The phrase "a serious process that" is correct and usable in written English.
It can be used when describing a process that requires significant attention, effort, or consideration.
Example: "Developing a new software application is a serious process that demands careful planning and execution."
Alternatives: "an important procedure that" or "a significant undertaking that".
And it's a serious process that goes into making each bottle.
A quick-fix settlement to provide just enough cover for its war-weary coalition to pull their troops out before Afghanistan descends into a civil war; or a serious process that might offer an enduring peace?
It's a serious process that every single must go through in order to find the right partner and relationship.
However, soil degradation is a serious process that is threatening the region's soil resources through its various forms and thus is affecting economic development, particularly agricultural production and associated food and nutrition security, provision of ecosystem services and increasing poverty.
Somehow or another, people have decided that looking for love is some hugely serious process that must be approached with reverence and decorum.
At a minimum, however, they must launch a serious negotiating process that would point clearly — preferably with a target date — to the end of the conflict and to the establishment of a Palestinian state.
"A cease-fire agreement is not likely to hold, even if leaders want it to, because there will be tremendous structural pressures unless you have a serious political process that begins to change the situation on the ground," said Shibley Telhami, a Middle East expert at the University of Maryland.
"It is vital that we do not play that card prematurely, but instead when there is a serious political process that will culminate in elections in which not only the people in Syria, but the 12 million or so that have been expelled are able to vote.
"In the midst of a serious budget process that affects the lives of all New Yorkers, it is counterproductive, disingenuous and dangerous to play games by announcing a so-called newly discovered crisis of the day," the governor's spokesman, Joshua Vlasto, said in a statement.
"All I would say with you about that gift is that it went through a serious process conducted by serious people.
But, back in Washington, Graham warned Lieberman and Kerry that they needed to get as far as they could in negotiating the bill "before Fox News got wind of the fact that this was a serious process," one of the people involved in the negotiations said.
