Accountability arrived before Responsibility...at least the on-line Merriam-Webster dictionary says that...the word Accountability joined the English language in 1770 and the word Responsibility arrived the following year.

Isn't that counter-intuitive?

Also, according to Merriam-Webster

Definition of ACCOUNTABILITY

:  the quality or state of being accountable; especially :  an obligation or willingness to accept responsibility or to account for one's actions

First known use 1770

and

Definition of RESPONSIBILITY

: the state of being the person who caused something to happen

: a duty or task that you are required or expected to do

First known use 1771

In the Merriam-Webster on-line dictionary we see Accountability defined in terms of 'accepting responsibility' and 'accounting for one's actions' and Responsibility defined in terms of 'a duty you are expected to do'. 

In business, Accountability is what we want.

In business we want people who accept responsibility for performing duties and understand the importance of accounting for their actions. When our businesses employ those sort of people we can rely on them to perform. And we can rely on them to let us know when they are having difficulties.

It's the communication implicit in accountability that caused it to arrive before responsibility.