(1) *Reliability function. *The continuous probabilistic approach to item reliability is represented by

the reliability function. It is simply the probability that an item has survived to time *t*. The mathematical

expression can be summarized by

(1)

where

Conversely, the probability of failure *F*(*t*) is simply

(2)

(2) *Hazard function or failure rate.*

(a) The failure rate or hazard function *h*(*t*) represents the proneness to failure of a component as a

function of its age or time in operation. It reflects how the reliability of a component changes with time

as a result of various factors such as the environment, maintenance, loading, and operating condition.

From Modarres (1993) it can be shown that

-*dR*(*t)*

(3)

(4)

where *f*(*t) *is the probability density function (pdf). This is a mathematical description for the curve

approximation of the number of the probable occurrences of a specific random variable (i.e., the failure of

a component for use in this ETL).

(b) The hazard function or instantaneous failure rate is the instantaneous conditional probability of

failure of an item in the next unit of time given that it has survived up to that time. The hazard function

can increase, decrease, or remain constant. It has been shown that the failure rate behavior of most

mechanical and electrical engineering devices follows that shown in Figure 1. This is known as the

constant. This is known as the infant mortality region and is a result of poor workmanship or quality

control. Region B represents the useful life phase. Here, failures occur because of random events.

Region C represents the wear-out phase where failures occur due to complex aging or deterioration.