An important factor in making decisions of conformity assessment is to allow for the risks of incorrect decision-making arising from uncertainty.

(a) Comparing a distribution (PDF) of entity values with a specification limit, SL

Test results clearly inside or outside the regions of permissible values can be lead readily to unambiguous decisions about conformity or non-conformity.

Uncertainty can lead to:

- correctly conforming entities being incorrectly failed on inspection
- non-conforming entities being incorrectly passed on inspection

particularly when a test result is close to a specification limit. As shown in the Figure* *(a), a test result, apparently within limits, might actually be non-conforming since the ‘tail’ of the probability distribution function extends slightly beyond the limit.

(b) Comparing a distribution (PDF) of entity values between two sets of observations

Uncertainty can also lead to ambiguity when assessing the significance in general of an apparent difference in pairs of measurement results. As shown in Figure* *(b), two measurement results can be examined as to whether they are significantly different by assessing the distance in entity value separating the two distributions PDF.

There is, as is well known, a complete set of statistical significance tests for distributions of individual and average values, as well as tests of variances. These include for variables the *t*-test and Normal tests to determine whether an unknown population mean differs from a standard population mean, and the *χ*^{2}-test and *F*-test to determine whether an unknown population standard deviation is greater or less than a standard value [Ferris *et al* 1946, Montgomery 1996]. Corresponding tests when sampling by attribute can be based on the binomial and Poisson distributions [Joglekar 2003]. The comparison and significance testing of multiple populations can be tackled by conducting analysis of variance (ANOVA) [Joglekar 2003].

Risks and the consequences of incorrect decision-making in conformity assessment of entities should be evaluated. They can be minimised by setting limits on maximum permissible measurement uncertainties and on maximum permissible consequence costs.

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