Virtual age, is it real? ‐ Discussing virtual age in reliability context

Abstract

Several settings, where the notion of virtual age is employed, are discussed. We argue that the age reduction imperfect repair modeling is often not sufficiently justified in practice, as it is not possible to execute repair in most of real situations that conforms with this model. On the other hand, a shock‐based virtual age model is suggested and justified via the probabilities of failures on shocks. The new notion of virtual age for degrading items is also introduced. We discuss how to recalculate virtual age after switching from one regime to another. Several examples illustrating different notions of virtual age are presented.

Rejoinder to “Virtual age, is it real?”

“…However, as it was shown and explained in the original paper, it is true only for the linear scale transformation function, that is, . This was based on considering the corresponding cdf on the whole axis with switching at x and then on the relevant transformation 1 . An important feature of this approach is that we use again the age correspondence (1) but equate in this case the probability of failure of an item operating in a baseline regime in [0, x ) to the probability of failure of this item that was incepted into operation at time τ ( x ) < x under the severe regime.…”

“…The two main shock models are the extreme shock models when an item fails under a shock with a given probability and the cumulative shock model when an item fails when the cumulative damage due to shocks exceeds the given threshold. In Finkelstein and Cha, 1 we had suggested the new approach explaining how an effect of a single shock in the extreme shock model (an item fails with probability p and it survives a shock with probability 1 − p ) can be transformed in the increase of the corresponding virtual age. Namely, the corresponding cdf was constructed for the shock that have occurred at t = t * where F b ( t ) is the cdf of an item without a shock and τ ( t *) is the increase in the age of an item due to the shock that was uniquely obtained via p and F b ( t ).…”

“…First, we are thankful to Professor Bo Lindqvist, who had pointed out on some inaccuracy in the corresponding section of Finkelstein and Cha 1 . Indeed, we had to state more clearly that Equation (25) is the result of applying the model (1) formally , when the baseline distribution is the mixture F m ( t ).…”

“…However, we will definitely employ the others as well in our future research. For convenience, we will call Finkelstein and Cha 1 the ‘original paper’, where appropriate.…”

Discussion of virtual age, is it real?

“…I think the excellent discussion paper on the virtual age was written by Profs. Finkelstein & Cha 1 (hereafter refer it as F&C paper), it might lead to a new impulse to the formal research on virtual age, because many important issues related to the virtual age have been clarified in the paper already. Here, I would like to mention the following points which may be thought of as a complement of the F&C paper.…”