King, M; Nayak, S (2023) An Economic Model for the Value Attributable to High-Quality Calibrations by Reducing Mistakes in Conformance Testing. NPL Report. IEA 19

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Abstract

Since NPL only earns income by selling services to customers wanting ‘first-hand’ calibrations, the value (economic benefit) created by the ‘fanout’ is missing from NPL’s revenue. The first part of this document develops an economic model for the value created when using measurement for conformity testing. This model shows how measurement information creates value by reducing mistakes (fewer “false positives” and “false negatives”) in conformity testing. The second part of this document introduces calibration as a perturbation on top of these measurement activities. Moreover, there can be value created from this reduction in uncertainty, which is where the services of NPL and the calibration laboratories play a key role.

Previous studies have explored the economic loss from making type-1 errors (“false positives”) and type-2 errors (“false negatives”) in the context of conformance testing. However, such studies do not treat the conditional probabilities of making type-1 and type-2 errors as “choice variables” that are under control of a decision maker. By treating these conditional probabilities as exogenous, they do not internalise the trade-off between type-1 and type-2 errors. In this paper, we address this gap in the literature by endogenizing the conditional probability of a type-1 error (α) and the probability of a type-2 error (β). The decision maker tries to minimise the total cost incurred due to these errors, subject to the trade-off that exists between them.

This is an economics study that borrows a little from metrology as opposed to a study by engineers that borrows a little from economics. Firstly, our analysis gives formulae for the relative uncertainty of the measurement process (σ) and a lower bound for the scrap rate (τ) as functions of the conditional probabilities for type-1 and type-2 errors (α and β). Secondly, this analysis yields a formula for the economic benefit created by using ‘first-hand’ calibrations to reduce the uncertainty of the measurement process. Hence, this document provides the mathematics behind a ‘calculator’ giving an estimate of the benefit from ‘first-hand’ calibrations based on assumptions about the parameters. Finally, this model will really come to life once we have estimates of the core parameters from a forthcoming measurement survey.

Item Type:	Report/Guide (NPL Report)
NPL Report No.:	IEA 19
Divisions:	Strategy Directorate
Identification number/DOI:	10.47120/npl.IEA19
Last Modified:	18 Sep 2023 08:37
URI:	https://eprintspublications.npl.co.uk/id/eprint/9816