A Causal Redefinition of Failure Rate-Theorems, Stress Dependence, and Application to Devices and Distributions

A formalism is established for calculating the reliability of devices starting from causal, physical analysis of the devices´ operational and failure modes. A measured device quantity q_i is expressed in terms of basic material properties p_j, which in turn may depend on time t and stresses s_k. Then defining a kinetic sensitivity θ_j = (∂q_i/∂p_j) x (∂p_j/∂S_k), and failure functionψ = /spl singma/_jθj, it is possible to prove very powerful theorems which show that the kinetics of the failure mechanisms are as important as the stress dependence of the failure mechanism in determining the stress dependence of the failure rate. The failure rate of a device F_i is defined as the reciprocal of the time to failure τi. The failure rate F (cumulant) for a distribution is defined as the arithmetic mean of the failure rates of the individual devices. It is shown that a number S = F_τ can be used to describe the width of a distribution and also to relate the failure rate of a distribution to that of the one device studied in the physical analysis of the devices´ operation. Certain prevailing reliability practices are found to have serious deficiencies in terms of underestimating the significance of early failures, when compared with the results of the above causal formalism.