”a material is tested (axial fatigue test) the resultant mean SN curve shows 50 % probablity of survival/failure.” 

I don’t know why you tacked on the phrase “as accepted by many researchers”, what do you mean by that?

You have to also say the stress ratio for the axial fatigue test. Was the stress varying between tensile and zero, or was the stress varying between tension and compression?  The latter has a zero mean stress.

Tensile strength is based on a one-time load event, so is a totally different number than the SN curve data.

Tensile strength is measured using many samples.  There will be variation in the values of those samples. There will be a mean strength, but no one uses that for design purposes. The data for all samples is analyzed to come up with an Allowable Strength value. Different standards are used to come up with that value. B-Basis is a strength value at which only 10 in 100 specimens will fail with a 95% confidence level. As more specimens are tested a higher value of strength can be used as a valid allowable.

Fatigue testing requires multiple samples to be tested at each stress level. Also, the cycles must be run until the sample breaks. This makes gathering data to create an SN curve very expensive.