One cut-point phase-type distributions in Reliability. An application to Resistive Random Access Memories

TL;DR

This paper introduces a novel non-homogeneous phase-type distribution with a cut-point for reliability data, reducing parameters needed for inference, and demonstrates its application to Resistive Random Access Memories with computational implementation.

Contribution

It proposes a new one cut-point phase-type distribution, extending phase-type models for reliability analysis, with practical estimation and application to memory devices.

Findings

The new distribution effectively models lifetime data with fewer parameters.

Application to Resistive Random Access Memories shows improved fit.

Method implemented in R for practical use.

Abstract

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 distributions enables to decrease the number of parameter in the estimate when inference is considered. Besides, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications by considering Resistive Random Access Memories compare 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.