SEMI M56 - Practice for Determining Cost Components for Metrology Equipment Due to Measurement Variability and Bias

Volume(s): Materials
Language: English
Type: Single Standards Download (.pdf)

This Standard was technically approved by the Silicon Wafer Global Technical Committee. This edition was approved for publication by the global Audits and Reviews Subcommittee on August 17, 2018. Available at and in October 2018; originally published November 2003; previously published May 2012.


This Practice covers a methodology to determine the costs associated with misclassification of product due to variability and bias of measurement equipment. These costs are associated with failing product that conforms with specifications and passing product that does not conform with specifications.


This Practice can be applied to make relative cost comparisons between two or more measurement gauges operating under conditions specified by the user. These conditions may include any aspects of the measurement system affecting the measurement results directly or indirectly (e.g., ambient conditions, throughput, recipe). This Practice can also be used to compare the relative costs of a single instrument under different operating conditions.


A measurement gauge is defined by a specific realization of systems and subsystems required to make measurements. Gauges that differ in at least one system or subsystem may be considered different for the purpose of comparison.


This Practice can be applied to any metrology equipment or to the metrology portion of any equipment that includes metrology.


This Practice covers the case in which the metrology equipment is used to make binary decisions about the item being measured, that is, only two outcomes are possible (e.g., pass/fail, go/no-go, ship/scrap). Models for decisions with more than two outcomes, such as the binning of data, are beyond the scope of this Practice.


To apply the formulae in this Practice, the user estimates either the probability density function (PDF) or cumulative distribution function (CDF) of the process characteristic or characteristics of interest. The distributions can be based on a theoretical model or on empirical information obtained from manufacturing data.


To apply the formulae in this Practice, the user estimates all biases and variances associated with the equipment being compared under the specified operating conditions and with respect to the process characteristic(s) of interest. These values can be obtained from a measurement system capability analysis (see SEMI E89).


To apply the methodology of this Practice, the user estimates the costs of classification and misclassification due to decisions made as a result of measurements. Estimates of such costs are obtained from the business model used to describe the manufacturing process in which the measurements are performed. Consequently, different users may arrive at different estimates of costs because their computations may contain different elements.


The output of this Practice is the cost component due to measurement variability and bias for each process characteristic and metrology system evaluated.


Referenced SEMI Standards

SEMI E35 — Guide to Calculate Cost of Ownership (COO) Metrics for Semiconductor Manufacturing Equipment
SEMI E89 — Guide for Measurement System Analysis (MSA)
SEMI M1 — Specifications for Polished Single Crystal Silicon Wafers
SEMI M59 — Terminology for Silicon Technology

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