International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
Gas Turbine Power Plant System: A Case Sudy of Rukhia Gas
Thermal Power Plant
1
Asis Sarkar,
1
2
Dhiren Kumar Behera
Department of Mechanical Engineering, NIT Agarthala, India -799055
2
Department of Mechanical Engineering, IGIT,Sarang,Odisha-759146
1
sarkarasis6@gmail.com, 2 dkb_igit@rediffmail.com
The traditional approach for addressing this
objective is to monitor the operation of
components and subsystems through their
degradation states [Chinnam, 2002[1].
Degradation of a subsystem or a component
may be reduced by two types of actions, viz.
repair and major overhaul [Pulcini, 2000[2]. In
view of this observation, a repairable system
may have two kinds of states: (i) operating state
(or ‗up‘ condition), and (ii) maintenance state
(or ‗down‘ condition, either corrective or
preventive type) [Nieuwhof, 1983; Jack,
1997[3,4]. While a component or subsystem
runs its several states, the current state of the
system may not be same as its original in the
beginning. When such a system fails, the repair
work, carried out to restore the system back to
its state just before the occurrence of its failure,
is minimum [Ansell and Phillips, 1989[5]. As
the frequency of failure of subsystems and/or
components increases over time, a corrective
maintenance action is performed to improve the
conditions of subsystems and components,
thereby reducing the probability of failure in
subsequent time-interval. Such a maintenance
action is often referred to as major overhaul
[Sherwin, 1983; Hokstad, 1997[6,7].
As a repairable system goes through different
phases of its bathtub curve (infant mortality
phase, useful life phase, and burn-in phase), it
is necessary to adequately model the reliability
of a system in terms of variations and
heterogeneity in failure rates of the components
and their impact on the operation of the system
[Hansen and Thyregod, 1990[8].
Abstract—The reliability of the GTPPS were analyzed
based on a five and half -year failure database. Such
reliability has been estimated by selecting Proper model and
different models for repairable system analysis were
discussed.
The
reliability
estimation
by
using
Nonhomogenious process and Homogenous renewal Process
are explained. Non Homogeneous Process was further
divided into Power law Process and Log Linear model. The
analysis showed that combustion chamber compressor and
Generator of gas turbine unit follow Power law process and
Turbine unit follow log linear model and Electrical system
follow the Renewal Process.. Reliability Pattern at different
Operating interval was drawn and the behavior was
analyzed. The behavior shows abnormality in some
component level. Finally Reliability Patern at system level
was analyzed by the reliability pattern at different
operating interval. From the Pattern of the Graph it can be
concluded that Parallel system reliability with two unit
standby is better than the Reliability with one unit standby.
.All the units showed consistent reliability improvement in
different operating intervals. Few components and the
whole system showed abnormal trend in Reliability. This
has to be further investigated The management of Power
Plant has option either to keep one unit as stand by or two
units as stand by or running all the units Parallaly. The
component Performances are also determined by this way
and one can have option how to run the plant in most
efficient way.
Keywords: Gas Turbine Power Plant (GTPP), reliability,
modeling, renewal, methodology
INTRODUCTION
In any real-life situation, the operation of a
repairable system, consisting of a number of
subsystems and components, is affected by a
number of factors, such as their configuration,
intensity of use, maintenance and repair, and
environmental stress. Any user of such a system
is typically interested in the analysis of
performance of the components, and/or
subsystems so as to suggest methods of
improving system utilization with reduced risk
and maintenance cost.
I.
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The use of such a reliability model would
help an analyst identify the problem causes and
suggest remedial measures so as to continually
improve its reliability. This would in effect
ensure a consistent performance of the system
as a whole.
The gas turbine based power plant is
characterized by its relatively low capital cost
compared with the steam power plant. The gas
turbine (GT) is also known to feature low
capital cost to power ratio, high flexibility, high
reliability without complexity [1],short delivery
time ,early commissioning and commercial
operation and fast starting–accelerating. The
gas turbine is further recognized for its better
environ- mental performance, manifested in
the curbing of air pollution and reducing
greenhouse gases. It has environmental
advantages and short construction lead-time.
However, conventional industrial engines have
lower efficiencies, especially at part load
Gas turbine engines experience degradations
over time that cause great concern to gas
turbine users on engine reliability, availability
and operating costs In gas turbine applications,
maintenance costs, availability and Reliability
are some of the main concerns of gas turbine
users. With Conventional maintenance strategy
engine overhauls are normally carried out in a
pre-scheduled manner regardless of the
difference in the health of individual engines.
As a consequence of such maintenance
strategy, gas turbine engines may be overhauled
when they are still in a very good health
condition or may fail before a scheduled
overhaul. Therefore, engine availability may
drop and corresponding maintenance costs
may arise significantly .For gas turbine engines
,one of the effective ways to improve
engine availability and reduce maintenance
costs is to move from prescheduled
maintenance
to failure analysis-based
maintenance by using gas turbine health
information provided by failure analysis.
