For example, if we wish to know the error in density if we're measuring the temperature and pressure of a gas:
$$\rho = \frac{P\,M}{R\,T}$$
If the error in the temperature and pressure sensors were random, we can add the uncertainties in quadrature as they are also independent.
$$\frac{\delta \rho}{\rho}=\sqrt{\left(\frac{\delta P}{P}\right)^2+\left(\frac{\delta T}{T}\right)^2}$$
However, if we have a systematic error in one of the sensors, eg. pressure transducer reads 1 bar above the real value, the errors are no longer random as they have a deviation from their "true" value. Can they still be added in quadrature or should they be added directly?
Additionally, if we know that the equation of state has an error of 1% respect to some tabulated data taken as the true value, should this 1% be added in quadrature too?