. 
Two consecutive subsets with no rejections are required to reach reduced inspection, unless there has 
been a rejection under normal inspection. Whenever a rejection occurs' under normal inspection, the 
next four lots must be accepted to prevent a transfer to tightened inspection. If these four lots are 
accepted, then two additional subsets of five lots with no rejections are required to reach reduced 
inspection. 

5. RESULTS 

We have examined the long-range fraction of lots accepted under the three schemes for several 
lot sizes and for four values of AQL—0.4-, 1.0-, 1.5-, and 2.5-percent defective. At each AQL, the 
incoming quality level was chosen as 0.2 AQL, 0.6 AQL, 0.8 AQL, 1.2 AQL, 2.0 AQL, and 3.0 AQL. 

Normal-Tightened Schemes 

Table 3 shows the results for a sampling scheme wherein only normal and tightened inspection 
are employed. 

The Japanese modification has the undesirable characteristic of decreasing, for all AQL’s investi¬ 
gated. the fraction of lots accepted when material of AQL or better quality is submitted. 

The authors’ proposed modification leads to virtually the same long range O.C. curve as MIL- 
STD-105D. 

Normal-Tightened-Reduced Schemes 

Table 4 shows the results for the three schemes when reduced inspection is included. Referring 
to the limit numbers (Table 1) for transfer to reduced inspection, it is apparent that the user of these 
plans has an option regarding reduced inspection when small lots are inspected (as indicated by the 
asterisk in Table 1). He may interpret Table 1 as forbidding the use of reduced inspection for these 
cases, or as permitting the inclusion of more than 10 lots to achieve the necessary sample size. In 
the former case, the results from Table 3 for these lot sizes should be used. Tible 4 has been constructed 
under the assumption that for plans labeled with an asterisk in Table 1, more than 10 lots may be used 
to obtain sufficient items. 

Where reduced inspection is included. Table 4 shows that, in general, the Japanese modifications 
provide superior long range O.C. curves to those of MIL-STD-105D, For lots of AQL quality or better, 
the fraction of lots accepted is nearly always higher than MIL-STD-105D, while for poorer quality 
lots, the fraction accepted becomes lower than MIL-STD-105D. 

The authors’ suggested modification is usually even better than the Japanese plan with respect to 
acceptance of lots at AQL quality or better, but the fraction of poorer quality lots accepted is a little 
higher, usually comparable to that provided by MIL-STD-105D. This simpler approach, without the 



670 


G. C. BROWN AND H. C. RUTEMILLER 


oomplication of limit numbers, appears to satisfy the objective of accepting more high quality lots 
while retaining the long range operating characteristics of MIL-STD-105D for poorer quality lots. 

A subsidiary advantage of the authors’ scheme is worth mentioning. The elimination of limit num¬ 
bers not only simplifies record keeping, but also permits a complete analysis of the normal sampling 
scheme as a pure Markov chain. Under these conditions, long range O.C. curves may be obtained with¬ 
out costly iterative solution required for semi Meurkov analyses. 


Table 1. Limit numbers from MIL-STD-105D, Table VIII for transfer from normal to reduced 
inspection. Numbers in body of table are maximum defective in most recent 10 lots 


Number of items in 
last 10 lots 

AQL 

Number of items in 
last 10 lots 

AQL 

0.40 

1.0 

1.5 

2.5 

0.40 

1.0 

1.5 

2.5 

20-29 

n 




320-499 

« 

0 

1 

n 

30-49 



H 

« 

500-799 

0 

2 

3 


50-79 



H 

« 

800-1,249 

0 

4 

7 

■9 

80-129 




0 

1,250-1,999 

2 

8 

13 

KB 

130-199 




0 

2,000-3,149 

4 

14 

22 

mSm 

200-319 

O 

0 

H 

2 

3,150-4,999 

8 

25 

_ 

38 

mM 


*MIL-STD-105D reqiiires at least 200 items to be inspected, so the number of items in last 10 lots is not sufficient to qualify 
for reduced inspection. In these instances, more than 10 lots may be used, if desired. 


