Page 315 - Improving Machinery Reliability

Life Cycle Cost Studies 285

Trade-off Tools For LCC

One helpful tool for easing LCC calculations involving probabilities is the effec-
tiveness equation that gives a figure of merit for judging the chances of producing
the intended results. The effectiveness equation is described in several different for-
mats in which each element varies as a probability and the issue is finding a system
effectiveness value that gives lowest long-term cost of ownership:

System effectiveness = effectiveness/LCC
Cost is a measure of resource usage (cost estimates can never include all possible
elements but hopefully include the most important elements). Effectiveness is a mea-
sure of value received (effectiveness rarely includes all value elements as many are
too difficult to quantify) and effectiveness varies from 0 to 1:

Effectiveness = availability * reliability * maintainability * capability
= availability * reliability * performance (maintainability * capability)
= availability * dependability (reliability * maintainability) * capability

In plain English, the effectiveness equation is the product of the chance the equip-
ment or system will be available to perform its duty, will operate for a given time
without failure, can be repaired without excessive maintenance loss time, and can
perform its intended production activity according to the standard. Each element of
the effectiveness equation is premised on a firm datum that changes with name plate
ratings to obtain a true value that lies between 0 and 1:

.Availability deals with the duration of uptime for operations and is a measure of
how often the system is alive and well. It is often expressed as (uptime)/(uptime +
downtime) with many different variants. Also availability may be the product of
many different terms such as

A = Ahardware * Asoftware * Ahumans * Ainterfaces * Aprocess
and similar configurations. Availability issues deal with at least three main factors
(Davidson 1988) for 1) increasing time to failure, 2) decreasing downtime due to
repairs or scheduled maintenance, and 3) accomplishing items 1 and 2 in a cost-
effective manner as the higher the availability, the greater is the capacity for mak-
ing money because the equipment has a higher in-service life.
a Reliability deals with reducing the frequency of failures over a time interval and is
a measure of the odds for fuilure-free operation during a given interval, Le., it is a
measure of success for a failure free operation. It is often expressed as

R(t) = exp (-t/MTBF) = exp (At)
where h is failure rate and MTBF is mean time between failure. MTBF measures
how often the system will fail. MTBF is a basic figure of merit for reliability (or