About trigonometric distributions for the description of failures of technical devices

Abstract

The purpose of this article is to offer and examine nonconventional trigonometric distributions in order to describe degradation failures of technical devices. Two methods for approximate description of reliability indices are proposed for an estimated value of mean time to failure. Firstly, as the parameter of a failure flow with operation time equal to mean time to failure tends to its stationary value equal to the opposite value of mean time to failure, it is offered to approximate the dependence of the parameter of a failure flow of the operation time by a piecewise linear function. Other reliability indices are defined using the Laplace transformation. For instance, the probability of reliable operation can be described by the cosine function, and the failure rate – by the tangent function. Secondly it is proposed to approximate the dependence of the density of failures distribution depending on the operation time by the sine function. Other reliability indices are defined using the Laplace transformation. For instance, the probability of reliable operation can be described by the function of squared cosine, and the failure rate – by the double tangent function. As a result of studies it has been concluded that since a failure rate of the offered distributions increases as the operation time increases, and the coefficient of variation is less than one, they can be used to describe degradation failures of technical devices. The obtained results have shown that reliability indices at these distributions are expressed by elementary functions and it can simplify the calculation of reliability indices of systems with different connections of their constituent elements.