Table 2.—Switching rules for MIL-STD-105D and two suggested modifications 


Switch 

MIL-STD-105D 

Japanese modification 

Authors’ proposed 
modification 

Normal to tightened 

2 out of any 5 consecu¬ 
tive lots rejected. 

a. A lot is rejected 
and b. Total defectives in 
last 5 lots ^ limit 
number.* 

Rejected lot, followed by a 
second rejection in the 
following 4 lots 

Tightened to normal 

5 consecutive lots accepted. 

No change 

No change from 105D. 

Tightened to "Discontinue" 

10 consecutive lots remain 
on tightened. 

Number of cumulative lots re¬ 
jected under tightened 
reaches 5. 

No change frpm 105D. 

Normal to Reduced 

a. 10 consecutive lots 
accepted and 

and b. Total defectives in 
the 10 lots £ limit 
number. 

and c. Production at a steady 

rate 

and d. Reduced inspection is 
deemed desirable. 

No change, except that limit 
numbers are reduced. 

"i- 

a. 10 consecutive lots 
accepted from the 
beginning of normal 
inspection. 

or b. 14 consecutive lots 
accepted after a re¬ 
jection during normal 
inspection 

c. and d. same as lOSD. 

Reduced to Normal 

Any lot with more than c de¬ 
fectives. 

No change in switching rules, 
except limit number, c, for 
plans with r= 2, is altered 
from 0 to 1. 



•The new limit numbers are the upper 0.5-percent probability points from the Poisson distribution, assuming that AQL 
quality material has been submitted. 




















































MIL-STD-105D SAMPLING ANALYSIS 


671 


Table 3. Long range operating characteristics of three sampling schemes 
employing normal and tightened inspection {MIL-STD-105D general 
inspection level II) 


AQL = 0.4 percent 


Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots accepted 

MIL-STD-IOSD 

Japanese 
Standard 
Assn. _ 

Authors' 

modification 

G 

0.08 

0.974 

0.969 

0.975 


0.24 

0.905 

0.895 

0.913 


0.32 

0.856 

0.846 

0.870 


0.40 

0.802 

0.789 

0.817 


0.48 

0.746 

0.729 

0.761 


0.80 

0.553 

0.516 

0.559 


1.20 

0.403 

0.352 

0.404 

K 

0.08 

0.995 

0.993 

0.995 


0.24 

0.958 

0.938 

0.961 


0.32 

0.915 

0.880 

0.926 


0.40 

0.845 

0.792 

0.865 


0.48 

0.754 

0.686 

0.776 


0.80 

0.429 

0.348 

0.433 


1.20 

0.233 

0.178 

0.233 

L 

0.08 

0.999 

0.995 

0.999 


0.24 

0.986 

0.951 

0.987 


0.32 

0.966 

0.898 

0.971 


0.40 

0.925 

0.816 

0.941 


0.48 

0.854 

0.716 

0.883 


0.80 

0.477 

0.367 

0.487 


1.20 

0.237 

0.173 

0.238 

M 

0.08 

1.000 

0.999 

1.000 


0.24 

0.992 

0.978 

0.993 


0.32 

0.979 

0.949 

0.980 


0.40 

0.949 

0.893 

0.957 


0.48 

0.886 

0.801 

0.907 


0.80 

0.452 

0.362 

0.458 


1.20 

0.193 

0.143 

0.193 

N 

0.08 

1.000 

1.000 

1.000 


0.24 

0.998 

0.985 

0.998 


0.32 

0.994 

0.959 

0.994 


0.40 

0.981 

0.895 

0.983 


0.48 

0.943 

0.778 

0.958 


0.80 

0.440 

0.283 

0.450 


1.20 

0.133 

0.081 

0.133 




672 


G. G. BROWN AND H. C. RUTEMILLER 


Table 3. Long range operating characteristics of three sampling schemes 
employing normal and tightened inspection {MIL-STD-105D general 
inspection level II) — Continued 


AOL = 1.0 Percent 


Lot size 
code letter 

r 

Incoming 

oercent 

defective 

Fraction of lots accepted 

MIL-STD-105D 

Japanese 

Standards 

Assn. 

