DEPENDABILITY OF OBJECTS WITH NON-STATIONARY FAILURE RATE
Authors: Baranov L. A. , Yermolin Yu. A. 
Published: November 2017

Among the diversity and various degrees of significance of the factors that affect an object’s failure flow, there is one, i.e. its “ageing,” that causes changes in the number of failures per time unit that makes it non-stationary (in terms of dependability). In this context, the elaboration of service procedures is of high importance, especially with regards to long lifecycle objects.

Methods of identifying dependability indicators of stationary objects are known and widely used in practice. Nevertheless, as regards non-stationary objects there are practically no generally accepted approaches to the identification of their dependability indicators that would be convenient for engineering calculations. Meanwhile, the analysis of publications dedicated to this subject given in this paper shows the relevance and potential demand for such methods in various technical matters.

The aim of this paper is in the development of an analytical model of evaluation of dependability indicators of non-stationary objects. The main concept of the proposed approach consists in substituting the real non-stationary object with a virtual analogue, of which the failure flow is stationary, i.e. a formal stationarization (in terms of dependability) of the object occurs, which legitimizes the use of well-developed methods of solving stationary tasks by extending them to the cases of non-stationary objects. The approach is rough. The main problem is identifying the value of the constant failure flow rate of the fake object expressed through the time-dependent parameters of the “ageing” characteristic of the real (non-stationary) object that in this paper is deemed to be known. In order to increase the generality of consideration, the definition of equivalent failure rate (or associated mean time to failure) in this paper is given for three cases: 1) The real object “ages”, i.e. its failure rate is an increasing function of time. Two approaches are suggested to the identification of the equivalent failure rate: a) based on the condition of equality of the mean times to failure of both objects (real and fake); b) based on the condition of equality of the dependability functions of the objects to the predefined prediction time. For some laws of “ageing” the task has been solved analytically in closed form. Using the numerical example, the comparative accuracy of the approaches has been evaluated. 2) The object is characterized by a piecewise constant failure rate that is typical to systems and devices that operate in “open” environments (with seasonal changes in failure rate). Both exact and approximate (in linear approximation) expressions for the dependability function and mean time to failure for such object have been obtained. 3) The object’s failure rate dependance is a piecewise constant non-periodical time function. Such model is sufficiently universal as after time discretization and piecewise constant approximation with a given accuracy many analytical time dependencies of failure rate can be reduced to it. Method-wise, the task is solved similarly to item 2), i.e. the non-periodic process is treated as a periodic one with an infinitely long period. Under the condition of reasonable practicality of object operation (e.g. for economic reasons) defined in this paper, expressions for the dependability function and mean time to failure have been obtained. The findings of the paper may be useful in solving the dependability-related tasks for non-stationary technical objects.