Figure 1. Typical bathtub curve

ETL 1110-2-560

30 Jun 01

h(t)

Region A

Region B

Region C

time

Figure 1. Typical bathtub curve

(c) The flat random or chance failure region (Region B) of the curve for electromechanical devices is

much longer than the other two regions. Electrical devices exhibit a much longer chance failure period

than mechanical devices. Methods presented in this ETL will attempt to determine reliability and predict

the characteristics of Regions B and C of the bathtub curve for mature equipment using the common

continuous distribution functions discussed in the next paragraphs. The infant mortality region (Region

A) will not be directly discussed in this ETL since the equipment considered for major rehabilitation

projects usually falls into Regions B or C.

(3) Exponential distribution.

(a) The exponential distribution is the most commonly used distribution used in reliability analysis.

The reliability function is

R(t) = e-λt

(5)

where

t = time

λ = failure rate

This distribution can be used to represent the constant hazard rate region (Region B) of the bathtub curve.

The hazard function for the exponential distribution remains constant over time and is represented as

simply λ:

h(t) = λ

(6)

Plots of the reliability and hazard functions for the exponential distribution are shown in Figures 2 and 3,

respectively.

4