Authors' 

modification 

E 

0^ 

0.974 

0.969 

0.974 


0.6 

0.904 

0.894 

0.912 


0.8 

0.854 

0.845 

0.867 


1.0 

0.799 

0.788 

0.814 


1.2 

0.743 

0.728 

0.757 


2.0 

0.550 

0.514 

0.556 


3.0 

0.400 

0.351 

0.402 

H 

0.2 

0.995 

0.993 

0.995 


0.6 

0.958 

0.938 

0.%1 


0.8 

0.915 

0.880 

0.926 


1.0 

0.845 

0.792 

0.865 


1.2 

0.754 

0.686 

0.776 


2.0 

0.429 

0.348 

0.433 


3.0 

0.233 

0.178 

0.233 

J 

0.2 

0.999 

0.995 

0.999 


0.6 

0.986 

0.951 

0.987 


0.8 

0.966 

0.898 

0.971 


1.0 

0.925 

0.816 

0.941 


1.2 

0.854 

0.716 

0.883 


2.0 

0.477 

0.367 

0.487 


3.0 

0.237 

0.173 

0.238 

K 

0.2 

1.000 

0.999 

1.000 


0.6 

0.993 

0.979 

0.993 


0.8 

0.980 

0.950 

0.981 


1.0 

0.951 

0.8% 

0.958 


1.2 

0.890 

0.806 

0.910 


2.0 

0.459 

0.368 

0.465 


3.0 

0.196 

0.145 

0.1% 

L 

0.2 

1.000 

1.000 

1.000 


0.6 

0.998 

0.985 

0.998 


0.8 

0.994 

0.959 

0.994 


1.0 

0.981 

0.895 

0.983 


1.2 

0.943 

0.778 

0.958 


2.0 

0.440 

0.283 

0.450 


3.0 

0.133 

0.081 

0.133 




MIL-STD-105D SAMPUNG ANALYSIS 


673 


Table 3. Long range operating characteristics of three sampling schemes 
employing normal and tightened inspection {MIL-STD-105D general 
inspection level II) — Continued 


AQL = 1.5 percent 


Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots accepted 

MIL-STD-105D 

Japanese 

Standards 

Assn. 

Authors’ 

modification 

D 

0.3 

0.976 

0.970 

0.976 


0.9 

0.911 

0.900 

0.920 


1.2 

0.866 

0.853 

0.880 


1.5 

0.815 

0.799 

0.831 


1.8 

0.762 

0.741 

0.777 


3.0 

0.571 

0.530 

0.578 


4.5 

0.418 

0.364 

0.420 

G 

0.3 

0.996 

0.993 

0.9% 


0.9 

0.962 

0.945 

0.965 


1.2 

0.925 

0.896 

0.934 


1.5 

0.864 

0.820 

0.882 


1.8 

0.782 

0.724 

0.803 


3.0 

0.460 

0.382 

0.465 


4.5 

0.255 

0.197 

0.255 

H 

0.3 

0.999 

0.9% 

0.999 


0.9 

0.989 

0.958 

0.989 


1.2 

0.973 

0.914 

0.976 


1.5 

0.941 

0.845 

0.953 


1.8 

0.884 

0.755 

0.919 


3.0 

0.527 

0.408 

0.540 


4.5 

0.268 

0.1% 

0.269 

J 

0.3 

1.000 

0.999 

1.000 


0.9 

0.994 

0.981 

0.994 


1.2 

0.982 

0.956 

0.983 


1.5 

0.958 

0.910 

0.964 


1.8 

0.908 

0.831 

0.925 


3.0 

0.495 

0.401 

0.503 


4.5 

0.216 

0.161 

0.217 

K 

0.3 

1.000 

1.000 

1.000 


0.9 

0.999 

0.988 

0.999 


1.2 

0.995 

0.968 

0.9% 


1.5 

0.986 

0.921 

0.987 


1.8 

0.962 

0.827 

0.970 


3.0 

0.515 

0.338 

0.533 


4.5 

0.166 

0.101 

0.166 




674 


G. G. BROWN AND H. C. RUTEMILLER 


Table 3. Long range operating characteristics of three sampling schemes 
employing normal and tightened inspection {MIL-STD-105D general 
inspection level II) — Continued 

AQL = 2.5 Percent 


Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots accepted 

MIL-STD-105D 

Japanese 

Standards 

Assn. 

