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 us to decrease the number of parameters in the estimate when inference is considered. Additionally, the likelihood distribution is built to estimate the model parameters by maximum likelihood. Several applications 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.
Highlights
Introduction in ReliabilityAn Application to Parametric probability distributions are used in several specific fields such as reliability of complex systems and different industrial applications, among them, electronics
The randomness connected to the physical mechanisms involved in the conductive filament (CF) formation is reflected in the experimental data variability
The good properties of phase-type distributions make this class of distributions a suitable candidate to model experimental data in the field of reliability
Summary
ΑeTx e is the probability of being in a transient state at time x As it has been mentioned in the introduction, one of the main problems when PH distributions are considered is the order and the internal structure of the matrix T and the number of parameters to estimate. The variable X2 , remaining time up to the event from a, follows a phase type distribution with representation αeT1 a , T2. = P( X2 > x − a) = αeT1 a eT2 (x−a) e This last scenario can be interpreted as follows: at time a the event does not occur and the initial distribution for this second period of time is αeT1 a , the probability of failure at a certain time after a is governed by matrix T2
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