The reliability analysis of repairable system
like gas turbine power plant is necessary in this
context to have a better performance in
operation, low maintenance cost, and improved
performance in all respect. Finding out the
reliability pattern of components and system
level will help to judge the performance of the
plant either decreasing or increasing.
Later it can be diagnosed what can be done or
what are the available procedures and what are
the supports available
to improve the
reliability. The study of reliability will help the
manager for advance planning of technology up
gradation, Logistic support and maintenance
planning.
Here a Case study of Rukhia gas turbine
Power plant is selected and the Reliability
analysis of the component and system level is
carried out to estimate the performance level in
both the component level and system level. The
arrangement of different section is as follows
Section 2 describe the description of the
system, Section 3 described the Methodology
for carrying out the analysis Section 4
described the Statistical tests and Reliability
models available, Section 5 described the
Results and Section 6 described the Discussions
, Section 7 described the conclusion of the
paper. and finally section 8 had ended up with
references.
II. SYSTEM DESCRIPTION
The gas turbine system is described in the
following manner. The first section described
the different components working in a unit. and
the second section described the arrangement
of units in the power plant. The gas turbine
obtains its power by utilizing the energy of
burnt gases and air, which is at high
temperature and pressure by expanding through
the several ring of fixed and moving blades. A
compressor is required to get the high pressure
of the order of 4 to 10 bar of working fluid; the
turbine drives the compressor and coupled to
the turbine shaft [9].Gas turbines are described
thermodynamically by the Brayton cycle, in
which air is compressed
isentropically,
combustion occurs at constant pressure, and
expansion over the turbine occurs isentropically
back to the starting pressure.
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As with all cyclic heat engines, higher
combustion temperatures can allow for greater
efficiencies .However, temperatures are limited
by ability of the steel, nickel, ceramic, or other
materials that make up the engine to withstand
high temperatures and stresses. To combat this
many turbines feature complex blade cooling
systems. As a general rule, the smaller the
engine the higher the rotation rate of the
shaft(s) needs to be to maintain tip speed. Blade
tip speed determines the maximum pressure
ratios that can be obtained by the turbine and
the compressor. This in turn limits the
maximum power and efficiency that can be
obtained by the engine. In order for tip speed to
remain constant if the diameter of a rotor were
to half the rotational speed must double. Thrust
and journal bearings are a critical part of
design. Traditionally, they have been
hydrodynamic oil bearing or oil-cooled ball
bearing. These bearings are being surpassed by
foil bearing, which have been successfully used
in micro turbines and units. In this paper the
journal bearing is designated as no#2bearing
and supportive thrust bearing is no#1 bearing.
Gas turbines are constructed to work with oil,
natural gas, coal gas, producer gas, blast
furnace gas and pulverized coal with varying
fractions of nitrogen and impurities such as
hydrogen sulfide are used as Fuel. Each unit of
GTPPS consists of five main components, viz
turbine, compressor, combustion chamber,
Generator and electric system supporting the
whole unit. The various stages of operation are
shown in the Figure 1 as shown below.
The main components of the GTPPS plant is
described with following section.
(1) Compressor: The compressor in a GTPPS
power plant handle a large volume of air or
working media and delivering it at about 4 to
10 atmosphere pressure with highest possible
efficiencies The axial flow compressor is used
for this purpose. The kinetic energy is given to
the air as it passes through the rotor and part of
it is converted into pressure. The common types
of failures applicable in the compressor of
GTPPS system is as follows. (a) Exhaust
temperature high: (b) Air inlet differential
Trouble
(2) Combustion Chambers: The combustion
chamber perform the difficult task of burning
the large quantity of fuel, supplied through
the fuel burner with extensive volume of air
supplied by the compressor and releasing the
heat in such a manner that air is expanded and
accelerated to give a smooth stream of
uniformly heated gas at all conditions required
by the turbine. The common types of failures
applicable in the combustion chambers of
GTPPS system is as follows.(a) Loss of Flame.
(b) Servo Trouble:
(3) Gas Turbine: A gas turbine used in power
plant converts the heat and kinetic energy of the
gases into work The basic requirements of the
turbines are lightweight, high efficiency;
reliability in operation and long working life.
The common types of failures applicable in the
Gas Turbine component of GTPPS system is as
follows. (a) High Pressure (H.P) Turbine under
speed. (b) Low Pressure (L.P) Turbine Over
speed. (c) Wheel space differential temperature
high. (d) Mist eliminator Failure/Trouble. (e)
Turbine Lube Oil Header Temperature High. (f)
Low hydraulic pressure. (g) Bearing drain oil
temperature high:
(4) Generator: generator is a machine which
converts mechanical energy into electrical
energy (or power).In a generator, an e.m.f. is
produced by the movement of a coil in a
magnetic field. The common types of failures
applicable in the Generator of GTPPS system is
as follows. a) P.M.G bolt broken:
Figure 1: Block Diagram of Single Shaft Gas Turbine
Power Plant
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(5) Electrical systems: The A.C. power circuit
ignition system receives an alternating current
that is passed through a transformer and
rectifier to charge a capacitor.
