PART IV: DESIGN FOR OPERATIONAL FEASIBILITY
8. Design for Reliability
EBW2409: SYSTEMS APPROACH TO ENVIRONMENTAL MANAGEMENT
8. DESIGN FOR RELIABILITY
System design and development is accomplished through the systems engineering
process, which requires the appropriate application of scientific and engineering efforts to
ensure that the ultimate product is operationally feasible. Operational feasibility implies
that the system will perform as intended in an effective and efficient manner for as long as
necessary. The accomplishment of such requires the proper integration of design-related
specialties such as reliability, maintainability, usability (human factors), etc., into the total
engineering design effort.
One of the most significant design parameters requiring attention is reliability. Many
systems (or products) in use today are highly sophisticated and will fulfill most
expectations when operating. However, experience has indicated that these systems are
inoperative much of the time, requiring extensive maintenance and the expenditure of
scarce support resources. Unreliable systems are unable to fulfill the mission for which
they were designed. In an environment of scarce resources, it is essential that reliability
be considered as a major system parameter during the design process. Reliability is a
characteristic inherent in design.
8.1 Definition and Explanation of Reliability
Reliability may be defined as the probability that a system or product will accomplish its
designated mission in a satisfactory manner or, the probability that it will perform in a
satisfactory manner for a given period when used under specified operating conditions.
Inherent within this definition are the elements of probability, satisfactory performance,
time or mission-related cycle, and specified operating conditions.
a) Probability, the first element in the reliability definition, is usually stated in quantitative
terms representing a fraction or a percent specifying the number of times that one can
expect an event to occur in a total number of trials. For instance, a statement that the
probability of survival of an item operating 80 hours is 0.75 (or 75%) indicates that one
can expect the item to function properly for at least 80 hours 75 times out of 100. When
there are several supposedly identical items operating under similar conditions, one may
wish to specify that 75% of the items will operate in a satisfactory manner when required
and for the duration of the designated mission. It can be expected that failures will occur
at different points of time; thus, failures are described in probabilistic terms.
b) Satisfactory performance indicates that specific criteria must be established that
describe what is considered to be satisfactory. This relates back to the definition of system
operational requirements, the functions to be accomplished, and the technical
performance measures the technical performance measures.
c) Time is one of the most important factors because it represents a measure against
which the degree of system performance can be related. One must know the time
parameter to assess the probability of completing a mission or a designated function as
scheduled. Of particular interest is the ability to predict the probability of an item surviving
(without failure) for a designated period. Reliability is often expressed in terms of mean
time between failure (MTBF) or mean time to failure (MTTF), making time critical in
reliability measurement.
d) The specified operating conditions include environmental factors, such as the
geographical location where the system is expected to operate and the anticipated period
1
, PART IV: DESIGN FOR OPERATIONAL FEASIBILITY
8. Design for Reliability
of time, the operational profile, and the potential impacts resulting from temperature
cycling, humidity, vibration and shock and so on. Such factors must not only address the
conditions during the period when the system is actually operating, but during the period
when the system (or a portion thereof) is in a storage mode or being transported from one
location to the next. Experience has indicated that the transportation, handling, and
storage modes are sometimes more critical from a reliability standpoint than are the
conditions experienced during actual system operational use.
8.2 Measures of Reliability
Measures of reliability include:
a) The Reliability Function
The reliability function (or the survival function), is determined from the probability that a
system (or product) will be successful at least for some specified time t. The reliability
function, R(t), is defined as
R(t) = 1–F(t) (8.1)
where F(t) is the probability that the system will fail by time t. F(t) is basically the failure
distribution function or unreliability function. If the random variable t has a density function
of f(t), the expression for reliability is
R (t ) 1 F (t ) f (t )dt (8.2)
t
If the time to failure is described by an exponential density function, then,
1
f (t ) e t / (8.3)
where is the mean life and t the time period of interest. The reliability at time t is
1
R (t ) e t / dt e t / (8.4)
t
Mean life, , is the arithmetic average of the lifetimes of all items considered, which for the
exponential function is MTBF. Thus,
R(t) = e-t/M = e-t (8.5)
where is the instantaneous failure rate and M the MTBF.
