# Chapter 4 Supplement Notes.doc

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Ryerson University

Global Management Studies

GMS 401

Wally Whistance- Smith

Winter

Description

Chapter 4 Supplement- Reliability
Reliability: The ability of a product, part, or system to perform its intended function under a prescribed set of
conditions.
In effect, reliability is a probability – (If an item has a reliability of .90, this also means that it has a 90%
probability of functioning as intended
The probability that it will fail (its failure rate) is 1- .90 = .10/10%. This means that the item will fail once in
every 10 trials
Normal Operating Conditions: the set of conditions under which an item’s reliability is specified
QUANTIFYING RELIABILTY
Reliability is used in two ways;
1. Instantaneous Reliability: the probability that the product or system will function when activated
- Focuses on one point in time, often used when an item must operate for one or a few number of times
2. Continuous Reliability: the probability that the product or system will function for a given length of time
- Focuses on the length of service
Probability Rules: used to determine whether a given product will operate successfully
Determining the probability when the product consists of a number of independent components requires the use
of the rules of probability for independent events. Independent Events have no relation to the occurrence or
non-occurrence of each other.
Rule 1:
If two or more events are independent and the success is defined as the probability that all of the events occur,
than the probability of success is equal to the product of the probabilities of the events
- Even though the individual components of a system might have high reliability, the system as whole can
have considerably less reliability b/c all components that are in a series must function.
(Example: One lamp has .90 reliability while the other has .80. Therefore the probability that both will
work becomes .90 x .80 which equals .72)
- As the number of components in a series increases, the system reliability decreases. (Example: eight lamps have .99 reliability each, therefore the system reliability becomes .99 to the
power of 8, which is .923)
- Ways to increase overall reliability ; overdesign (enhancing the design), design simplification (reducing
the # of parts in a product), to use Redundancy: The use of backup components to increase reliability
Rule 2:
If two events are independent and success is defined as the probability that at least one of the events will occur,
the probability of success is equal to the probability of either one plus (1- that probability) multiplied by the
other probability
Rule 3:
If three events are involved and success is defined as the probability that at least one of the events will occur,
the probability of success is equal to the probability of the first one (any of the events), plus the product of (1-
that probability) and the probability of the second event (any of the remaining events), plus the product of (1-the
first probability) and (1-the second probability) and the probability of the third event.
- Example: three lamps have probabilities of .90, .80, .70

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