shows the errors measured in each of the control samples
(column labeled C2), a statistical summary (column labeled
C3), and the count of positional defectives (column labeled
C4). Now because we decided that
AQL
c1
=
6.5 we must pay
attention to the column labeled C6 in Table 4. Here the ac-
ceptance and rejection values are presented: (“Ac-Re” in the
Table 4 under column C6). Now we must think that lots arrive
one by one, and make a decision of acceptance or rejection
one by one, and apply the switching rules if necessary. This
decision is taken comparing the amount of positional defec-
tives with the acceptance value as explained before. So a
decision is made, and the column labeled D under column
C6 shows “A” when accepted and “R” when the correspond-
ing lot is rejected. In this case any lot is rejected. In this case
switching rules are not needed and the complete inspection is
run under the normal inspection severity.
Now let us suppose the same data supply but consider-
ing [
Tol =
16.3 m;
AQL
c2
=
10 percent ]; because
AQL
c2
>
AQL
c1
>
π
the exigency of positional quality is lesser here. Table 4
shows the results for this case. In the column labeled C7 the
acceptance and rejections values and the final decision are
presented. As can be observed, there is no rejection, and all
lots are accepted.
Finally let us suppose the same data supply but consider-
ing
[Tol =
16.3 m;
AQL
c3
=
4 %]; because
AQL
c3
<
π
the exigency
of positional quality is greater here. Table 4 shows the results
for this case, so in the column labeled C5 the acceptance and
rejection values and the final decision are presented. As can be
observed, there two rejections (lots numbers 6 and 8). Because
2 of 5 or fewer consecutive lots are not accepted, the Interna-
tional Standard requires passing to tightened inspection. This
means greater severity and is achieved by decreasing the
Ac
and
Re
values (now
Ac =
1
, Re =
2) while maintaining sample
size. Normal inspection is not re-instated because there are not
five consecutive lots accepted under tightened inspection.
It has to be remarked that in the above three examples the
ISO
2859-1 assures that the producer risk is in the order of 5
percent, and user risk in the order of 10 percent by means of
applying the switching rules.
For the example of application of
ISO
2859-2 consider now
a supply of an isolated lot of characteristics similar to the
previous case (same
BaM
- Figure 4,
Tol =
16.3 m,
AQL
=
6.5
%
, size belonging to the interval [91, 150]). This standard is
indexed by the
LQ
parameter and the recommendation of the
standard is: “the limiting quality should be chosen realisti-
cally at a minimum of three times the desired quality.” So we
consider
LQ
=
20 % because it is the nearest to 3 × 6.5 % of
the preferred
LQ
value proposed in the standard. Entering into
Table A of
ISO
2859-2 (shown in Figure 9) with
LQ
=
20 % and
the lot size, results in the following sampling plan:
n =
13,
Ac
=
0. The acceptation/rejection decision is taken by compar-
ing the amount of positional defectives with the acceptance
value. If we find 0 positional defectives in the sample the lot
is accepted. But prior to applying this sampling plan, we must
agree with its estimated performance. This can be analyzed by
means of the corresponding
OC
curve, which is offered by
ISO
2859-2 in Table B9 “Single sampling plans for limiting quality
20.0 percent.” Additionally, information of risks (user’s and
producer’s) is offered by
ISO
2859-2 in Table D1. The outputs
of the last table are: (a) 4.8 percent probability of acceptance
at the limiting quality (20.0 percent) (the risk of the user); (b)
0 percent probability of rejection at 0 percent nonconforming
(the risk of the producer). If we consider that the sampling
plan performance is satisfactory, we can start its application.
Now we analyze the following sample: {5.87; 13.33; 2.05;
9.82; 9.55; 6.13; 4.38; 4.55; 7.2; 7.71; 2.93; 8.88; 7.92}. In this
sample there is no case greater than the tolerance, so
d =
0 and
because
d
≤
Ac =
0 the conclusion is that the lot is accepted.
Figure 9. Figure of “Table A - Single Sampling Plans Indexed by Limiting Quality (LQ) (Procedure A)” from ISO 2859-2 (ISO 1985).
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August 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
