You might get the error: OLE DB or ODBC error: Login failed for user 'NT Service\MSSQLServerOLAPService' when processing a cube/dimension. Here is what causes this error and how you can resolve the problem:
SQL Server Analysis Services will use the service account(by default) to pull data from the data source (the database server that hosts the data). If your Analysis Services instance is running under the account 'NT Service\MSSQLServerOLAPService', then this account will be used(by default) to read data from the databases and if the account doesn't have read access, you will get the above error. To resolve this, just grant the account read access to the relational database(s) you are trying to pull data from.
Also, please note that it is recommended to setup the data sources to use a domain account and to setup Analysis Services to run under a domain account. More details on data source impersonation options can be found here - http://technet.microsoft.com/en-us/library/ms187597.aspx