https://hdl.handle.net/10481/17723 Sat, 04 Apr 2026 18:36:11 GMT 2026-04-04T18:36:11Z https://hdl.handle.net/10481/106891 Algorithmic analysis of a complex reliability system subject to multiple events with a preventive maintenance strategy and a Bernoulli vacation policy through MMAPs Ruiz Castro, Juan Eloy; Zapata Ceballos, Hugo Alaín In this work, a single-unit multi-state system is considered. The system is subject to internal failures, as well as external shocks with multiple consequences. It also incorporates a preventive maintenance strategy and a Bernoulli vacation policy for the repairperson. It is algorithmically modeled in both continuous and discrete time using Marked Markovian Arrival Processes (MMAP). The system’s operation/degradation level is divided into an indeterminate number of levels. Upon returning from a vacation period, the repair technician may initiate corrective repair, perform preventive maintenance, replace the unit, remain idle at the workplace, or begin a new vacation period. The decision in the latter two cases is made probabilistically based on the system’s operational level. This methodology allows the model and its associated measures to be algorithmically derived in both transient and stationary regimes, presented in a matrix-algorithmic form. Analytical-matrix methods are used to obtain the system’s steady-state behaviour as well as various performance measures. Costs and rewards are introduced to analyze when the system becomes profitable. Measures associated with costs over time and in the stationary regime are defined and considered for optimization studies. A numerical example demonstrates the versatility of the model by solving a probabilistic optimization problem using a multi-objective Pareto analysis approach and performing a comparative evaluation of multiple models. Genetic algorithm is applied to find the optimization results in the reduced solution space. All modeling and associated measures have been computationally implemented in Matlab. https://hdl.handle.net/10481/106891 https://hdl.handle.net/10481/103698 Characterizing the functional ANOVA model for repeated measures via PCA application to biomechanical data Ortiz, Helena; Acal González, Christian José; Escabias Machuca, Manuel; Aguilera Del Pino, Ana María Gait analysis is a branch of biomechanics where its purpose is the study of mechanical laws relating to the way the body moves from one place to another. In most cases, the data sets for human gait analysis consist of continuous recordings of multiple physical activities, including kinematics and muscle performance. Despite the registered data being functions, the most common practice to detect any anomalies among experimental conditions consists of analyzing the vector of discrete observations or even summary measures of the curves. This fact causes an important information loss since the continuous nature of the data is being ignored. A suitable solution is to apply functional data analysis for analyzing continuous biomechanical data as functions, revealing the true nature of movement and allowing us to model and forecast the data with more precision. In the current paper, a new functional methodology for the analysis of variance with repeated measures was introduced. In particular, since functional data variability can be summarized by their first principal component scores, we proposed to turn the functional model into a multivariate one for the response of the most explicative principal components, and then, considered a semi-parametric approach to overcome the restrictive assumptions required in the classic repeated measures design. The motivation of this research was to contrast the differences in gait patterns of elementary school students when walking to school, depending on the type of bag they use to carry their school materials. The analysis reveals that gait joint movement is influenced by sex and the type of schoolbag, regardless of the load carried. https://hdl.handle.net/10481/103698 https://hdl.handle.net/10481/99403 Algorithmic modelling of a complex redundant multi-state system subject to multiple events, preventive maintenance, loss of units and a multiple vacation policy through a MMAP Ruiz Castro, Juan Eloy; Zapata Ceballos, Hugo Alaín A complex multi-state redundant system undergoing preventive maintenance and experiencing multiple events is being considered in a continuous time frame. The online unit is susceptible to various types of failures, both internal and external in nature, with multiple degradation levels present, both internally and externally. Random inspections are continuously monitoring these degradation levels, and if they reach a critical state, the unit is directed to a repair facility for preventive maintenance. The maintenance place is managed by a repairperson, who follows a multiple vacation policy dependent on the operational status of the units. The repairperson is responsible for two primary tasks: corrective repair and preventive maintenance. The time durations within the system follow phase-type distributions, and the model is constructed utilizing Markovian Arrival Processes with marked arrivals. A variety of performance measures, including transient and stationary distributions, are calculated using matrix-analytic methods. This methodology allows for the representation of significant outcomes and the general behavior of the system in a matrix-algorithmic structure. To enhance the model's efficiency, both costs and rewards are incorporated into the analysis. A numerical example is presented to showcase the model's flexibility and effectiveness in real-world applications. https://hdl.handle.net/10481/99403 https://hdl.handle.net/10481/99370 MMAPs to Model Complex Multi-State Systems with Vacation Policies in the Repair Facility Ruiz Castro, Juan Eloy; Acal González, Christian José Two complex multi-state systems subject to multiple events are built in an algorithmic and computational way by considering phase-type distributions and Markovian arrival processes with marked arrivals. The internal performance of the system is composed of different degradation levels and internal repairable and non-repairable failures can occur. Also, the system is subject to external shocks that may provoke repairable or non-repairable failure. A multiple vacation policy is introduced in the system for the repairperson. Preventive maintenance is included in the system to improve the behaviour. Two types of task may be performed by the repairperson; corrective repair and preventive maintenance. The systems are modelled, the transient and stationary distributions are built and different performance measures are calculated in a matrix-algorithmic form. Cost and rewards are included in the model in a vector matrix way. Several economic measures are worked out and the net reward per unit of time is used to optimize the system. A numerical example shows that the system can be optimized according to the existence of preventive maintenance and the distribution of vacation time. The results have been implemented computationally with Matlab and R (packages: expm, optim). https://hdl.handle.net/10481/99370 https://hdl.handle.net/10481/99287 An approach to non-homogenous phase-type distributions through multiple cut-points Ruiz-Castro, Juan Eloy; Acal González, Christian José; Roldán Aranda, Juan Bautista A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al. (One cut-point phase-type distributions in reliability. An application to resistive random access memories. Mathematics 9(21):2734, 2021) for more than one cut-point. Multiple interesting measures such as density function, hazard rate or moments, among others, were worked out both for the continuous and discrete case. Besides, a new EM-algorithm is provided to estimate the parameters by maximum likelihood. The results have been implemented computationally in R and simulation studies reveal that this new distribution reduces the number of parameters to be estimated in the optimization process and, in addition, it improves the fitting accuracy in comparison with the classical phase-type distributions, especially in heavy tailed distributions. An application is presented in the context of resistive memories with a new set of electron devices for nonvolatile memory circuits. In particular, the voltage associated with the resistive switching processes that control the internal behavior of resistive memories has been modeled with this new distribution to shed light on the physical mechanisms behind the operation of these memories. https://hdl.handle.net/10481/99287