When the voltage in the capacitor is equal to
the breakdown value of a sealed discharge gap,
the capacitor discharges the energy across the
face of the ignition plug. Safety and discharge
resistors are fitted in the circuit. Except this
various circuit breakers, Relay system, Bus
Bars, control panels, transformers are used in
electrical systems. The main function is linking
the produced generation to hungry consumers‘.
The common types of failures found in the
Electrical systems of GTPPS system is as
follows
(a) De synchronization with Grid. The overall
Diagram of GTPPS Plant is described in
GTPPS operation diagram.
collection procedure. After that flow chart for
reliability analysis is carried out. The different
parameters and variables are identified and
presented in the Parameters and variable sections.
This detail descriptions is divided into three
section
(a) Data collection
(b) Reliability Logic Diagram
(c) Parameters and variables.
Data collection: The collection of Data is necessary
to carry out the analysis. The data are collected
from the maintenance logbook available in the plant
and asking questions to the operators, supervisors
and managers of the plant. Data are required to be
collected over a period of time for providing
satisfactory representation of the true failure
characterization of the machine. Data used in recent
studies have been collected for a period of 5 and
half years. Approximately 956 failure data is
collected for all the seven units over the stated
Period. These Data are segregated according to
component wise and unit wise. The failure time
repair time and time of breakdowns reasons for
failures are also collected.
(a) Reliability Logic Diagram:
Before carrying out any research work
Understanding of the system is necessary. Block
diagram of the system will help to understand the
inner physics of any system. So a block diagram is
necessary to understand the behavior of the system.
Figure 3 represents the block diagram of Rukhia
gas turbine Power plant. Proper planning is
necessary to carry out any research work. For the
repairable system analysis a flowchart of where to
start, what are the things to do; a step by step
working procedure is necessary. This Framework is
presented in figure 3,and it is attached in Appendix
A. In this framework a detailed working procedure
and step by step model identification is presented.
Parameters and variables.
Step-II: Component- and System-level Analysis
Decisions regarding relevance of component- or
system-level analysis are to be taken on the basis of
the following considerations. These considerations
are taken under the heading of Component-level
Analysis and System-level Analysis. The details of
the analysis are described in the next section.
Component-level Analysis . On completion of
preliminary analysis of data, components with
significant number of failures in a given time period
are to be selected. The appropriate reliability tests
III. ARRANGEMENT OF UNITS IN POWER PLANT
Before carrying out any research work
understanding of the system is necessary. Block
diagram of the system will help to understand the
inner physics of any system. So a block diagram is
necessary to understand the behavior of the system.
Figure 2 represents the block diagram of Rukhia
gas turbine Power plant. Proper planning is
necessary to carry out any research work. For the
repairable system analysis a flowchart of where to
start, what are the things to do; a step by step
working procedure is necessary. This Framework is
presented in figure 3(Appendix B). In this
framework a detailed working procedure and step
by step model identification is presented.
(Appendix A : Figure 2 gives the GTPPS
Operation Diagram of Rukhia Gas Turbine Power
Plant.)
Methodology: In any Reliability analysis the
identification of Proper model is necessary. As per
the flow diagram the methodology for reliability
modeling of Turbine, Compressor, Generator and
Combustion Chamber and Electrical System
consists of following steps
Step I: Identification of Relevant Parameters and
Variables, and Collection of Relevant Data. Here
all the failure data are collected as per the data
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(normal or accelerated life tests) are to be conducted
for such components for reliability analysis.
Measurement and evaluation of reliability of such
components would follow the analysis of test data.
(APPENDIX B : Figure 3 gives the Methodology
for Reliability Analysis of turbine, compressor,
combustion chamber and electrical system)
may be analyzed with such techniques. In this case
the trend test is done on the data and presented in
the result section of trend test .
The electrical system follow the Renewal Process
as dependency were not proved in the serial
correlation tests. Hence Branching Poison Process is
rejected.
Step III: Development of Appropriate
(c) Parameters and variables
The parameters of Turbine, Compressor, and
Combustion chamber Generators are mentioned in
Table 1 given in Appendix C.
Reliability Model. In this section the
appropriate reliability model is described
into following three sections. Statistical tests
used: The statistical tests used here are trend test,
serial correlation test, Laplace test and Military
handbook tests. The procedure for carrying out all
these tests are described in the Statistical tests and
Reliability models section.
