I think you may find papers on insulation tracking resistance of HV insulatiors

and IEC specifications on the same might be of help...

Cheers

As an example  the surface resistivity  on insulator surface  is given by

rhosurface = Rs *d/l where Rs is resistance measured between

 two electrodes of width d and distance l ...this is from ref book (see also P52)

"Electrical  Engg Materials "' by N.P. Bogoroditsky  Mir publishers

Cheers

@Narasim Ramesh-Thanks for your answer.

Dear Libimol,

If the high impedance surface results in arcing, which depends on the system voltage level, there are several publication on such issue.

Attached is one of the very last publications on the mathematical modeling of what we call High Impedance Fault.

Bests,

Amin

Article Detection of High Impedance Fault in Power Distribution Syst...