Hello everyone…
I am not some protocol expert but long time ago i worked on this scenario and reached the following conclusion. Please note that its based solely on my “own understsanding” and sharing it just for reference.
So to simplify things lets take the two scenarios.
First “UE Send MSG3 but MSG4 not Received” and secondly “NACK Received for MSG3”
UE Send MSG3 but MSG4 not Received
When UE send MSG3 two timers start in parallel. One is T300 and other one is Contention Resolution Timer
If the UE do not receive msg4 (Contention Resolution message) within this timer, then it go back to Step 1 i.e. transmitting Random Access Preamble
Please note that Contention Resolution Timer expires while T300 is still running because T300 > Contention Resolution Timer.
Assume that events were successful till MSG3 i-e eNB receive MSG3 but no MSG4 received in DL. Now UE will send the preamble again after Contention Resolution timer expiry and this time all next events in chain become successful (and all this happened before expiry of T300).
In above mentioned scenario eNB received MSG3 twice before expiry of T300 (As indicated by tick marks). This new attempt will be pegged in pmRrcConnEstabReatt in Ericsson. These Re-Establishments are subtracted from accessibility formula.
If the Random Access attempt of a UE fails, either because the preamble sent by the UE was not detected by the eNB or the UE lost the contention resolution, the UE has to start the process over again. To avoid contention and overload, the eNB can signal the UEs that they have to wait a certain time before they try to connect again. The parameter that controls this is called the Backoff indicator (BI) and is signaled by the eNB in the random access response.
NACK Received for MSG3
If there is a HARQ NACK for msg3 (RRCconnectionRequest) and it has to be re-transmitted then this Contention Resolution Timer will be re-started
UE wait for NACK or CRT (Contention Resolution Timer) expiry. NACK can be received any time before CRT Expiry. If NACK received (before CRT Expiry) UE will do Re-Transmission (How Many Retransmissions from UE Side → It is given in SIB 2 under maxHARQMsg3Tx). If no NACK Received and CRT Expires UE send preamble again with stepped up (As shown in bellow figure)
After reading multiple articles I reached this conclusion so far… Would love if someone relate it with 3GPP [Either +vely or -vely]… 
Cheers 