(a). Available reliability model: The different
reliability models used here are Power law process
and log linear process under the non homogenious
poisson process and renewal process under the
homogeneous poison process. The procedure for
carrying out all these tests are described in the
Statistical tests and Reliability models section. In
addition
the different reliability models and
estimation of parameters and reliability estimation
are described in the Statistical tests and Reliability
models section. Selection of appropriate reliability
model: The appropriate Reliability model is selected
by different testing procedure as described in
section (b), i.e. by Trend test , Serial correlation
test, Military Handbook test and Laplace test, and
renewal process. Based on the above test described
in Result section the following conclusion is
attained and described in table 2.
IV. SYSTEM LEVEL ANALYSIS
For this kind of analysis, the configuration of the
system as a whole is to be known. Both parametric
as well as nonparametric approaches for reliability
measurement and evaluation are a possibility. The
conditions under which parametric or nonparametric approach is recommended are as
follows:
Condition of Parametric approach: The number
of data points related to a system is made available
within the given time period and sufficient enough
to verify the distributional assumption for the
variables under consideration at an acceptable level
of significance. A parametric approach may be
applied in three situations: When the failure data
follows a homogeneous Poisson process (HPP) (no
trend and dependence in data), or (ii)
nonhomogeneous Poisson process (NHPP) (trend in
data), and (iii) Branching Poisson process (BPP) (no
trend but dependence in data). The parameters of
the three processes as mentioned may be estimated
with a number of tools and techniques, such as
‗probability plot‘ and ‗maximum likelihood
estimation‘
Conditions for Nonparametric Approach:
Model
Power law process.
A nonparametric approach is recommended
when the following conditions are met. The
number of data points related to a system is
made available but insufficient enough to verify
the distributional assumptions for the variables
under consideration at an acceptable level of
significance. Special tools and techniques, such
as Kaplan-Meier estimator, simple and standard
actuarial methods, and regression analysis, are
used in this case. The failure rate data of Turbine,
Generators
Power law process.
Combustion chamber
Power law process.
Electrical system
Renewal Process
Turbine
Log linear model
Table 2: Result of Final model selection of different units.
Compressor, Combustion Chamber and Generator
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Laplace test: To find out the data pattern follow
Log linear process .All these aforesaid tests are
stated below.
Trend Test:- The graphical trend test and
serial correlation test of TBF data of Turbine ,
compressor, Generator, combustion chamber
and electrical components and their subsystems
are necessary for validity of assumption that
failure data are independently distributed (iid)
in an analysis of failure distribution model. The
trend test is done by plotting the cumulative
time between failure (CTBF) against
cumulative frequency of occurrence. Serial
correlation test is done by means of plotting ith
TBF against (i-1) th TBF. Trend plot of
Turbine, compressor, Generator, combustion
chamber and electrical components and their
subsystems will be five curves presented in
figure.. In the test, weak or absolute trends were
found for Turbine, compressor, Generator,
combustion chamber and no trend in electrical
components and exhibited concave upward and
concave downward respectively in trend
test..The trend test were further elaborated by
Trend test 1 and Trend test 2 in Reliability
modeling to determine Homogeneous poison
process or Non Homogeneous poison process in
trend test 1 and Renewal process or Non
Renewal Process in Trend test 2 Finally the
Reliability of each system are calculated by
selecting the Proper model in analysis and the
models are followed in the manner as described
below.
Serial Correlation test: Serial correlation test
is done by means of plotting ith TBF against (i1) th TBF. The condition is = Points are not
randomly scattered and in straight line . *Data
are dependent and Branching Poison Process
can be applied . Points are randomly scattered
and not in straight line ≠ Data have no
correlation and dependence = Data are
independent and identically Distributed.
In the entire correlation test from turbine,
compressor, Generator, combustion chamber
there is no correlation among the data points.
So the failure Data can be assumed to be
independently and identically distributed In
Step IV: Verification and Validation of the
Proposed Approach.
The proposed models are to be tested for its
verification and validation in a number of
situations and conditions as discussed for the
testing Procedure. Modifications in the
proposed model are based on analysis of
difference between the actual and estimated
performance data over a period. The
methodology for reliability modeling of GTPPS
and its subsystems like turbine compressor,
combustion
chambers
and
Generators
considered to be a repairable system, is
explained in detail with the help of flow
diagram shown in Figure 3.This methodology is
applied for reliability analysis of GTPPS and its
subsystems
like
turbine
compressor,
combustion chambers and Generators and the
details of the application of methodology are
given below.
4. Statistical tests and Reliability models:
Various statistical tests are available for the
analysis of data. These are Trend tests, TTT
plot, Nelson Allen Plot, Serial correlation test,
Duane Growth model, Apart from for deciding
the appropriate reliability models the Military
handbook tests and Laplace stets are used. The
various Reliability models available are
homogeneous
poison
process,
non
homogenious poison process, branching
poisson process, renewal process and models
for non repairable items. The various statistical
tests and reliability models are described under
the following two sections described below (1)
statistical models (2) Reliability models
(1) Statistical Tests: The various Statistical
tests used in this paper are described below.
