## 4 Conclusions  
A systematic AQbD approach was used to improve the knowledge around the HS-SPME/GC-MS method for TMA and DMA analysis in fish samples. After the extraction optimization, the proposed conditions for its implementation were based on the use of DVB/CAR/PDMS fiber, with 0.5 mL of the sample, 1 mL of the NaOH solution (15 M), and 1 mL of the NaCl solution (35%), in a water bath at 35 \({}^{\circ}\)C for 30 min. For GC-MS analysis, the best instrumental conditions achieved with a BP-20 column were an oven temperature of 80 \({}^{\circ}\)C, ramp speed of 50 \({}^{\circ}\)C/min to a maximum of 220 \({}^{\circ}\)C, and gas flow rate (helium) of 1.0 mL/min. The method robustness was demonstrated through the Monte Carlo simulation and capability analysis process (1.36-1.49 Cpk). The method validation revealed the satisfactory figures of merit, demonstrating its suitability for the target analysis (Table 3). The method was tested on GSB specimens through the simulation of a degradation experiment, using complementary methodologies to confirm the shelf life results, such as microbial analysis, sensory analysis, and physical analysis. The outcome allows the proposal that the criteria of rejection through TMA analysis (12 mg/100g), was reached between 9 and 10 days. Additionally, analyzing all the results, it is possible to suggest a shelf life period of 9 days (\(\pm\)1 day) for GSB, under the specific conditions of the present study. Besides, not all fish species generate TMA during degradation, and the proposed HS-SPME/GC-MS methodology revealed a reliable alternative to the traditionally used distillation techniques. The following are available online at [[http://www.mdpi.com/2304-8158/9/9/1321/s1](http://www.mdpi.com/2304-8158/9/9/1321/s1)]([http://www.mdpi.com/2304-8158/9/9/1321/s1](http://www.mdpi.com/2304-8158/9/9/1321/s1)), Figure S1: Ishikawa diagram for quality risk assessment; Figure S2: Pareto chart analysis for HS-SPME and GC-MS; Figure S3: Desirability surface contour method analysis for the effects of all CMPs; Figure S4: The pareto ranking analysis for CG-MS(BP20); Table S1: Chemical methods used for fish freshness determination; Table S2: Gas chromatography works related with TMA and/or DMA extraction; Table S3 - Scheme of the Quality Index Method (QIM) proposed for _Sparus aura_ (GSB); Table S4: Results from DoE 34\({}^{-1}\) level, for HS-SPME Knowledge of space, for all tested fibres; Table S5:The HS-SPME/MODR results for the observed vs. predicted values agreement; Table S6: GC-MS MODR results, from DOE fractional factorial design 33\({}^{-1}\) level; Table S7: GC-MS/MODR observed vs. predicted values analysis; Table S8: Fractional Factorial Design 33\({}^{-1}\) level, for HS-SPME(DVB/CAR/PDMS) robustness analysis; Table S9: GC-MS Robustness results, from DOE fractional factorial design 33\({}^{-1}\) level; Table S10: Analysis of agreement between observed and predicted values for HS-SPME robustness; Table S11: GC-MS robustness evaluation by, observed vs. predicted values analysis; Table S12: Attributes evaluation for QIM analysis. Conceptualization: J.F., P.S., P.V.-P. and J.S.C. ; methodology; J.F., P.S., P.V.-P. and J.S.C. ; software: J.F. and P.S. ; validation: [PERSON] and [PERSON]; formal analysis: [PERSON]; investigation: [PERSON]; resources: [PERSON], [PERSON]-P. and [PERSON]; data curation: [PERSON]; writing--original draft preparation: [PERSON]; writing--review and editing: [PERSON], [PERSON], [PERSON]-P. and [PERSON]; visualization: [PERSON]; supervision: [PERSON]-P. and [PERSON]; project administration: [PERSON]; funding acquisition: [PERSON]. All authors have read and agreed to the published version of the manuscript. The authors acknowledge FCT-Fundacao para a Ciencia e a Tecnologia through the CQM Base Fund-UIDB/00674/2020, the Programmatic Fund-UIDP/00674/2020, and by ARDTIT-Agencia Regional para o