Change-point detection methods are proposed for the case of temporary failures, when an unexpected disorder is ultimately followed by an adjustment and return to the initial state. A known base distribution of the in-control state changes to an unknown out-of-control distribution only temporarily. Durations and patterns of out-of-control segments vary, but the eventual return to the base distribution is inevitable. Sequential and retrospective methods are proposed for the detection and estimation of each pair of change-points. Examples of similar problems are shown in quality and process control, energy finance, and statistical genetics, although the meaning of disorder and adjustment change-points is quite different in these applications.
[Acknowledgment: The work of M. Baron is supported by U.S. National Science Foundation grant 1737960. The work of S. Malov is supported by the Russian Science Foundation grant 20-14-00072.]