These are
Trend test- Cumulative failures verses
cumulative time between failures.
Serial Correlation test: to find whether Data is
independently and identically distributed.
Military Handbook test: To find the data pattern
follow Power law process
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serial correlation test, the points are randomly
scattered not in a straight line. For example,
serial correlation test of Turbine, compressor,
Generator, combustion chamber and electrical
components are presented in different figures.
So the above failure data can be assumed to be
independently and identically distributed (iid)
linear model. The generalization of the
Laplace‘s test statistic for more than one
process may be given by
m nˆi
m
1
t

nˆi (bi  ai )


ij
i 1 j 1
i 1 2
------------------LC 
1 m
nˆi (bi  ai ) 2

12 i 1
------------------------------------------(23)
Where n̂i = n or (n-1) if the process is time
truncated or failure truncated, respectively
[Kvaloy and Lindquist, 1998].[33] This test
statistic is asymptotically standard normally
distributed under the null hypothesis. The
Laplace statistics value is calculated
corresponding to failure parameters of
component and compared with chi square
value of N degree of freedom and if chi square
value is < than the Laplace value than Null
hypothesis is rejected otherwise Null
hypothesis is accepted. thus deciding Log linear
model or Power law process. (2) Reliability
models: The various Reliability models used in
this paper are described below. These are
Homogeneous
Poisson
Process,
Non
homogeneous Poisson Process, and Branching Poison
Process, Renewal Process and Non repairable
items
Military Hand book test:
The Military Handbook test is a test for the
null hypothesis H 0 : HPP versus alternative
hypothesis H1 : NHPP with increasing power
law process. The test statistic of this test for
more than one process is given by
m nˆi
b  ai
M C  2 ln( i
) ---------------------------tij  ai
i 1 j 1
-----------------------------------------(22)
And it is chi-square distributed with 2q degrees
of freedom,
m
Where q   nˆ i under the null hypothesis of
i 1
HPP [Kvaloy and Lindquist, 1998]. The Mc
value is calculated corresponding to failure
parameters of component and compared with
chi square value of 2N degree of freedom and
if chi square value is > than Mc value than
Null hypothesis is rejected otherwise Null
hypothesis is accepted. thus deciding Log linear
model or Power law process. In case the null
hypothesis is not accepted for both the tests,
then the conflict regarding NHPP with loglinear model or power law process is resolved
by calculating the so-called probability or Pvalues of the tests as mentioned. The P-value
for a normal distribution is defined to be the
probability value corresponding to the z-value
against Laplace‘s test statistic. For Military
Handbook test, P-value corresponds to the χ2value with one degree of freedom. A smaller Pvalue is indicative a stronger evidences a null
hypothesis [Rigdon and Basu, 2000][32].
Laplace test:- Laplace‘s test is conducted for
the null hypothesis, H 0 : HPP versus the
Homogeneous Poisson Process
The homogeneous Poisson process is a Poisson
process with constant intensity function
[Rigdon and Basu, 2000][11]. Since the
systems are identical, the failure process of
1
each system is an HPP with intensity , and 

is same for all systems. A counting process is a
homogenous Poisson process with parameter λ
>0 if :
N (0)=0.
The process has independent
increments
The number of failures in any interval of length
t is distributed as a Poisson distribution with
parameter λt . The following formulas apply:
alternative hypothesis, H1 : NHPP with log561
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-λt
F(t) = 1- e
= The cumulative density
function of the waiting time to the next failure
(or interarrival time between failures)
N(T) = the cumulative number of failures from
time 0 to time T. P{N(t)=k} = (λT) k e-λt / k│
M (T) =λt = the expected number of failures by
time T, λ = the rate of occurrence of failure
ROCOF, 1/λ = The Mean time between
failures (MTBF). So the reliability R(t) in the
case of Homogeneous Process =- e-λt ------------------(1)
Branching Poison Process:
The number of of subsidiary failures that follow
from a primary failure is a discrete random
variable. Lewis (1964) and cox and Lewis
(1966)[15,16] describe the cases where the
random variable has a geometric, negative
binomial and poison distribution. It is assumed
that both kind of failures (primary and
secondary) are indistinguishable. Define G to
be the number of subsidiary failures
corresponding to a single primary failure
conditioned on there being at least one such
subsidiary failures and let
S be the
(unconditional) number of subsidiary failures.
Note that S=0 when the repair is done correctly.
Let Z1, Z2 ---- denote the times between the
primary failures and let Yi (1), Yi(2),----------------Yi(s),
times between the subsidiary failures
that are triggered by ith primary failures.
