pioneering reference related to positional controls comes from
the Norwegian Mapping Authority, which has been applying
ISO
3951 for many years (Statens Kartverk, 2007).
The lot is a crucial element to both international standards;
a lot is a set of elements. Quality is fitness for purpose, thus
the elements have to be selected taking in consideration the
purpose of the product or control, with a utilitarian focus.
Therefore, we first have to define what elements make up the
population of interest (e.g., an image, an aerial photo, a build-
ing, a property, a well-defined point, a road, etc.). In some
cases we can consider different elements, for instance, in the
case of controlling a road data base: (a) each instance record-
ed in the dataset, (b) each section of a kilometer in length,
(c) each administrative section, and (d) each arc or segment
between two nodes of a topological dataset, etc.
One main feature of a lot is its size. The size is the number
of items in the lot. Therefore, the size depends on the establish-
ment of an element type. For the above example on a road, each
of the possible elements carries a different lot size. Another main
feature of a lot is homogeneity. Lots should be homogeneous,
which means that the units in the lot should have a common
origin (e.g., the same contractor or surveying company, same
methods, same processes, same machines, same operators, etc.).
These two international standards (
ISO
2859 and
ISO
3951)
are about acceptance sampling (applying sampling plans). Ac-
ceptance sampling is a form of inspection that is applied to lots
of items before or after a process. By means of a sample, the
purpose is to decide whether a lot satisfies a predefined quality
standard (e.g., is the imagery acceptably geo-registered or not).
Lots that satisfy these standards are passed or accepted, and
those that do not are rejected. Acceptance sampling is concerned
with inspection and decision-making regarding products, one
of the oldest aspects of quality assurance. Here, it is important
to highlight two aspects of acceptance sampling (Montgomery,
2001): (a) the purpose is to sentence lots, accept or reject, not
to estimate quality (it is not an estimation process), and (b) the
most effective use of acceptance sampling is not to inspect qual-
ity in the product, but rather as an auditing tool to ensure that
the output of a process conforms to the requirements. Sampling
schemes designated in these standards are applicable, but not
limited, to inspection of (
ISO
2859-1): end items, components
and raw materials, operations, materials in process, supplies in
storage, maintenance operations, data or records, and admin-
istrative procedures. As can be understood, the application of
ISO
2859 to control the positional quality, and in general to any
quantitative aspect of spatial data, allows for a single common
framework for all the aspects, quantitative and qualitative, of
cartographic production (e.g., completion, consistence, theme,
records and administrative procedures, services, etc.). This is of
great interest to companies and mapping agencies.
The use of these industrial standards for positional accu-
racy control is possible. Since positional errors are a continu-
ous variable, this can be achieved directly my means of the
ISO
3951 parts 1 (single sampling plans for lot-by-lot inspec-
tion for a single quality characteristic) and 2 (single sampling
plans for lot-by-lot inspection of independent quality charac-
teristics). This idea was mentioned by
ISO
19114 and now has
been extended with new examples by
ISO
19157 (see Annex
F of
ISO
19157 or Statens Kartverk (2007) for examples).
However,
ISO
3951 has a major drawback: it is only applicable
when the controlled errors follow a Normal distribution and
is very sensitive to the presence of outliers. The assumption
of normality is critical because it is used in all sampling plans
in order to calculate the defective fraction of a lot or process
(Montgomery, 2001). Small deviations from normality can
generate great differences in the calculated defective fraction,
generating bad acceptance decisions. Furthermore, it is as-
sumed that measurement error is negligible, so it is necessary
that the accuracy of the control method be ten times better
than the product being controlled (
ISO
3951).
In this paper we propose the use of
ISO
2859-1 and
ISO
2859-2 for positional quality control. This standard has been
designed for general quality control when using counting
of errors (defects or defective items), which in a spatial data
context means the counting of thematic and attribute errors,
inconsistency errors, completeness errors, etc. But positional
errors are a continuous statistical variable. In order to pass
from a continuous variable to a counting variable, we use the
statistical method proposed by Ariza-López and Rodríguez-
Avi (2014). This method offers the possibility to work with
parametric and non-parametric models.
We believe that statistical models based on distribution
functions (parametric models) are suitable for situations, such
as those of the past, where few data were available, when data
collection was expensive, and when computational resources
were scarce. The current situation is different; we now talk
about big data, and therefore we consider that statistical para-
metric models must give way to new methods based on work-
ing directly with the populations of data (errors in this case).
The proposal we make in this paper goes in this direction.
After this introduction the paper is organized in five sec-
tions. The following section presents the main ideas about
statistical testing in acceptance sampling. The next is cen-
tered on the International Standard
ISO
2859-1 because it is
the basis of the proposal; the historical origins and its most
important features are presented. The fourth section sum-
marizes how to pass from quantitative values (measured
positional errors) to counting values (positional defectives);
this is achieved by the model proposed by Ariza-López and
Rodríguez-Avi (2014). An example of a positional control ap-
plied to a sequence of lots is given in the Example of Applica-
tion section. Finally, the conclusions are presented aiming to
highlight the main features of this proposal.
User and Producer Risk in Acceptance Sampling
The purpose of quality control is to establish and maintain
the conformity of products with design requirements, mainly
expressed as standards or specifications. One of the most im-
portant aspects of statistical quality control is the acceptance
control of products. Acceptance sampling is useful in the case
of some quality elements of spatial data (e.g., positional ac-
curacy, completeness, etc.) in the following situations:
• When the cost of 100 percent inspection is extremely high.
• When 100 percent inspection is not technologically
feasible or would require so much time that production
would be impacted.
• When there are many items to be inspected and the
inspection error rate is high.
• When there is potential product liability risk and con-
tinuous monitoring of the product is necessary.
Positional controls can be understood as industrial ac-
ceptance processes based on sampling in order to control
SDS
coming from suppliers (internal or external). When accep-
tance sampling is performed in industry a sampling plan is
required. Sampling plans are the key elements of acceptance
sampling. Given a lot of size
N
, a sampling plan is no more
than a plan that specifies the sample size
n
and the accep-
tance/rejection criteria (acceptance number
c
). Thus, follow-
ing the example of Montgomery (2001), if the lot size is
N =
10,000, the sampling plan
n =
89,
c =
2 means that from a lot
of size 10,000 a random sample of
n =
89 units is inspected
and the number of nonconforming (defective items or defects)
d
is observed. If the number of observed defectives
d
≤
c =
2,
the lot will be accepted and if
d >c
the lot will be rejected.
Many of the
PAAM
s (e.g.,
NMAS
) are fully equivalent to the ac-
ceptance process described above; if the data meet accuracy
658
August 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
