Conclusions
This paper presents a method for positional quality control
valid for
n
-dimensional spatial data (e.g., 1D, 2D, 3D) based
on acceptance sampling by means of
ISO
2859-1. In order to
understand this method, we have presented the basics of ac-
ceptance by sampling, including the user and producer risks,
and the International Standard
ISO
2859-1. The capability for
dealing with positional errors within a standard originated for
non-quantitative values is achieved by the model proposed
by Ariza-López and Rodríguez-Avi (2014), and this model
have been summarized. An example of its application to a
sequence of lots has been shown for a specific metric toler-
ance
Tol
and discussing the relation of the
AQL
parameter in
relation to the actual quality of the lots.
The main features of the proposed method can be summa-
rized as follows:
• It is not limited by the requirement of normality of
positional errors, one of the major drawbacks of other
existing methods (e.g., The
NSSDA
or
ISO
3951).
• No previous underlying assumption is needed for the
base statistical model of errors, which means that the
application is universal (e.g., 1D, 2D, 3D, etc. with
parametric or non-parametric error models).
• It is based on a statistical contrast process and requires
smaller sample sizes than statistical accuracy estima-
tion processes.
• This method introduces the user and producer risk into
positional accuracy controls, which is a very desirable
circumstance because it gives transparency to trade
relations.
• It can be applied to any type of positional and geo-
metric controls (points, line-strings, etc.) because the
statistical basis is very simple.
• Positional quality is expressed in a very simple and
understandable way by the percentage of positional
defectives combined with a metric tolerance.
• Positional quality is expressed in the same way as other
spatial data quality elements and can be expressed by
the percentage of defectives or defects.
• The same control framework is valid for other quality
aspects (e.g., thematic, completeness, logical consis-
tence), which is a very desirable circumstance in order
to facilitate quality analysis, management, and reporting.
• The method can be applied to lot by lot data supplies;
this situation is very new for positional accuracy con-
trols and is of great interest for supply contracts.
• It is based on the application of a very well-known
international standard (
ISO
2859-1), and this can stimu-
late the transfer of knowledge and best practices from
other sectors of the industry to the geomatic sector.
• The use of a
BaM
as described opens up the opportunity
of applying all the possibilities that the
ISO
2859 series
of standards offers: isolated lot inspection (
ISO
2859-2),
skip-lot sampling (
ISO
2859-3), assessment of declared
quality levels (2859-4), and sequential sampling plans
(
ISO
2859-5).
Acknowledgments
This work has been funded by the Ministry of Science and
Technology of Spain and the European Regional Develop-
ment Fund under Grant No. BIA2011-23217. The authors also
acknowledge the Regional Government of Andalusia (Spain)
for the financial support since 1997 for their research group
(Ingeniería Cartográfica) with code PAIDI-TEP-164.
References
Abbas, L., P. Grussenmeyer, and P. Hottier, 1995. Contrôle de la
planimétrie d´une base de données vectorielles: Une nouvelle
méthode basée sur la distance de Hausdorff: El méthode du
contrôle linéaire,
Bulletin Societé Française de Photogrammétrie
et Télédétection
, 137:6–11.
Ariza-López, F.J, and J. Rodríguez-Avi, 2014a. A statistical
model inspired by the National Map Accuracy Standard,
Photogrammetric Engineering & Remote Sensing
, 80(3):271–281.
Ariza-López, F.J, and J. Rodríguez-Avi, 2014b. A method of positional
quality control testing for 2D and 3D line strings, Transactions in
GIS, doi: 10.111/tgis.12117.
Ariza-López, F.J., A.D. Atkinson-Gordo and J. Rodríguez-Avi, 2008.
Acceptance curves for the positional control of geographic data
bases,
Journal of Surveying Engineering
, 134(1):26–32.
Ariza-López, F.J., A.D. Atkinson-Gordo, J. Rodríguez-Avi, and
J.L. García-Balboa, 2010. Analysis of user and producer risk
when applying the ASPRS Standards for Large Scale Maps,
Photogrammetric Engineering & Remote Sensing
, 76(5):625–632.
Ariza-López, F.J, A.T. Mozas-Calvache, M.A. Ureña-Cámara, M.V.
Alba-Fernández, J.L. García-Balboa, J. Rodríguez-Avi, and J.J.
Ruiz-Lendínez, 2011. Influence of sample size on line-based
positional assessment methods for road data,
ISPRS Journal of
Photogrammetry and Remote Sensing
, 66(5):708–719
ASCE, 1983.
Map Uses, Scales and Accuracies for Engineering and
Associated Purposes
, American Society of Civil Engineers,
Committee on Cartographic Surveying, Surveying and Mapping
Division, New York.
ASPRS, 1990. ASPRS Accuracy Standards for Large Scale Maps,
Photo-
grammetric Engineering & Remote Sensing
, 56(7):1068–1070.
ASPRS, 2004.
ASPRS Guidelines: Vertical Accuracy Reporting for
Lidar Data,
American Society for Photogrammetry and Remote
Sensing, Bethesda, Maryland.
ASPRS, 2015. ASPRS Positional Accuracy Standards for Digital
Geospatial Data, November 2014,
Photogrammetric Engineering
& Remote Sensing
, Volume 81, No. 3, 53 p., URL:
http://
, doi:10.14358/
PERS.81.4.281.281.
Banovac, E., D. Pavlovic, and N. Vistica, 2012. Analyzing the
characteristics of sampling by attributes,
Recent Researches in
Circuits, Systems, Multimedia and Automatic Control
(V. Niola,
Z. Bojkovic, and M.I. Garcia-Planas, editors), WSEAS Press,
pp:158–163.
Bonin, O., and F. Rousseaux, 2005. Digital terrain model computation
from contour lines: How to derive quality information from
artifact analysis,
GeoInformatica
, 9:253–268.
Cayo, M.R., and T.O. Talbot, 2003. Positional error in automated
geocoding of residential addresses,
International Journal of
Health Geographics
, 2:10.
Dodge, H.F., 1969. Notes on the evolution of the acceptance sampling
plans, Part III,
Journal of Quality Technology
, 1(2):77–88.
Duncan, A.J., 1986.
Quality Control and Industrial Statistics
, Fifth
edition, Irwin, Homewood, Illinois, 992 p.
Ferrell, W.G., and A. Chhoker, 2002. Design of economically optimal
acceptance sampling plans with inspection error,
Computers &
Operations Research
, 29(10):1283–1300.
FGDC, 1998.
FGDC-STD-007: Geospatial Positioning Accuracy
Standards, Part 3. National Standard for Spatial Data Accuracy
,
Federal Geographic Data Committee, Reston, Virginia.
Goodchild, M.F., and G. Hunter, 1997. A simple positional
accuracy measure for linear features,
International Journal of
Geographical Information Science
, 11(3):299–306.
Hsu, L., and J. Hsu, 2012. Economic design of acceptance sampling
plans in two-stage supply chain,
Advances in Decision
Sciences
, Volume 2012, Article ID 359082, 14 p., doi:
10.1155/2012/359082.
ISO, 1985.
ISO 2859-2:1985 Sampling Procedures for Inspection by
Attributes - Part 2: Sampling Plans Indexed by Limiting Quality
(LQ) for Isolated Lot Inspection
, International Organization for
Standardization, Geneva.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
August 2015
667
