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

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 system with vacations in the repair

A complex multi-state system subject to wear failure and given preventive maintenance is considered. Various internal levels of degradation are assumed. The repair facility is composed of a repairperson, who may take one or more vacations during the period considered. A policy is established for the repairperson’s vacation time. Two types of task may be performed by the repairperson: corrective repair and preventive maintenance. All embedded times in the system are phase type distributed. The transient and stationary distributions are determined and several reliability measures are developed in a matrix-algorithmic form. Costs and rewards are included in the model. The results are implemented computationally with Matlab. A numerical example shows that the distribution of vacation time can be optimised according to the net reward established.Junta de Andalucía, Spain, FQM-307Ministerio de Economía y Competitividad, España, under Grant MTM2017−88708−PEuropean Regional Development Fund (ERDF

One Cut‐Point Phase‐Type Distributions in Reliability. An Application to Resistive Random Access Memories

A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non‐homogeneous phase‐type distribution. It is built by considering one cut‐point in the non‐negative semi‐line of a phase‐type distribution. The density function is defined and the main measures associated, such as the reliability function, hazard rate, cumulative hazard rate and the characteristic function, are also worked out. This new class of dis‐ tributions enables us to decrease the number of parameters in the estimate when inference is con‐ sidered. Additionally, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications considering Resistive Random Access Memories com‐ pare the adjustment when phase type distributions and one cut‐point phase‐type distributions are considered. The developed methodology has been computationally implemented in R‐cran.This paper is partially supported by the project FQM‐307 of the Government of Andalu‐ sia (Spain), by the project PID2020‐113961GB‐I00 of the Spanish Ministry of Science and Innovation (also supported by the European Regional Development Fund program, ERDF) and by the project PPJIB2020‐01 of the University of Granada. Additionally, the first and second authors acknowledge financial support by the IMAG–María de Maeztu grant CEX2020‐001105‐M/AEI/10.13039/501100011033. They also acknowledge the financial support of the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía (Spain) and the FEDER programme for projects A.TIC.117.UGR18, IE2017‐5414, B.TIC.624.UGR20 and A‐FQM‐66‐UGR20

A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.Spanish Ministry of Science, Innovation and Universities (FEDER program) MTM2017-88708-P TEC2017-84321-C4-3-RGovernment of Andalusia (Spain) FQM-307Andalusian Ministry of Economy, Knowledge, Companies and Universities A-TIC-117-UGR18 FPU18/0177

Different PCA approaches for vector functional time series with applications to resistive switching processes

This paper is motivated by modeling the cycle-to-cycle variability associated with the resistive switching operation behind memristors. Although the data generated by this stochastic process are by nature current–voltage curves associated with the creation (set process) and destruction (reset process) of a conductive filament, the statistical analysis is usually based on analyzing only the scalar time series related to the reset and set voltages/currents in consecutive cycles. As the data are by nature curves, functional principal component analysis is a suitable candidate to explain the main modes of variability associated with these processes. Taking into account this data-driven motivation, in this paper we propose two new forecasting approaches based on studying the sequential cross-dependence between and within a multivariate functional time series in terms of vector autoregressive modeling of the most explicative functional principal component scores. The main difference between the two methods lies in whether a univariate or multivariate PCA is performed so that we have a different set of principal component scores for each functional time series or the same one for all of them. Finally, the sample performance of the proposed methodologies is illustrated by an application on a bivariate functional time series of reset/set curves.Universidad de Granada / CBU

Phase-type distributions for studying variability in resistve memories

A new statistical approach has been developed to analyze Resistive Random Access Memory (RRAM) variability. The stochastic nature of the physical processes behind the operation of resistive memories makes variability one of the key issues to solve from the industrial viewpoint of these new devices. The statistical features of variability have been usually studied making use of Weibull distribution. However, this probability distribution does not work correctly for some resistive memories, in particular for those based on the Ni/HfO2/Si structure thar has been employed in this work. A completely new approach based on phase-type modelling is proposed in this paper to characterize the randomness of resistive memories operation. An in-depth comparision with experimental results shows that the fitted phase-type distribution works better than the Weibull distribution and also helps to understand the physics of the resistive memories.Spanish Ministry of Economy and Competitiveness (FEDER program) TEC2017-84321-C4-3-R MTM2017-88708-PIMB-CNM (CSIC) (Barcelona

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

The ecology of diatoms inhabiting cryoconite holes in Antisana Glacier, Ecuador

Published for International Glaciological Society, IGS[EN] In the ablation zone of glacier habitats, cryoconite holes are known to harbor diverse microbial communities, including unique diatom floras distinct from those of surrounding aquatic and terrestrial systems. Besides descriptive studies, little is known about the diversity of cryoconite diatoms and their response to environmental stressors, particularly in low-latitude glaciers. This paper documents an extremely diversified diatom community in Antisana Glacier (Ecuador), reporting 278 taxa found in 54 surface holes, although with low individual abundances. Contrary to our expectations, assemblage structure did not respond to water physical or chemical characteristics, nor to cryoconite hole morphology, but to elevation. We demonstrate that elevation is a driver of diatom assemblages. Both alpha diversity (measured as Fisher's index) and species richness (corrected for unequal sample sizes) correlated negatively with elevation, suggesting a replacement toward simplified, poorer communities along this gradient. The taxonomic composition also changed significantly, as revealed by multivariate statistics. In summary, cryoconite holes are sites of high taxonomic diversity composed of taxa that are allochthonous in originSIThe authors are thankful to the ‘Fonag’, EPMAPS” and ‘Ministerio del Ambiente’, Ecuador, for collection permission No. MAE-DNB-CM 2018-0028-0093. The research was funded by Proyecto de Investigación DII-UISEK-P041516_3, (SC) ‘Índice Biótico de Calidad de Agua para el Ecuador’, Universidad Internacional SEK and Convenio Marco de Cooperación entre la Universidad de León, España y La Universidad Internacional SEK, Ecuado

A general piecewise multi-state survival model: Application to breast cancer

Multi-state models are considered in the field of survival analysis for modelling illnesses that evolve through several stages over time. Multi-state models can be developed by applying several techniques, such as non-parametric, semi-parametric and stochastic processes, particularly Markov processes. When the development of an illness is being analysed, its progression is tracked periodically. Medical reviews take place at discrete times, and a panel data analysis can be formed. In this paper, a discrete-time piecewise non-homogeneous Markov process is constructed for modelling and analysing a multi-state illness with a general number of states. The model is built, and relevant measures, such as survival function, transition probabilities, mean total times spent in a group of states and the conditional probability of state change, are determined. A likelihood function is built to estimate the parameters and the general number of cut-points included in the model. Time-dependent covariates are introduced, the results are obtained in a matrix algebraic form and the algorithms are shown. The model is applied to analyse the behaviour of breast cancer. A study of the relapse and survival times of 300 breast cancer patients who have undergone mastectomy is developed. The results of this paper are implemented computationally with MATLAB and R.Ministerio de Economía y Competitividad FQM-307European Regional Development Fund (ERDF) MTM2017-88708-PUniversity of Milano-Bicocca 2014-ATE-022