Whenever a judge of the supreme court or a judge of the district court of this state who is not a member of the public employees retirement system becomes unable, because of mental or physical disability, to perform the judicial duties of the office during the remainder of the term for which that judge has been elected or appointed and makes a written application to the chief justice or acting chief justice of the supreme court for retirement, setting forth the nature and extent of such disability, the supreme court judges and the district court judges shall make such investigation as they deem advisable. If two-thirds of the supreme court judges and the district court judges thereby determine that disability exists and that the performance of that judge’s judicial duties is thereby substantially impaired and that the impairment will not likely be remedied, the chief justice or acting chief justice, by written order to be filed in the office of the secretary of state, shall thereupon direct the retirement of the judge. The order must specify the    effective date of the retirement and thereby create a vacancy in the office which must be filled by appointment as provided by law. A copy of the order must be transmitted to the office of management and budget. If the disability renders the judge unable to make or direct the making of the application, it may be made by a legally appointed guardian of the judge.