Authors’ 

modification 

C 

0.5 

0.975 

0.969 

0.975 


1.5 

0.907 

0.896 

0.916 


2.0 

0.851 

0.847 

0.873 


2.5 

0.806 

0.791 

0.821 


3.0 

0.750 

0.731 

0.766 


5.0 

0.558 

0.518 

0.564 


7.5 

0.407 

0.354 

0.408 

F 

0.5 

0.995 

0.993 

0.995 


1.5 

0.958 

0.938 

0.961 


2.0 

0.915 

0.880 

0.926 


2.5 

0.845 

0.792 

0.865 


3.0 

0.754 

0.686 

0.776 


5.0 

0.429 

0.348 

0.433 


7.5 

0.233 

0.178 

0.233 

G 

0.5 

0.999 

0.995 

0.999 


1.5 

0.986 

0.951 

0.987 


2.0 

0.966 

0.898 

0.971 


2.5 

0.925 

0.816 

0.941 


3.0 

0.854 

0.716 

0.883 


5.0 

0.477 

0.367 

0.487 


7.5 

0.237 

0.173 

0.238 

H 

0.5 

1.000 

0.999 

1.000 


1.5 

0.993 

0.979 

0.993 


2.0 

0.980 

0.950 

0.981 


2.5 

0.951 

0.896 

0.958 


3.0 

0.890 

0.806 

0.920 


5.0 

0.459 

0.368 

0.465 


7.5 

0.196 

0.145 

0.196 

J 

0.5 

1.000 

1.000 

1.000 


1.5 

0.998 

0.985 

0.998 


2.0 

0.994 

0.959 

0.994 


2.5 

0.981 

0.895 

0.983 


3.0 

0.943 

0.778 

0.958 


5.0 

0.440 

0.283 

0.450 


7.5 

0.133 

0.081 

0.133 




ML-STD-IOSD SAMPLING ANALYSIS 


Table 4. Long range operating characteristics of three sampling schemes 
employing normal, tightened and reduced inspection {MIL-STD-105D 
general inspection level II) 


AQL^O.4 percent 


Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots acce 

pted 

MIL-STD-105D 

Japanese 

Standards 

Assn. 

Authors’ 

modification 

G* 

0.08 

0.987 

0.987 

0.988 


0.24 

0.935 

0.942 

0.944 


0.32 

0.889 

0.901 

0.902 


0.40 

0.832 

0.846 

0.852 


0.43 

0.770 

0.780 

0.792 


0.80 

0.559 

0.531 

0.571 


1.20 

0.403 

0.355 

0.407 

K 

0.08 

0.998 

0.999 

0.998 


0.24 

0.970 

0.983 

0.972 


0.32 

0.930 

0.947 

0.935 


0.40 

0.859 

0.871 

0.870 


0.48 

0.764 

0.755 

0.778 


0.80 

0.430 

0.355 

0.434 


1.20 

0.233 

0.178 

0.233 

L 

0.08 

1.000 

1.000 

1.000 


0.24 

0.996 

0.991 

0.997 


0.32 

0.984 

0.972 

0.989 


0.40 

0.947 

0.933 

0.968 


0.48 

0.871 

0.852 

0.916 


0.80 

0.478 

0.384 

0.498 


1.20 

0.237 

0.173 

0.238 

M 

0.08 

1.000 

1.000 

1.000 


0.24 

0.997 

0.994 

0.998 


0.32 

0.986 

0.981 

0.991 


0.40 

0.957 

0.955 

0.971 


0.48 

0.892 

0.984 

0.919 


0.80 

0.452 

0.370 

0.460 


1.20 

0.193 

0.143 

0.193 

N 

0.08 

1.000 

1.000 

^ 1.000 


0.24 

1.000 

0.999 

1.000 


0.32 

0.996 

0.994 

0.998 


0.40 

0.983 

0.981 

0.993 


0.48 

0.945 

0.938 

0.970 


0.80 

0.440 

0.294 

0.641 


1.20 

0.133 

0.081 

0.133 


*16 lots required to meet minimum sample assignment of Table VIII for AQL = 0.4, 
1.0, 2.5. 17 lots required for AQL = 1.5. 




