Resulting errors of measurement chains

This paper presents a theoretical analysis of error calculations during a system design. A system is understood as a measurement chain that consists of units called transducers. In general, transducers are connected in three basic configurations; serial, parallel and with feedback. In order to illustrate the analysis of error calculations we consider only two connected units for each configuration of a measurement chain. In this paper, we analyze two types of error calculations for these three basic configurations. First, a standard error calculation is described assuming that transducer errors in a measurement chain are mutually correlated. System designers frequently assume an error correlation and therefore use standard error calculations. Second, error calculations are performed assuming that transducer errors are not mutually correlated. The case of mutually uncorrelated transducer errors is very common in a real system design since the numerical specifications of individual transducers are obtained from multiple independent catalogs. Thus, it is the uncorrelated nature of transducer errors that requires a modification of standard error calculations. We analyze error calculations for each configuration of transducers and for mutually correlated and uncorrelated transducer errors. In conclusion, the error formulas assuming mutually uncorrelated transducer errors model a real system design more accurately than the standard error formulas.