Finally let T1< T2< T3 denotes the failure time
regardless of the type. In practice we observe
only the Ti‘s and not the type of failure. The
ROOCOF function for the BPP can be obtained
as follows. Let H(t) denote the expected
number of subsidiary failure from a single
primary failure to an interval interval of length
t and let Fk (t) and fk (t) denote the cdf and pdf
respectively of the random variable Z1 + Z 2 +------+ Zk(i.e. the time of the k th primary
failure) Given that Z1=z the expected events in
the interval[0,t] from the first subsidiary
process, the first subsidiary process, then E[N
(1)
(t) the number of failures in (0,t) due to first
subsidiary process then
(1)
(1)
E[[N
(t)]=
E{
N
(t)│Z1]}
Figure: 4 Example of Branching Process, Ref [12]
The Branching Poison Process: In some cases
failures tend to be bunched together . This may
indicate that the system is not correctly repaired
causing a number of subsequent failures. A
model that can account the phenomenon is the
branching Poisson Process (BPP). The BPP was
originally proposed by Bartlett (1963)[13] as a
model for Traffic flow., where a slow moving
vehicle may be followed immediately by a
number of other vehicles. This is analogous to
to a single failure causing a number of
subsequent failures. Lewis (1965)[14] applied
the BPP to failure times of computers. To be
more precise suppose the primary failures are
generated according to poison process with rate
λ . After each failure there is probability 1-r that
the repair will be done correctly; In this case
the next failure will occur when the next
primary failures occurs. With probability r, the
repair is not done correctly; In this case the
primary failure will spawn a finite renewal
process of subsidiary failures.
∫
=
∫
=
(t)ІZ2=z] f1(z) dz
(z)dz
A similar analysis could be applied to the time
of the k th failure. The expected no of failure N
(1)
(t) in (0,t) due to the kith subsidiary process is
E[N (1)(t)] = ∫
562
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The expected number of failure of any type in
[0,t] is thus Λ(t) =E[N,(t)]=E( Number of
Primary
failure
in
[0,t])
+∑
from
k th primary failure)
= Λz(t) +∑
= Λz (t) +∫
F (t) =
------- (6)
Where a and b are the scale and shape parameters,
respectively. The ML estimators for parameters a
and b are [18,19]:
∫
∑
(z)]dz
=
= Λz (t) + ∫
(z) dz----[3}
The ROCOF for the branching process is
therefore
∑
[
]
---------------------------------
(7)
=Λ(t). =Λz (t) + d/dt ∫
∑
zdz. .If no subsidiary failure is there the
ROCOF =λ---------------------------------------------------- (2)
The Reliability function is = e-λt
[
]
-- ^
∑
=
∑
----------------- (8)
Where ti is the observed time between successive
failures and n is the total number of failures
observed. A close form solution to estimate the
expected number of failures in the case of Weibull
distribution has not been developed yet. Instead, a
group of numerical solutions can be obtained.
Smith and Lead [20] better have proposed an
iterative solution to the renewal equation for cases
where the failure interarrival times follow a Weibull
distribution.
Renewal Process: RP is defined as a process in
which the different times to failure of a component
or system, Xi, are considered independently and
identically distributed random variables. This is
consistent with the primary underlying notion of
this process that assumes that the system is restored
to its original (like new) condition following a
relatively instant repair action. Because it represents
an ideal situation, this model has very limited
applications in the analysis of repairable systems,
unless the system consists of primarily nonrepairable (replaceable) components in sockets.
That is, when a part of the system fails, it will be
taken out and replaced by a new one [17] . The
expected number of failures in a time interval [0, t]
is given by: Λ (t) = F(t) +∫
----------------------------------(3)
The maximum likelihood estimation is done by
and β¯ and Reliability is estimated by the formula
=
------------------------------ (9)
Non repairable item
For this model illustrated in figure 3. there is neither
preventive maintenance
nor corrective nor
preventive maintenance, and the failure intensity
equals 0 after failure has occurred. The component
history (step 2) is recorded by X(t), where
X(i) =1, if i<X, and 0 otherwise------------- (10)
The variable Keeps track of whether the failure has
occurred or not, which is the only event relevant to
IC(t)The intensity process
IC(t) (step 3) is
completely determined by this X(t), and the
inherent TTF,X, whose hazard rate λ(x) is
specified in step 1. The model specification can now
be summarized by presenting its intensity process
IC(t) =λ(t).X(t)--------------------------------------[11]
Where F (t) is the cumulative distribution function
(cdf) of the time between successive repairs or
replacements of the system. By taking the derivative
of both sides of Eq. (1) with respect to t:
λ(t) = f(t) + ∫
---------------------(4)
Where f(t ) is the probability density function (pdf)
of the time between successive failures. In case of
the two parameter Weibull distribution, representing
the random variable t, the cdf and the pdf are of the
form:
F (t) = 1-
---------------------
------------------------------- (5)
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Thus the intensity process is the hazard rate of the
inherent TTF, truncated at time of failure and I(t)
–E[ IC(t) –E[λ(t),X(t)]= λ(t).E[X(t)]= λ(t).R(t) =f(t)
–-------------------------------------(12)
This is a special case of eqn(12) and again gives the
result that the mean intensity, I(t), for a
nonreplicable items equals the pdf, f(t). The
interpretation is that at time [t,t+dt) equals f(t). dt
The probability that a particular system will
experience n failures over its age (0, T) is given by
the Poisson expression [Rigdon and Basu,
1989][31],

(T  )n eT
P( N (t )  n) 
, n  0, 1, 2,... ---n!
