Hello!,
With 3-D Solid tetrahedral elements the most important quality checks are jacobian and TET Collapse (also named TET-AR): jacobian never bigger than 0.7, this is my limit, unless 0.6 is the maximum allowable value.
Here you have the Element Quality Check imposed by FEMAP V2020.2 valid for any FEA solver (if you need explanation of the meaning of any item please let me know it):



And here you have the Element Quality checks of the Simcenter Nastran solver from SIEMENS:

Warp = Warping
IAMin = Minimum Internal Angle in degrees
IAMax = Maximum Internal Angle in degrees
AR = Aspect Ratio
EPLR = Edge Point Length Ratio
EPIA = Edge Point Internal Angle in degrees
DetJ = Jacobian

Which element checks are available depend on element topology:

Quadrilaterals - Quad Skew, Quad Warp, Quad AR, Quad Taper, Quad IAMin, Quad IAMax
Triangles - Tria Skew, Tria AR, Tria IAMax, Tria EPLR
Tetrahedrals - Tetra AR, Tetra DetJ, Tetra EPLR, Tetra EPIA
Hexahedrals (Bricks) - Hex AR, Hex DetJ, Hex EPLR, Hex EPIA, Hex Warp
Wedges - Penta AR, Penta DetJ, Penta EPLR, Penta EPIA, Penta Warp
Pyramids - Pyr AR, Pyr DetJ, Pyr EPLR, Pyr EPIA, Pyr Warp



Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48004 BILBAO (SPAIN)
WEB: http://www.iberisa.com
Blog de FEMAP & NX Nastran: http://iberisa.wordpress.com/

It seems that you use Abaqus. In such case check the documentation chapter "Verifying your mesh". It explains all the element quality criteria used during mesh verification (including shape factor and aspect ratio).

Thank You BlasMolero and FEA Way.

Kind regards,