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This paper exposes the existing problems for optimal industrial preventive maintenance intervals when decisions are made with right-censored data obtained from a network of sensors or other sources. A methodology based on the use of the z transform and a semi-Markovian approach is presented to solve these problems and obtain a much more consistent mathematical solution. This methodology is applied to a real case study of the maintenance of large marine engines of vessels dedicated to coastal surveillance in Spain to illustrate its usefulness. It is shown that the use of right-censored failure data significantly decreases the value of the optimal preventive interval calculated by the model. In addition, that optimal preventive interval increases as we consider older failure data. In sum, applying the proposed methodology, the maintenance manager can modify the preventive maintenance interval, obtaining a noticeable economic improvement. The results obtained are relevant, regardless of the number of data considered, provided that data are available with a duration of at least 75% of the value of the preventive interval. [ABSTRACT FROM AUTHOR]

Research on mathematics teachers' knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student' learning of PS. [ABSTRACT FROM AUTHOR]