14)
And the reliability may be given by, R(t) =
exp{intensity function -λt}. Maximum likelihood
estimation of the parameters may be described as
follows: Let, tij denotes the jth failure of ith system.
Suppose, ni failures are observed for system i.
Applying the joint pdf theorem, the MLE of
parameters of power law process is given by and
estimated as stated. Hence, the intensity function of
power law process for GTPPS -unit is given .With
the help of this intensity function the reliability of
the GTPPS -unit may be calculated
Nonhomogenious Poison Process:
Nonhomogeneous Poisson processes are also useful
for modeling repairable system reliability [Bertkeats
and Chambal, 2002; Ryan, 2003].[21,22] The
failure process between two successive overhaul
actions is described by a nonhomogeneous process
[Ascher and Feingold, 1984; Engelhard and Bain,
1986][23,24]. The NHPP model also assumes
‗minimal repair‘, which means that after each
failure and following repair, the system is in the
same state as it was just prior to that failure
[Heggland and Lindqvist, 2007][25]. Moreover, it is
also assumed that the failed part is small one of the
system. During and after repair or replacement of
this part the other parts will not be affected. The
assumption for modeling of more than one system is
that all systems are identical with respect to their
technology and mean time between failures. Also,
all systems are time-truncated with same starting
and finishing points. Among the NHPP‘s, large
attention has been devoted to the power law process
[Walls and Bendell, 1986; Pulcini, 2001] [26,27]
and log-linear processes [Cox and Lewis, 1966;
Baker, 2001].[28,29] In this context, it is mentioned
that if the failure data of a system rejects the null
hypothesis of Laplace‘s Test, the data is considered
to follow the log-linear model. On the other hand, if
the failure data of a system rejects the null
hypothesis of Military Handbook test, the data
follows the power law model. The following
sections describe the procedures for estimation of
parameters for the two models (Power Law and
Log-linear Processes), as mentioned.
Power Law Process
The intensity function of power law process is
given
as
follows
[Crow,
1990]:[30].
  t    t  1 , λ
k
 ˆ 
 ni
i 1
k
 tin
------------------------------ (15)

i 1
k
and
 ni
 ˆ 
i 1
k
k
ni
--
ˆ  tin  log(tin )   log(tij )
i 1
i 1 j 1
(16)
If the systems are time-truncated and tin=T for all
systems, the above-mentioned estimates may be
written as
k
ˆ 
 ni
i 1
--------------------------------- (17)
kT 
and
k
 ˆ 
 ni
k
i 1
ni
----------------------------(18)
T
 log( t )
i 1 j 1
ij
Reliability R(t) = e –intensity function
Log Linear Model
where, , , t > 0, and t is the
age of the system. Hence, the power law mean value
function is given by,
E ( N (t ))  t  , t  0 ----------------------------(13)
The intensity function of log-linear process is
shown as follows [Ascher and Feingold, 1984][23]
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are randomly scattered and not in straight line in the
serial correlation test.
 (t )  e   t ----------------------------------- (19)
Where , , t>0, and t is the age of the system.
Similar to power law process the maximum
likelihood estimates of parameters of log-linear
process for more than one system is calculated as
follows
Plot of CTBF verses cumulative failures of compressor
failures datas
60000
k
e 
k (e
i 1
ˆT
 1)
----------------------------(20)
k
k
and
ni
  tij 
i 1 j 1
cumulative T.B. F.
ˆ
ˆ  ni
 ni
i 1
ˆ
ˆ

k
Te  T  ni
(e
ˆT
i 1
 1)
50000
40000
Series1
(20)
30000
Series2
20000
10000
0
0-
1
4
7 10 13 16 19 22 25 28 31 34
cumulative nos of failures
(21)
Reliability R(t) = e –intensity function
Figure :-5 Cumulative Failure nos verses cumulative time between
failure Data of compressor system
V. RESULTS
Serial Corelation test of compressor failure
Datas
I th T.B.F.
Data used in recent studies have been
collected for a period of 5 and half years.
