LTPD  Lot
Tolerance Percent Defective
Acceptance sampling
is an
important aspect of statistical quality control. It originated back in
World War II when the military had to determine which batches of ammunition
to accept and which ones to reject. They knew that they couldn't test
every bullet to determine if it will do its job in the field. On
the other hand, they had to be confident that the bullets they're
getting will not fail when their lives are already on the line.
Acceptance sampling was the answer  testing a few representative
bullets from the lot so they'll know how the rest of the bullets will
perform.
Acceptance
sampling is a compromise between not doing any
inspection at all and 100% inspection. The scheme by which
representative samples will be selected from a population and tested
to determine whether the lot is acceptable or not is known as an
acceptance plan
or
sampling plan. There are two major
classifications of acceptance plans: based on attributes ("go,
nogo") and based on variables.
Sampling plans can be single, double or multiple. A
single sampling plan for attributes consists of a sample of size n
and an acceptance number c. The procedure operates as
follows: select n items at random from the lot. If the number of defectives
in the sample set is less than c, the lot is accepted.
Otherwise, the lot is rejected.
In
order to measure the performance of an acceptance or sampling plan,
the Operating Characteristic (OC) curve is
used. This
curve plots the probability of accepting the lot (Yaxis) versus the lot
fraction or percent defectives.
LTPD
 Lot Tolerance Percent Defective
The
LTPD
of a sampling plan is the level of quality routinely rejected by the
sampling plan. It is generally defined as the percent defective (number
of defectives per hundred units X 100%) that
the sampling plan will
reject 90% of the time. In other words, this is also the percent
defective that will be accepted by the sampling plan at most 10% of the time. This means
that lots at or worse than the LTPD are rejected at least 90% of the
time and accepted at most 10% of the time.
The LTPD can be determined using the operating
characteristic (OC) curve by finding that quality level on the bottom
axis that corresponds to a probability of acceptance of 0.10 (10%) on
the left axis.
Associated with the LTPD is a confidence statement one can make. If the
lot fails the sampling plan, one can state with 90% confidence that the
quality level of the lot is worse than the LTPD (i.e., the defective
rate of the lot > LTPD).
On the other hand, if a lot passes the sampling plan, then one can state
with 90% confidence that its quality level is equal to or better than the LTPD.
The LTPD of the sampling plan describes what the
sampling plan will reject, but it is also important to know what the sampling
plan will accept. Information on what the sampling plan will accept is provided by the
AQL
of the sampling plan.
Table 1. LTPD Sampling Table based on the MilS19500 and MilM38510
Max %
Defective 
20% 
15% 
10% 
7% 
5% 
3% 
2% 
1.5% 
1% 
0.7% 
0.5% 
Acceptance Number (c); rejects=c+1 
Minimum Sample Size Needed 
0 
11 
15 
22 
32 
45 
76 
116 
153 
231 
328 
461 
1 
18 
25 
38 
55 
77 
129 
195 
258 
390 
555 
778 
2 
25 
34 
52 
75 
105 
176 
266 
354 
533 
759 
1056 
3 
32 
43 
65 
94 
132 
221 
333 
444 
668 
953 
1337 
4 
38 
52 
78 
113 
158 
265 
398 
531 
798 
1140 
1599 
5 
45 
60 
91 
131 
184 
308 
462 
617 
927 
1323 
1855 
The
acceptable
quality level
or
AQL of a sampling plan is
a measure of the level of quality routinely accepted by that
sampling plan. It is defined as the percent defective
(defectives per hundred units X 100%) that the
sampling plan will
accept 95% of the time. This means lots at or better than the AQL are
accepted at least 95% of the time and rejected at most 5% of the
time.
The AQL can be determined using the operating
characteristic (OC) curve
by finding that quality level on the bottom axis that corresponds to a
probability of acceptance of 0.95 (95%) on the left axis.
Associated with the AQL is
a confidence statement one can make. If the
lot passes the sampling plan, one can state with 95% confidence that the
quality level of the lot is equal to or better than the AQL (i.e., the defective
rate of the lot < AQL).
On the other hand, if the
lot fails the sampling plan, one can state with 95% confidence that the
quality level of the lot is worse than the AQL.
The AQL describes what the
sampling plan will accept, but it is also important to know what the sampling
plan will reject. Information on what the sampling plan will reject is provided by the
LTPD
of the sampling plan.
Table 2. AQL Sampling Table based on the MilSTD105D

Acceptable Quality Levels for Normal Inspection (% defective) 
Lot
Size/
Sample
Size 
.01 
.015 
.025 
.04 
.065 
.10 
.15 
.25 
.40 
.65 
1.0 
1.5 
2.5 
4.0 

Lot
Acceptance (Ac) Number (maximum number of rejects to accept the
lot) 
LS=2 to
8
SS=2 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
LS=9 to
15
SS=3 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
LS=16 to
25
SS=5 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
LS=26 to
50
SS=8 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
1 
LS=51 to
90
SS=13 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
1 
91 to
150
SS=20 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
2 
151 to
280
SS=32 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
2 
3 
281 to
500
SS=50 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
2 
3 
4 
501 to
1200
SS=80 
0 
0 
0 
0 
0 
0 
0 
0 
0 
1 
2 
3 
5 
7 
1201 to
3.2K
SS=125 
0 
0 
0 
0 
0 
0 
0 
0 
1 
2 
3 
5 
7 
10 
3201 to
10K
SS=200 
0 
0 
0 
0 
0 
0 
1 
1 
2 
3 
5 
7 
10 
14 
1000135K
SS=315 
0 
0 
0 
0 
0 
0 
1 
2 
3 
5 
7 
10 
14 
21 
35001150K
SS=500 
0 
0 
0 
1 
1 
1 
2 
3 
5 
7 
10 
14 
21 
 
150001500K
SS=800 
0 
0 
0 
1 
1 
2 
3 
5 
7 
10 
14 
21 
21 
 

.01 
.015 
.025 
.04 
.065 
.10 
.15 
.25 
.40 
.65 
1.0 
1.5 
2.5 
4.0 
See
also: AQL; AQL Table
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