Microsoft has a status page which was getting updated regularly which is good but the details were a little light, e.g. "focused on remediation" and "users may be able to access the service by logging in to their Outlook.com accounts with a web browser as an alternative method". The problem existed almost a week.
Again this is a free service but these are situations you need to consider as you explore moving a service to the cloud.
Go read some of the comments:
I've got better reliability and almost the same service and functions as my company OWA account, free of charge as well.Cloud is a way to free up the expense of operating your own IT services.
But putting your eggs into the hands of Microsoft, Google, Amazon or any other single entity to which you represent 0.00000000001% of their annual income is a stupid idea.Realize that you are less than a rounding error to the cloud provider.