An approach to non-homogenous phase-type distributions through multiple cut-points

• Published in: Quality engineering 2023-01, Vol.35 (4), p.619-638
• Main Authors: Ruiz-Castro, Juan Eloy, Acal, Christian, Roldán, Juan B.
• Format: Article
• Language: English
• Subjects: Algorithms; EM-algorithm; Markov processes; Mathematical models; Memory devices; modeling; multiple cut-points; Optimization; Parameters; phase-type distributions; Random access memory; Reliability analysis; resistive random access memory (RRAM); simulation
• ISSN: 0898-2112; 1532-4222
• DOI: 10.1080/08982112.2023.2168202

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.