Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

Abstract

A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time t the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at x ∈ ( u , t ) , which is finalized to measure the goodness of the replacement procedure. The characterization and the properties of the differential entropy of the system lifetime are also discussed. Finally, an example of application to the firing activity of a stochastic neuronal model is provided.

Some examples of noncentral moderate deviations for sequences of real random variables

“…This example does not seem to have interesting applications to concrete models. However it could give some interesting ideas for the construction of more advanced examples based on other replacement models (see, e.g., the replacement model in [6]). The study of some possible new examples could be the subject of a future work.…”

Ordering Awad–Varma Entropy and Applications to Some Stochastic Models

“…), which are useful in many technological areas like Physics, Communication Theory, Probability, Statistics, Economics etc. More exactly, there are specific areas where the entropies are used: optimal reactive power dispatch (see [1]), reinforcement learning (see [2]), income distribution (see [3,4]), non-coding human DNA (see [5]), earthquakes (see [6]), stock exchanges (see [7]), Markov chains (see [8][9][10]), biostatistics (see [11,12]), model selection (see [13,14]), statistical mechanics (see [15,16]), internet (see [17]). These concepts can be also linked with bayesian control (see [18]).…”

The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections

“…In the past decades, a lot of scholars have shown extreme interest in investigating the lifetimes of a coherent system or the components of a coherent system. There have been many articles regarding the residual lifetime and past lifetime of coherent systems in the literature; one can refer to [6][7][8][9][10][11][12][13][14][15]. However, there are few results in the literature about the residual lifetime and past lifetime of components in a coherent system.…”