Linearity is a separate concept from LOD or LOQ. The data describes the response.

As William mentioned, LOQ or LOD are determined with a different approach (e.g. s/n ratio) compared to linearity which is a relation between signal and concentration. LOQ/LOD gives you an idea of the detection sensitivity. In some cases, LOQ falls inside the calibration curve, but in other cases, LOQ can be lower than the lower limit of the calibration curve.

@ William @ Marcos: Thanks for the reply. For LOD determination using 3.3SD/Slope formula, the SD and Slope is the standard deviation of the area under linearity curve and slope of the linearity calibration curve... Is it correct?

I suggest you to have a look to these analytical method validation guidelines in which you will find the existing methodologies for LOD/LOQ.

https://www.ema.europa.eu/en/documents/scientific-guideline/ich-q-2-r1-validation-analytical-procedures-text-methodology-step-5_en.pdf

LoD can definitely fall outside the linearity. According to FDA guidelines, LoQ (they use the term lower limit of quantification, LLOQ, instead) must fall within the linearity. (linearity is the range between LLOQ and ULOQ).

Please look at the following below links which may help you in your analysis:

https://juniperpublishers.com/omcij/pdf/OMCIJ.MS.ID.555722.pdf

https://ec.europa.eu/jrc/sites/jrcsh/files/lod_loq_guidance_document_food_contaminants_2016.pdf

Thanks

LOD = Limit of Detection & LOQ = Limit of Quantitation.

Linearity should cover LOQ, because it is the lower level of quantitation limit of your method. Your method quantitation level start from LOQ.

LOD it not required to cover in Linearity as it is only a limit of detection.

Conclusion: Only LOD can fall outside the linearity range.