Mean life and failure rate are related as
1 1
(8.6)
MTBF
b) The Failure Rate
The rate at which failures occur in a specified time interval is called the failure rate for that
interval. The failure rate per hour is expressed as
2
8. Design for Reliability
EBW2409: SYSTEMS APPROACH TO ENVIRONMENTAL MANAGEMENT
8. DESIGN FOR RELIABILITY
System design and development is accomplished through the systems engineering
process, which requires the appropriate application of scientific and engineering efforts to
ensure that the ultimate product is operationally feasible. Operational feasibility implies
that the system will perform as intended in an effective and efficient manner for as long as
necessary. The accomplishment of such requires the proper integration of design-related
specialties such as reliability, maintainability, usability (human factors), etc., into the total
engineering design effort.
One of the most significant design parameters requiring attention is reliability. Many
systems (or products) in use today are highly sophisticated and will fulfill most
expectations when operating. However, experience has indicated that these systems are
inoperative much of the time, requiring extensive maintenance and the expenditure of
scarce support resources. Unreliable systems are unable to fulfill the mission for which
they were designed. In an environment of scarce resources, it is essential that reliability
be considered as a major system parameter during the design process. Reliability is a
characteristic inherent in design.
8.1 Definition and Explanation of Reliability
Reliability may be defined as the probability that a system or product will accomplish its
designated mission in a satisfactory manner or, the probability that it will perform in a
satisfactory manner for a given period when used under specified operating conditions.
Inherent within this definition are the elements of probability, satisfactory performance,
time or mission-related cycle, and specified operating conditions.
a) Probability, the first element in the reliability definition, is usually stated in quantitative
terms representing a fraction or a percent specifying the number of times that one can
expect an event to occur in a total number of trials. For instance, a statement that the
probability of survival of an item operating 80 hours is 0.75 (or 75%) indicates that one
can expect the item to function properly for at least 80 hours 75 times out of 100. When
there are several supposedly identical items operating under similar conditions, one may
wish to specify that 75% of the items will operate in a satisfactory manner when required
and for the duration of the designated mission. It can be expected that failures will occur
at different points of time; thus, failures are described in probabilistic terms.
b) Satisfactory performance indicates that specific criteria must be established that
describe what is considered to be satisfactory. This relates back to the definition of system
operational requirements, the functions to be accomplished, and the technical
performance measures the technical performance measures.
c) Time is one of the most important factors because it represents a measure against
which the degree of system performance can be related. One must know the time
parameter to assess the probability of completing a mission or a designated function as
scheduled. Of particular interest is the ability to predict the probability of an item surviving
(without failure) for a designated period. Reliability is often expressed in terms of mean
time between failure (MTBF) or mean time to failure (MTTF), making time critical in
reliability measurement.
d) The specified operating conditions include environmental factors, such as the
geographical location where the system is expected to operate and the anticipated period
1
, PART IV: DESIGN FOR OPERATIONAL FEASIBILITY
8. Design for Reliability
of time, the operational profile, and the potential impacts resulting from temperature
cycling, humidity, vibration and shock and so on. Such factors must not only address the
conditions during the period when the system is actually operating, but during the period
when the system (or a portion thereof) is in a storage mode or being transported from one
location to the next. Experience has indicated that the transportation, handling, and
storage modes are sometimes more critical from a reliability standpoint than are the
conditions experienced during actual system operational use.
8.2 Measures of Reliability
Measures of reliability include:
a) The Reliability Function
The reliability function (or the survival function), is determined from the probability that a
system (or product) will be successful at least for some specified time t. The reliability
function, R(t), is defined as
R(t) = 1–F(t) (8.1)
where F(t) is the probability that the system will fail by time t. F(t) is basically the failure
distribution function or unreliability function. If the random variable t has a density function
of f(t), the expression for reliability is
R (t ) 1 F (t ) f (t )dt (8.2)
t
If the time to failure is described by an exponential density function, then,
1
f (t ) e t / (8.3)
where is the mean life and t the time period of interest. The reliability at time t is
1
R (t ) e t / dt e t / (8.4)
t
Mean life, , is the arithmetic average of the lifetimes of all items considered, which for the
exponential function is MTBF. Thus,
R(t) = e-t/M = e-t (8.5)
where is the instantaneous failure rate and M the MTBF.
Mean life and failure rate are related as
1 1
(8.6)
MTBF
b) The Failure Rate
The rate at which failures occur in a specified time interval is called the failure rate for that
interval. The failure rate per hour is expressed as
2