G. G. BROWN AND H. C. RUTEMILLER 


Table 4. Long range operating characteristics of three sampling schemes 
employing normal, tightened and reduced inspection {MIL-STD-105D 
general inspection level II) — Continued 

AQL=1.0 Percent 


— 

Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots accepted 

MIL-STD-105D 

Japanese 

Standards 

Assn.' 

Authors' 

modification 

E* 


0.987 

0.988 

0.988 



0.935 




0.8 

0.889 


0.904 


1.0 

■ 0.831 

0.845 

0.855 


1.2 

0.768 

0.778 

0.791 



0.556 


0.568 



0.401 


0.404 

H 

0.2 

0.998 

0.999 

0.998 


0.6 



0.972 


0.8 

0.930 

0.947 

0.935 


1.0 


0.871 

0.870 


1J2 


0.755 

0.778 


2.0 

0.430 


0.434 


3.0 

0.233 

0.178 

0.233 

J 


1.000 

1.000 

1.000 



0.996 

0.991 



0.8 

0.984 

0.972 



1.0 

0.947 

0.933 

0.968 


1.2 

0.871 

0.852 

0.916 


2.0 

0.478 

0.384 

0.498 


3.0 

0.237 

0.173 

0.238 

K 

0.2 

1.000 

1.000 

1.000 


0.6 

0.997 

0.994 



0.8 

0.985 




1.0 

0.956 


0.972 


1.2 

0.894 

0.898 

0.922 


2.0 

0.459 

0.377 

0.468 


3.0 

0.1% 

0.146 

0.197 

L 


1.000 

1.000 -fc 

1.000 



1.000 

0.999 

1.000 


0.8 

0.9% 

0.994 

0.998 


1.0 

0.983 


0.993 


1.2 

0.945 


0.970 



0.440 

0.294 

0.641 



0.133 

0.081 

0.133 


*16 lots required to meet minimum sample assignment of Table VIII for AQL —0.4, 
1.0, 2.5. 17 lots required for AQL = 1.5. 
































MIL-STD-105D SAMPLING ANALYSIS 


677 


Table 4. Long range operating characteristics of three sampling schemes 
employing normal, tightened and reduced inspection {MIL-STD-105D 
general inspection level II) — Continued 

AQL = 1.5 Percent 


Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots accepted 

MIL-STD-105D 

Japanese 

Standards 

•Assn. 

Authors’ 

