Joruri Method (浄瑠璃方式 Jōruri Hōshiki) is the term used to refer both to a method used to create artificial humans and to those same artificial humans.
The Joruri Method is used to create artificial humans akin to living dolls, similar to a western automata being created by a clockmaker. A Joruri Method is capable of acting, talking and thinking like a normal human. They look human on the outside, but their insides are made of completely different materials. For example, Renge Meinokawa has ribs made of wood polished to an amber color. Her organs are far removed from soft masses of dark red. Inside her body there are shells shaped like the different organs, but these do not look alive and look more like handmade leather bags. These organs pulsate, but there is no heartbeat or mechanical noises. Her gears move so smoothly they produce no noise.
A Joruri Method is presumably physically superior to a normal person, as Renge attributed her continued escape from her Guard of Honor's pursuers to her constitution, and Kyousuke Shiroyama considered the feat outside his own abilities, though maybe possible to someone like Lu Niang-Lan. Renge is also capable of freely opening her torso to reveal her artificial organs without suffering any harm.
The Meinokawa family has long worked in this field, having initially been dedicated to performing doll funerals. Before Repliglass became widespread, the family secretly built Joruri Method vessels. The ideal form was to have a human summoner and a Joruri Method vessel to control the Material with no interference whatsoever. However, Higan Meinokawa was born with great talent to be a vessel, preventing her from being a summoner. After a failed attempt to remove that talent that caused Higan's hair and eye color to change, Renge Meinokawa was built as the world's first fully artificial summoner. The skeletal structure, arrangement of organs, and other basic features of Higan’s body were combined into the "ideal Meinokawa Higan" that the entire family felt should have been born. That is why Renge is treated like the elder twin despite being made later. Since Renge was created as the ideal Higan Meinokawa based on her body, her organs would be able to be transplanted to Higan with no issue.
Due to her nature as a copy of Higan, Renge is capable of synchronizing with her and overwriting her current summoner-vessel contract.