When the mandate of an arbitrator terminates in accordance with R.S. 9:4253 or 4254 or because of his withdrawal from office for any other reason or because of the revocation of his mandate by agreement of the parties or in any other case of termination of his mandate, a substitute arbitrator shall be appointed according to the rules that were applicable to the appointment of the arbitrator being replaced.
La. R.S. § 9:4255