A discrete MMAP for analysing the behaviour of a multi-state complex dynamic system subject to multiple events.

A complex multi-state system subject to different types of failures, repairable and/or nonrepairable, external shocks and preventive maintenance is modelled by considering a discrete Markovian arrival process with marked arrivals (D-MMAP). The internal performance of the system is composed of several degradation states partitioned into minor and major damage states according to the risk of failure. Random external events can produce failures throughout the system. If an external shock occurs, there may be an aggravation of the internal degradation, cumulative external damage or extreme external failure. The internal performance and the cumulative external damage are observed by random inspection. If major degradation is observed, the unit goes to the repair facility for preventive maintenance. If a repairable failure occurs then the system goes to corrective repair with different time distributions depending on the failure state. Time distributions for corrective repair and preventive maintenance depend on the failure state. Rewards and costs depending on the state at which the device failed or was inspected are introduced. The system is modelled and several measures of interest are built into transient and stationary regimes. A preventive maintenance policy is shown to determine the effectiveness of preventive maintenance and the optimum state of internal and cumulative external damage at which preventive maintenance should be taken into account. A numerical example is presented, revealing the efficacy of the model. Correlations between the numbers of different events over time and in non-overlapping intervals are calculated. The results are expressed in algorithmic-matrix form and are implemented computationally with Matlab.Junta de Andalucía, Spain, under the grant FQM307Ministerio de Economía y Competitividad, España, MTM2017-88708-PEuropean Regional Development Fund (ERDF

Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model

A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units

In this study, a multi-state k-out-of-n: G system subject to multiple events is modeled through a Markovian Arrival Process with marked arrivals. The system is composed initially of n units and is active when at least k units are operational. Each unit is multi-state, each of which is classified as minor or major according to the level of degradation presented. Each operational unit may undergo internal repairable or non-repairable failures, external shocks and/or random inspections. An external shock can provoke extreme failure, while cumulative external damage can deteriorate internal performance. This situation can produce repairable and non-repairable failures. When a repairable failure occurs the unit is sent to a repair facility for corrective repair. If the failure is non-repairable, the unit is removed. When the system has insufficient units with which to operate, it is restarted. Preventive maintenance is employed in response to random inspection. The system is modeled in an algorithmic and computational form. Several interesting measures of performance are considered. Costs and rewards are included in the system. All measures are obtained for transient and stationary regimes. A numerical example is analyzed to determine whether preventive maintenance is profitable, financially and in terms of performance.Junta de Andalucía (Spain) FQM-307Ministerio de Economía y Competitividad (España) MTM2017-88708-PEuropean Regional Development Fund (ERDF

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

Program behaviour modelling with flexible logical entity abstraction

"This study extends the use of abstration in program behaviour modelling, and provides a flexible abstraction technique that allows modelling in terms of the logical abstract concepts with which a program operates. This technique is called a Logical Entity Abstracted Program Behaviour Modelling (LEAPBM)."--leaf [ii]Doctor of Philosoph

The management of complexity in project management – a qualitative and quantitative case study of certified project managers in Germany

With the increased globalization and expansion of the markets worldwide, companies have to struggle with increased competition. Therefore, organisations have begun to offer advantages such as a personalisation of products to potential customers. Market conditions and legal policies can make it challenging to predict whether those ad-vantages can be realized. Project managers are often in the position of having to fulfil these requirements; in continuously changing influencing factors that make tasks diffi-cult to manage. These circumstances create complexity. Frequently, managers are una-ware that complexity has created problems in a specific project. Often, the traditional standards of project management no longer provide a sufficient support to managers of complex projects. This research investigates how current standards of project management address com-plexity, and whether a supplement is necessary. Complexity strengtheners are investi-gated. One standard Project Management Institute (PMI) is selected as an example to analyze the influence of strengtheners on PM-processes. A funnel model is developed based on these research findings. This is aimed to help managers in their daily practice and support them in categorizing the complexity of their projects. Based on this model, managers should be able to recognize the actual strengtheners of complexity and which processes of their project are affected. Finally, a possible adaption of the standard is re-searched. A proposition for a new comprehensive guide is designed to support manag-ers carrying out complex projects. The key managerial implication of this research is the development of a five-step model for handling complexity in projects: forming, storming, norming, performing, and ad-journing. Furthermore, the intent of this thesis is to make a valid contribution to the management literature. For handling complexity the new funnel model should close the gap between the recognition of complexity in a project and underlying causes. The new five-step model thus provides project managers helpful guidelines for handling complex projects. This research applies a mixed method, consisting of a survey (quantitative method) and focus interviews (qualitative method) with experts of project management (PMI) in Germany. There are approximately 4.900 PMI certified project managers in Germany; more than 170 participated in the survey (3.6%). This is considered sufficient to provide reliable results for this research. Further, three focus interviews deepen the knowledge and validate the results of the survey: Complexity is an actual problem in project man-agement. Existing standards are sufficient for project management, but complexity can-not be standardized. This thesis proposes to help project managers to resolve project complexity by providing guidelines for navigating through complex projects