Statistical Decisions in Quality Audits — a Possibilistic Interpretation of Single Statistical Tests

  • Olgierd Hryniewicz
Conference paper
Part of the Frontiers in Statistical Quality Control book series (FSQC, volume 7)


Properties of statistical tests which are used in statistical quality control have very good interpretation in the case of sequences of similar tests, for example in the acceptance sampling of series of production lots. However, there is no convincing practical interpretation of test results when tests are performed only once, as in the case of the acceptance sampling of isolated lots. This happens especially in quality auditing, when auditors have to verify claims about declared quality levels using only the available statistical data. For such a case we propose a simple interpretation of tests results in terms of the theory of possibility [10]. Alternative hypotheses concerning the declared quality levels are validated using Possibility of Dominance (PD), Possibility of Strict Dominance (PSD), Necessity of Dominance (ND), and Necessity of Strict Dominance (NSD) indices.


Quality Level Sampling Plan Quality Audit Possibility Distribution Statistical Quality Control 
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  1. 1.
    Bickel, P. J., Doksum, K.A. (1977) Mathematical Statistics. Basic Ideas and Selected Topics. Holden Day, Inc., San Francisco.Google Scholar
  2. 2.
    Cutell, V., Montero, J. (1999) An Extension of the Axioms of Utility Theory Based on Fuzzy Rationality Measures. In: Preference and Decisions under Incomplete Knowledge, J. Fodor, B. De Baets, P. Perny (Eds.), Physica-Verlag, Heidelberg, 33–50.Google Scholar
  3. 3.
    Dubois, D., Prade, H. (1983) Ranking fuzzy numbers in the setting of possibility theory, Information Sciences, 30, 184–244.CrossRefMathSciNetGoogle Scholar
  4. 4.
    Dubois, D., Prade, H. (1997) Qualitative possibility theory and its applications to reasoning and decision under uncertainty, Belgian Journal of Operations Research, Statistics and Computer Science, 37, 5–28.MATHMathSciNetGoogle Scholar
  5. 5.
    Dubois, D., Prade, H., Sabbadin, R. (2001) Decision-theoretic foundations of qualitative possibility theory. European Journal of Operational Research, bfl28, 459–478.CrossRefMathSciNetGoogle Scholar
  6. 6.
    ISO 2859-1: 1989, Sampling procedures for inspection by attributes — Part 1: Sampling plans indexed by acceptable quality level (AQL) for lot-by-lot inspection.Google Scholar
  7. 7.
    ISO 2859-2: 1985, Sampling procedures for inspection by attributes — Part 2: Sampling plans indexed by limiting quality (LQ) for isolated lot inspection.Google Scholar
  8. 8.
    ISO 2859-4: 1999, Sampling procedures for inspection by attributes — Part 4: Procedures for assessment of stated quality levels.Google Scholar
  9. 9.
    Lehmann, E.L. (1986) Testing Statistical Hypotheses, 2nd ed., J.Wiley, New York, 1986.CrossRefMATHGoogle Scholar
  10. 10.
    Zadeh, L.A. (1978) Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3–28.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Olgierd Hryniewicz
    • 1
  1. 1.Systems Research Institute of the Polish Academy of SciencesUniversity of Applied Informatics and ManagementWarsawPoland

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