Revised Reliability Presentation (1).ppt

Assessment of Reliability, Availabilityand Repairabilityof Field Equipment
Abstract
Large equipment involving huge capital expenditure should be always measured in terms of performance to assess
the utilization and profitability. Reliability analysis helps in understanding the failure characteristics of large
equipment in mines. Availability assessment helps in understanding the maintenance requirements of the
equipment and its critical parts. Repairability indicators help in measuring the performance of both machine and
manpower in the maintenance exercise.
The presentation deals with the exact measurement methods of the above with case studies in a surface mine.
Jayanta Bhattacharya

Specify maintainability
goals and concepts
Address secondary
factors
Determine system effectiveness and
life-cycle costs
Complete design
Carry out
maintenance, analysis,
prediction, and
assessment
Allocate maintainability to
components
Implement design
methods
Goals
achieved ?
Yes No
Fig.1. Reliability improvement programme
When developing a new equipment this
method is followed

The above figure shows the division of time when a particular component fails and goes to repair, and finally put back in
the service. This is important to under the cost and loss due to failure.
Failure occurred

The design process should begin by defining system maintainability objectives and
specifications. These must include a quantifiable measure of the repair process as well
as a qualitative description of the manner in which repair is to be accomplished (that is,
under what prescribed conditions). Once this has been accomplished for the system,
the maintainability criteria can be allocated to the lower-level components.
Measurements and Specifications
Quantifiable measures of maintainability include the following:
The mean time to repair (MTTR) As an average, this measure has the disadvantage of
attempting to summarize the repair distribution with a single value. Two distributions
having the same mean can provide a considerably different range of repair times. An
improvement would be to specify an upper bound on the variance (or equivalently, the
standard deviation) of the repair times along with the mean. A small variance will
ensure more consistent repair times that are closer to the MTTR.
MAINTENANCE REQUIREMENTS

Median time to repair. The median is also an average and has the same disadvantage as
the MTTR. It is preferred over the MTTR if the repair times are highly skewed. For example,
a few very large repair times would influence the MTTR more than the median. In addition
to the 50th percentile (that is, the repair time at which 25, 75, and 100 percent of the
repairs would be accomplished would be part of the specification.
Maximum time, tp, in which a certain percentage p of the failures must be repaired.
Generally this measure is preferred over the MTTR and median time since it identifies an
acceptable (maximum) repair time for the majority of the failures. Mathematically.
Pr{T ≤ tp } = H(tp ) ≤ p (1)

Maintenance:
Three types: a. Preventive maintenance: The regular maintenance done to
extend or control the time of failure. Oiling , cleaning, filter and lubrication
changes .
Corrective maintenance: The maintenance done after an equipment has
failed. Ex: replacement of the failed parts or change of parts.
Predictive maintenance: microprocessor based monitoring of vibration, heat,
thickness and alignment to observe the running of the equipment and when it
would require a breakdown maintenance ,or to predict when the corrective
maintenance will be required.

Mean system downtime . Mean system downtime is the average downtime including
scheduled maintenance but not including supply or maintenance by design. It is
appropriate to include scheduled downtime as part of the design criteria. Mathematically.
(2)
Where Tpm =the (mean) time between performances of preventive maintenance.
td =the system design( or economic) life
MPMT =the mean preventive maintenance time
m(td) = the expected number of failures in the interval (0, td) as defined in
for either a steady-state renewal process or minimal repair.
For a constant failure rate, m(td)= td and therefore td can be factored out of Eq. (2).
Once failure data is collected, m(t) is the number of observed failures over the time, t.

Mean time to restore (MTR). Mean time to restore is the average unscheduled system
downtime including delays for maintenance and supply resources. This is an appropriate
measure when maintenance and supply resources are included within the system design
specifications.
MTR = MTTR + MDT + SDT
Where MDT is the mean administrative delay for maintenance, and SDT is the mean delay
time for supply resources.
Maintenance work hours per operating hour (MH/OH). The number of maintenance work
hours per operation hour combines reliability and repair time with the number of
maintenance personnel (crew size) necessary to complete repair. It is a measure of the
maintenance work generated. Mathematically,
(3)
Where m(td) is defined above and CREW is the average crew size.

For a constant failure rate, m(t) = t, Eq. (3) becomes
(4)
If mean preventive maintenance time (MPMT) is to be included in the work-hour
calculation, then
(5)
Where CREWpm is the average crew size for preventive maintenance. The time period t
could be a specified period of time or could reflect the design life of the system. An
improved maintainability measure may be the maintenance cost per operating hour,
obtained by multiplying the above by a labor rate. Since the labor cost per hour reflects to
some degree the skill level, experience, and education necessary to perform the repair
tasks, this measure combines several aspects of maintainability and contributes directly to
a life-cycle cost analysis.

CONCEPTS AND DEFINITIONS of Availability
Availability is the probability that a system or component is performing its required
function at a given point in time or over a stated period of time when operated and
maintained in a prescribed manner. Like reliability and maintainability, availability is a
probability. Therefore the rules of probability theory can be applied to availability when
it is being quantified. Availability may be interpreted as the probability that a system is
operational at a given point in time or as the percentage of time, over some interval, in
which the system is operational. This is made clearer with the following definitions:

A(t) is the availability at time t, referred to as the point availability.
(5)
Is the average availability over the interval [0,T].
The average availability can be generalized into what is often called a mission or interval
availability,
(6)
Which represents the average availability over the interval (for example, mission time)
from t1 to t2.
(7)
Is the steady-state or loch-run equilibrium availability.
There are several different forms of the steady-state availability depending of the
definitions of uptime and downtime. These are discussed in the following.

