ORA-01078: failure in processing system parameters ORA-01565: error inidentifying file '+DATA/ORCL/spfileorcl.ora' ORA-17503: ksfdopn:2 Failed to open file +DATA/ORCL/spfileorcl.ora ORA-01034: ORACLE not available ORA-27123: unable to attach to shared memory segment Linux-x86_64 Error: 13: Permission denied

There are many things for occur error:

ORA-01078: failure in processing system parameters 
ORA-01565: error inidentifying file '+DATA/ORCL/spfileorcl.ora'; 
ORA-17503: ksfdopn:2 Failed to open file +DATA/ORCL/spfileorcl.ora 
ORA-01034: ORACLE not available 
ORA-27123: unable to attach to shared memory segment 
Linux-x86_64 Error: 13: Permission denied

I write here often issues and their solutions:
first of all check permission on $ORACLE_HOME/bin/oracle file in both ASM and RDBMS home, this file is oracle executable file, there must be permission 6751 for this file. let me check

ls -l $ORACLE_HOME/bin/oracle
-rwxrwxrwx 1 oracle asmadmin /u01/app/oracle/product/11.2.0/dbhome_1/bin/oracle

change it with root user

chmod 6751 /u01/app/oracle/product/11.2.0/dbhome_1/bin/oracle

another often issue is that oracle user have not proper groups in operating system level, for normal work there must be this groups

[oracle@node1]$ id
uid=54321(oracle) gid=54321(oinstall) groups=54321(oinstall),54322(dba),54323(asmadmin),
54324(asmdba),54326(oper)

if they aren't then add oracle user in these groups with command

usermod -G usermod -G oinstall,dba,oper,asmdba,asmadmin oracle

if you have grid user also check for it, there must be groups shown below

[grid@node1]$ id
uid=54322(grid) gid=54321(oinstall) groups=54321(oinstall),54322(dba),54323(asmadmin),
54324(asmdba),54325(asmoper)

i hope this will usefull for you, because i spent many time for solve this error.
thank you.