The phrase "rigorous manner" is correct and usable in written English.
You can use this phrase when you want to describe how something is done in an extremely thorough and exacting way. For example, "She performed her work in a rigorous manner, ensuring that all of the details were taken care of."
A spokesman for the DfE said it collected its data in a "robust and rigorous" manner.
"Even we, astronauts, are a small team, we train in a rigorous manner and we wear a blue suit".
That the authorities nevertheless take these comments seriously can be seen in the rigorous manner in which they are monitoring events in Qom.
People had speculated about why this should be so, but nobody had come up with a model that explained it in a rigorous manner.
The same urge to examine what politicians get up to informed all the programmes he made, to which he brought a rigorous manner and a verbal dexterity that were second to none.
Identifying those at risk for this disease in their 50s and 60s is challenging, and the draft F.D.A. guidance seeks to deal with that challenge in a scientifically rigorous manner.
This is just not so, says Piketty, and he makes his case in a clear and rigorous manner that debunks everything that capitalists believe about the ethical status of making money.
The theories of the Neogrammarians, a group of German historical linguists and classical scholars who first gained prominence in the 1870s, were especially important because of the rigorous manner in which they formulated sound correspondences in the Indo-European languages.
The coupling between the fluid and plate is taken into account in a rigorous manner.
Bayesian techniques provide powerful tools for integrating, in a rigorous manner, the two types of uncertainties.
The coupling between the fluid and laminate is taken into account in a rigorous manner.
