Navigate to the final approach course after radio failure under IFR
First, squawk 7600 to let ATC know you have lost two way radio communications and to clear traffic out of your way.

Then, from the AIM, Section 4. Two-way Radio Communication Failure  

Section 6-4-1.c. includes:  


  1. General. Unless otherwise authorized by ATC, each pilot who has two-way radio communications failure when operating under IFR must comply with the rules of this section.


and  


  2. VFR conditions. If the failure occurs in VFR conditions, or if VFR conditions are encountered after the failure, each pilot must continue the flight under VFR and land as soon as practicable.


This is the preferable solution, but the question said to assume the conditions are IFR. Which leads to (displaying only applicable sections):  


  3. IFR conditions. If the failure occurs in IFR conditions, or if subparagraph 2 above cannot be complied with, each pilot must continue the flight according to the following:  
  
  (a) Route.
   ...
  (2) If being radar vectored, by the direct route from the point
  of radio failure to the fix, route, or airway specified in the vector
  clearance;  
  
  (c) Leave clearance limit.  
  
  (1) When the clearance limit is a fix from which an approach begins,
  commence descent or descent and approach as close as possible to the
  expect further clearance time if one has been received, or if one has
  not been received, as close as possible to the Estimated Time of
  Arrival (ETA) as calculated from the filed or amended (with ATC)
  Estimated Time En Route (ETE).  


So the expectation of ATC would be that the crew would fly outbound, make a right turn and intercept the localizer and fly the approach.  

It would be a challenge to fly it without DME, but not impossible from the starting point. Radar or DME (or GPS) is needed to get to the IAF. If the pilot had a good estimate of his location when comm was lost, it would be to fly outbound for about 1 minute and then a right 180 deg turn to intercept the localizer. Once the glideslope is intercepted, being on GS plus altitude allows to to estimate passage of TIMSE and FUMBL. The rest of the approach can be timed.