Preface to the special issue on degradation and maintenance, modelling and analysis

The 13th spring meeting of the ENBIS society was held in Grenoble, France, on May 19–20 2022. ENBIS is the European Network for Business and Industrial Statistics. Its objective is to connect people and organisations throughout Europe to improve statistical methods and their applications in the field of business and industry. ENBIS organizes each year a one-week congress and a 2- or 3-days spring meeting.

The topic of the 13th spring meeting in Grenoble has been “Degradation and Maintenance, Modelling and Analysis”. In fact, in the field of reliability studies, the multiplication of equipment control and monitoring systems implies that degradation models become more and more prominent over lifetime models. The modelling of degradation processes, the statistical analysis of the corresponding data and their use for the predictive maintenance of industrial systems are important and challenging issues.

The aim of this Special Issue of ASMBI is not only to publish selected extended versions of papers presented during ENBIS 2022 spring meeting, but also to promote high-quality, innovative, and original works relevant to the application of statistical methods and probability models to the field of degradation and maintenance and more generally reliability analysis.

After an exhaustive peer review process, this Special Issue includes nine papers that contribute significantly to advance of the knowledge in the reliability and maintenance field. Here we introduce this collection of papers which cover both mathematical developments and practical applications.

Another modelling framework discussed in this special issue, is Phase type distributions. Any lifetime distribution can be approximated arbitrarily close by a phase type distribution. This fact makes this distribution very attractive as parametric model to failure time data with degradation trend. In this sense, Lindqvist⁶ shows how phase-type distributions can be used for modelling the effect of degradation and maintenance. The paper focuses on Phase-type models used in competing risks framework who consider multiple absorbing states on their continuous time Markov chain. Instantaneous transitions are added at certain stages to model repair actions bringing failed system into working conditions. Two different approaches are proposed, and their long run properties are studied in term of measure of reliability and maintenance efficiency.

The guest editors of this Special Issue thank all the persons who helped to make this issue possible. They are thankful to Fabrizio Ruggeri, the Editor in Chief of ASMBI, for giving them the opportunity of editing this Special Issue and for his support and guidance during the editorial process. They are also grateful to the reviewers for their careful work and constructive revisions that contribute to improve the papers. At last, they are very grateful to the authors, and more generally to all the participants of the ENBIS 2022 spring meeting, for their contributions that make this Special Issue possible.