.. modification 

D* 

0.3 

0.989 

0.989 

0.990 


0.9 

0.942 

0.948 

0.952 


1.2 

0.900 

0.911 

0.917 


1.5 

0.847 

0.860 

0.871 


1.8 

0.788 

0.797 

0.815 


3.0 

0.577 

0.549 

0.595 


4.5 

0.419 

0.367 

r 

0.424 

G 

0.3 

0.998 

0.999 

0.998 


0.9 

0.970 

0.985 

0.975 


1.2 

0.933 

0.955 

0.943 


1.5 

0.871 

0.893 

0.888 


1.8 

0.786 

0.793 

0.806 


3.0 

0.460 

0.391 

0.466 


4.5 

0.255 

0.197 

0.255 

H 

OJ 

1.000 

1.000 

1.000 


0.9 

0.997 

0.9M 

0.998 


1.2 

0.985 

0.978 

0.992 


1.5 

0.955 

0.949 

0.977 


1.8 

0.895 

0.888 

0.940 


3.0 

0.527 

0.437 

0.556 


4.5 

0.268 

. 0.197 

0.269 


0.3 

1.000 

1.000 

1.000 


0.9 

0.998 

0.995 

0.998 


1.2 

0.988 

0.984 

0.993 


1.5 

0.964 

0.963 

0.977 


1.8 

0.912 

0.917 

0.938 


3.0 

0.495 

0.415 

0.506 


4.5 

0.216 

0.161 

0.217 






K 

0.3 

1.000 

1.000 

1.000 


0.9 

1.000 

0.999 

1.000 


1.2 

0.997 

0.996 

0.999 


1.5 

0.988 

0.987 

0.995 


1.8 

0.963 

0.961 

0.982 


3.0 

0.514 

0.361 

0.539 


4.5 

0.166 

0.101 

0.166 


*16 lots required to meet minimum sample assignment of Table VIII for AQL=0.4, 
1.0, 2.5. 17 lots required for AQL = 1.5. 




G. G. BROWN AND H. C. RLTEMILLER 


Table 4. Long range operating characteristics of three sampling schemes 
employing normal, tightened and reduced inspection {MIL-STD-105D 
general inspection level II) — Continued 

AQL=2.5 percent 


Lot size 
code letter 

Incoming 

percent 

defective 

Fractions of lots accepted 

MIL-STD-105D 

Japanese 

Standards 

Assn. 

Authors’ 

modification 

C* 

0.5 

0.987 

0.9BO 

0.988 


1.5 

0.938 

0.944 

0.946 


2.0 

0.893 

0.905 

0.908 


2.5 

0.838 

0.850 

0.858 


3.0 

0.777 

0.785 

0.799 


5.0 

0.564 

0.534 

0.578 


7.5 

0.407 

0.357 

0.411 

F 

0.5 

0.998 

0.999 

0.998 


1.5 

0.970 

0.983 

0.972 


2.0 

0.930 

0.947 

0.935 


2.5 

0.859 

0.871 

0.870 


3.0 

0.764 

0.755 

0.778 


5.0 

0.430 

0.355 

0.434 


7.5 

0.233 

0.178 

0.233 

G 

0.5 

1.000 

1.000 

1.000 


1.5 

0.996 

0.991 

0.997 


2.0 

0.984 

0.972 

0.989 


2.5 

0.946 

0.933 

0.%7 


3.0 

0.871 

0.852 

0.915 


5.0 

0.478 

0.384 

0.497 


7.5 

0.237 

0.173 

0.238 

H 

0.5 

1.000 

1.000 

1.000 


1.5 

0.997 

0.994 

0.998 


2.0 

0.985 

0.982 

0.991 


2.5 

0.956 

0.956 

0.972 


3.0 

0.894 

0.898 

0.922 


5.0 

0.459 

0.377 

0.467 


7.5 

0.196 

0.146 

0.197 

J 

0.5 

1.000 

1.000 ^ 

1.000 


1.5 

1.000 

0.999 

1.000 


2.0 

0.9% 

0.994 

0.998 


2.5 

0.983 

0.981 

0.992 


3.0 

0.945 

0.938 

0.970 


5.0 

0.440 

0.294 

0.454 


7.5 

0.133 

0.081 

0.134 


* 16 lots required to meet minimum sample assignment of Table VIII for AQL = 0.4,1.0, 
2.5. 17 lots required for AQL= 1.5. 




MIL-STD-105D SAMPLING ANALYSIS 


679 


REFERENCES 

[1] Brown, G. and H. Rutemiller, “A Cost Analysis of Sampling Inspection Under Military Standard 

105D,” Nav. Res. Log. Quart. 20, 181 (Mar. 1973). 

[2] Duncan, A. J., Quality Control and Industrial Statistics (R. C. Irwin and Co., Homewood, Illinois, 

1965). 

[3] Grant, E. L. and R. S. Leavenworth, Statistical Quality Control (McGraw-Hill, New York, 1972). 

[4] MIL-STD-105D 29 April, 1963 Military Standard—Sampling Procedures andTables for Inspection 

by Attributes. Washington, D.C.: United States Government Printing Office (1%2). 

[5] Ohmae, U., and R. Suga, “Basic Policy and Scheme on Modified MIL-STD-105D,” International 

Conference on Quality Control, Tokyo (1969).