'rigorous process' is a perfectly correct and usable phrase in written English. You can use it when referring to a process that requires considerable effort, determination, and discipline. For example, "The job applicant had to go through a rigorous process in order to be considered for the position.".
Valve harvest, processing, and manufacturing follow a rigorous process.
This is a rigorous process".
"It's a rigorous process, it's really tough," Chompff said.
"It's gone through a rigorous process of checks," she insists.
Military officials describe a rigorous process of picking targets.
They go through a rigorous process to meet new standards.
When student work is discussed, it has to be a safe but rigorous process.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.