= Internal-standard-normalized process efficiency
\b[Internal-standard-normalized process efficiency] compares the overall preparation-and-response efficiency of an <analyte> with that of an <internal standard>. With matched corresponding amounts, let $\mathrm{PE}_A$ and $\mathrm{PE}_{IS}$ be their <mass spectrometry process efficiencies>. The normalized quantity is
$$
\mathrm{PE}_{\rm norm}=\frac{\mathrm{PE}_A}{\mathrm{PE}_{IS}}
=\frac{r_A}{r_{IS}}\frac{\mathrm{MF}_A}{\mathrm{MF}_{IS}},
$$
where $r$ denotes <extraction recovery> and MF a <mass spectrometry matrix factor>. It combines recovery matching with the <internal-standard-normalized matrix factor>.
The underlying separation between recovery and matrix response is important in quantitative mass spectrometry.<Strategies for the assessment of matrix effect in quantitative bioanalytical methods based on HPLC-MS MS by B. K. Matuszewski and others>[Abstract, experimental separation of matrix effects and recovery.]{ref} A ratio near one can conceal substantial losses affecting both signals.
For original stipulated values, let analyte and standard each have recovery $0.6$ and matrix factor $0.5$. Their process efficiencies are both $0.3$, so the normalized value is 1 even though each observed response is only 30% of its matched neat reference. Now change only standard recovery to $0.9$. Its process efficiency becomes $0.45$ and the normalized value becomes $0.3/0.45=2/3$, despite identical matrix factors.
Addition timing changes the comparison. If the standard is added after the extraction stage, its recovery through that stage is effectively 1 by construction. Equal matrix responses can then cancel while the analyte's preparation loss remains. A standard added earlier can track more of the process, but equivalent behavior still requires evidence.
The desired property is a stable, appropriately calibrated analyte-to-standard response relationship. A constant nonunity normalized efficiency can be incorporated into a valid calibration; an unmodeled change across samples or levels can bias results. Report the reference, addition stage, quantities compared and blank correction rather than treating normalization as a guarantee of full material recovery.
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