ENBIS: European Network for Business and Industrial Statistics

OPTIMISED UNCERTAINTY & COST OPERATING CHARACTERISTICS: NEW APPROACHES TO STATISTICAL SIGNIFICANCE TESTING IN GLOBAL CONFORMITY ASSESSMENT

23 September 2009, 10:25 – 10:45

Abstract

Submitted by

Leslie Pendrill

Authors

LESLIE R PENDRILL

Affiliation

SP Technical Research Institute of Sweden, Measurement Technology Box 857, SE-501 15 Borås, Sweden,leslie.pendrill@sp.se

Abstract

There is increasing interest and enhanced insight into decision-making by extending classical, purely statistical treatment of customer and supplier risks, towards a more ‘stakeholder’ motivated (and ultimately optimised) approach in terms of effective costs associated with manufacture, testing and incorrect decision-making. Discussion is in terms of new decision-theory tool – the “operating cost characteristic” – combined with an optimized uncertainty methodology.

In general, the impact of a wrong decision in conformity assessment is expressed as a risk R, defined as the probability p of the wrong decision occurring multiplied by the cost C of the consequences of the incorrect decision:
R = p x C (1)
- a more general, historical expression of statistical expectation.

Incorrect acceptance of a non-conforming object on inspection will lead to customer costs associated with out-of-tolerance product. Overall costs, E, consisting of a sum of testing costs, D, and the costs, C, associated with customer risk, can be calculated with the expression:
(2)
with , where RPV denotes the region of permissible values and σ is a measure of dispersion.

Overall costs , according to (2) can be either plotted over:
• a range of quantity values of for a given dispersion, , and ‘guard-band’ factor H close to a (lower) specification limit LSL – yielding an “operating cost characteristic” analogous to the traditional, probability-based operating characteristic
• a range of test uncertainties, , for a given mean quantity value , the so-called “optimised uncertainty curve”
A complete, 3D surface of overall cost can indicate the optimum level of measurement effort of these two ranges, as recently published by the author, and is applied to amongst others: optimized acceptance sampling; optimized testing of measurement instruments; and an analysis of optimised calibration intervals and ‘guard-banding’.

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