The Judicial Conduct and Disability Act of 1980, 28 U.S.C. §§ 351-364 (link is external) establishes a process by which any person can file a complaint alleging a federal judge has engaged in “conduct prejudicial to the effective and expeditious administration of the business of the courts” or has become, by reason of a mental or physical disability, “unable to discharge all the duties” of the judicial office.
"conduct prejudicial" sounds like misconduct and as examples
Actions that can be classified as judicial misconduct include: conduct prejudicial to the effective and expeditious administration of the business of the courts (as an extreme example: "falsification of facts" at summary judgment); using the judge's office to obtain special treatment for friends or relatives; accepting bribes, gifts, or other personal favors related to the judicial office; having improper discussions with parties or counsel for one side in a case; treating litigants or attorneys in a demonstrably egregious and hostile manner; violating other specific, mandatory standards of judicial conduct, such as judicial rules of procedure or evidence, or those pertaining to restrictions on outside income and requirements for financial disclosure; and acting outside the jurisdiction of the court, or performance of official duties if the conduct might have a prejudicial effect on the administration of the business of the courts among reasonable people.
as a note of commentary, I will refer you specifically back to the last Senate hearing when J Kavanaugh gave his introductory remarks and allow you to derive your own conclusions as to relevance to actually complaints