One Cut‐Point Phase‐Type Distributions in Reliability. An Application to Resistive Random Access Memories
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AuthorAcal González, Christian José; Ruiz Castro, Juan Eloy; Maldonado Correa, David; Roldán Aranda, Juan Bautista
One cut‐point phase‐type distributionMaximum likelihoodEstimationRRAMVariability
Acal, C.; Ruiz‐Castro, J.E.; Maldonado, D.; Roldán, J.B. One Cut‐Point Phase‐Type Distributions in Reliability. An Application to Resistive Random Access Memories. Mathematics 2021, 9, 2734. https://doi.org/10.3390/ math9212734
SponsorshipThis 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 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.