Inherent Availability
The inherent availability, Ainh, is defined as follows:
(8)
Inherent availability is based solely on the failure distribution and repair-time
distribution. It can therefore be viewed as an equipment design parameter, and
reliability maintainability trade-off can be based on this interpretation. Here the MTBF
and MTTF are synonymous. Inherent availability is the maximum of availability as we
do not consider the system and sourcing delays ( if done so, the denominator will
increase)
EXAMPLE. An office machine has a time-between-failure distribution that is lognormal
with a shape parameter s = 0.86 and a scale parameter tmed = 40 operating hours. The
repair distribution is normal with a mean of 3.5 hr and a standard deviation of 1.8 hr.
Therefore MTBF =40e0.73961/2 =57.9 and Ainh =57.9/(57.9.+3.5) = 0.943.

Achieved Availability
The achieved availability, Aa is defined as
(9)
where the mean time between maintenance (MTBM) includes both unscheduled and
preventive maintenance and is computed from
(10)
and is the mean system downtime as defined by Eq. (2). Tpm is the preventive
maintenance interval, td is the design life, and m(td ) is the cumulative average number
of failures over the design life. For constant failure rates, m(td ) =td, and td can be
factored out .

If it is performed too frequently, preventive maintenance can have a negative impact
on the achieved availability even though it may increase the MTBF. The assumption
was made that MTBF =a + b/Tpm where a, b >0. Therefore lesser the preventive
maintenance interval, the less is the effect of preventive maintenance has a positive
effect on the time between failures. However, the longer the preventive
maintenance interval, the less is the effect of preventive maintenance on the MTBF.
Very short preventive maintenance intervals resulting in frequent downtimes have
availability less than the (inherent) availability. As the preventive maintenance
interval increases, the achieved availability will reach a maximum point and then
gradually approach the inherent availability.

Operational Availability
The operational availability, Ao, is defined as
(11)
Where is determined by replacing MTTR With MTR = MTTR + SDT + MDT in Eq. (2).
This definition includes all supply and maintenance delays as part of the unscheduled
downtime. It is useful when there is queuing for maintenance and backorders for
replacement parts. Therefore it is a useful definition when making trade-offs concerning
the number of spares and the numbers of repair channels. From a product design point of
view, the inherent or achieved Where is determined by replacing MTTR With MTR =
MTTR + SDT + MDT . This definition includes all supply and maintenance delays as part of
the unscheduled downtime. It is useful when there is queuing for maintenance and
backorders for replacement parts. Therefore it is a useful definition when making trade-offs
concerning the number of spares and the numbers of repair channels. From a product
design point of view, the inherent or achieved availability is of more interest since spares
and repair capability involve resources and trade-offs external to the product design.

Generalized Operational availability
The generalized operational availability, AG, is
(12)
When the system is not operating continuously and the time to failure and preventive
maintenance interval time are measured in operating time, the nonoperating time,
must be accounted for. This definition assumes that there are no failures during the
ready, standby, or idle time. An alternative approach is to define time to failure and
time between preventive maintenance in clock or calendar time and use .
An Example
A mine shovel maintenance sheet shows the following monthly record:
No of failures= 5
No. of preventive maintenance task= 3
Total preventive maintenance task time = 20 hours.
Total scheduled working time = 400 hours
Total working time = 300 hours
Total Corrective maintenance time = 50 hours
Corrective maintenance crew size = 3
Preventive maintenance crew size = 4

Utilization
Utilization = Total Uptime / Total time including all the delays , downtime,
repair and uptime

 The mine would like to know the following:
 Mean system down time.
 Mean time to restore
 Maintenance work hours per operating hour.
 Inherent availability
 Achieved Availability
 Operational Availability.
 The Result:
 Mean System Downtime = 8.52 hrs
 Mean Time to Restore= 20 hrs.
 MH/OH= 0.76
 A in = 0.857
 Aac = 0.87
 A op = 0.81

 The Inference
Mean system downtime show that for every failure the average system down time
is 8.52 hours that can be reduced. The administrative and supply delay, on an
average, is taking some 11 hours .Can the supply chain be strengthened for better
results? The maintenance hour per work hour is also on the higher side. It can be
because of old equipment, lesser maintenance persons, lack of availability of
spares. Ideally, MH/OH should be 0.50.Availability figures should be above 90
percent – might be less because of high repair time, delay time and non-
availability of working faces.
 Conclusion
Correct Maintenance policies and measurement of results are the key to the
economic success of using large equipment in mines. Benchmarking to certain
standards of performance can lead to operational efficiency and effectivity. Correct
measurement methods, often found absent in the mines, can be of great use for
the management to control operations, procurement, and asset non-performance.

. A mine Dump-truck maintenance sheet shows the following monthly
record:
a) No of failures= 6
b) No. of preventive maintenance tasks = 3
c) Total preventive maintenance task time = 24 hours.
d) Total scheduled working/calendar time = 500 hours
e) Total working time = 350 hours
f) Total Corrective maintenance time = 70 hours
g) Corrective maintenance crew size = 3
h) Preventive maintenance crew size = 4
Find the following:
1. Mean time to Repair
2. Mean system down time.
3. Mean time to restore
4. Maintenance work hours per operating hour.
5. Mean time between Maintenance
6. Inherent availability
7. Achieved Availability
8. Generalized Operational Availability

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