Approximately 956 failure data is collected for
all the seven units over the stated Period. These
Data are segregated according to component
wise and unitwise.The failure time repair time
and time of breakdowns reasons for failures are
also collected. These failure data of different
units were collected from the maintenance log
book. Failure behavior of these machines has an
influence on availability or failure pattern of the
machine as a whole. The basic methodology for
reliability modeling is presented in figure 3. It
shows a detailed flow chart for model
identification and is used here as a basis for the
analysis of failure Data So TBF are arranged in
a chronological order for using statistical
analysis to determine the trend in failure and
other aspects of Reliability. In this section the
detail analysis of the test carried out on
different components are discussed.
Compressor: The Cumulative TBF verses
cumulative failures datas are drawn in a plot
and the plot is shown below in figure 5.
Similarly the failure Data of ith failure verses
(i-1) th failure
data are plotted in figure 6.
The result shows that Failure data line has
slight deviation from straight line. and the points
10000
5000
Series1
0
0
5000
10000
( i -1)th T.B.F
Figure: 6 Serial correlation test of Compressor units of
GTPPS.
Conclusion: Data is modeled by NHPP.and data
are independently and identically distributed. Now
to select the model for Log linear or Power law
process the data are further processed by carrying
out military Handbook Test. The result of Military
Handbook Test is described in table 2.
It is mentioned that if the failure data of a system
rejects the null hypothesis of Laplace‘s Test, the
data is considered to follow the log-linear model.
On the other hand, if the failure data of a system
rejects the null hypothesis of Military Handbook
test, the data follows the power law model. Data
Pattern follow the Power Law Process. By applying
the Formula of intensity function and appropriate
formula of Reliability the Reliability at different
time intervals are calculated and it is shown
graphically in the figure 7 mentioned below.
565
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MC
value
Compre
ssor
30.354
Sam
ple
size
35
Χ2N,,0.5val
ue
Result
Χ235,,0.5=4
5.5
Null
hypothesis
rejected
Cumulative T.B.F. verses cumulative failures of
Combustion chamber failure data
50000
cumulative T.B.F.
Compon
ent
Table: 2 Result of Military Handbook test of Compressor
30000
20000
10000
0
Reliability at different intervals of Compressor
1
10 19 28 37 46 55 64 73 82 91 100 109
cumulative failures
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Figure 8:-Cumulative failure vs. Cumulative T.B.F of combustion
chambers used in GTPPS system
Serial corelation of combustion chamber failure
data
10000
0
100 200- 300
400
500
600
700
800
900 1000
i th T.B.F.
Reliability
40000
operating Time
Figure 7 Reliability at different intervals of compressor units.
8000
6000
4000
2000
Compon
ent
Combust
ion
Chamber
MC
valu
e
104.
3
Samp
le
size
60
Χ2N,,0.5valu
e
Result
<Χ260,,0.5=
88.38
Null
hypothesis
rejected
0
0
2000
4000
6000
8000
10000
(i-1)th T.B.F.
Figure:--9 Serial correlation test of Combustion Chamber units of
GTPPS.
Conclusion: Data is modeled by NHPP.and data are
independently and identically distributed. Now to
select the model for Log linear or Power law
process the data are further processed by carrying
out military Handbook Test. The result of Military
Handbook Test is as follows. It is mentioned that if
the failure data of a system rejects the null
hypothesis of Laplace‘s Test, the data is considered
to follow the log-linear model. On the other hand, if
the failure data of a system rejects the null
hypothesis of Military Handbook test, the data
follows the power law model. Data Pattern follow
the Power Law Process. By applying the Formula of
intensity function and appropriate formula of
Reliability the Reliability at different time intervals
are calculated. and it is shown graphically in the
figure 10 mentioned below.
Table: 3 Result of Military Handbook test of
Combustion Chamber
Combustion Chamber: The Cumulative TBF
verses cumulative failures datas are drawn in a plot
and the plot is shown below in figure 8. Similarly
the failure Data of ith failure verses (i-1) th failure
data are plotted in figure 9. The result shows that
Failure data line have slight deviation from straight
line. and the points are randomly scattered and not
in straight line in the serial correlation test.
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Reliability at different intervals of combustion
Chamber
Serial corelation test of Generator system failure data
7000
6000
1.2
I th T.B.F.
Reliability
1
0.8
0.6
0.4
0.2
100 200- 300
400
500
600
700
800
900 1000
0
Operating intervals
correlation test.
Compon
ent
MC
value
Generat
or
-46.85
Sam
ple
size
60
Χ2N,,0.5val
ue
Result
Χ260,,0.5=8
8.38
Null
hypothesis
rejected
4000
6000
8000
Figure 12: Serial correlation tests of Generator units of GTPPS.
Conclusion: data is modeled by NHPP.and data are
independently and identically distributed. Now to
select the model for Log linear or Power law
process the data are further processed by carrying
out military Handbook Test. The result of Military
Handbook Test is as follows
Compone MC
nt
value
Generator -46.85
Sampl
e size
60
Χ2N,,0.5valu
e
Χ260,,0.5=88.
38
Result
Null
hypothesi
s rejected
Table 4: Result of Military Handbook test of Generator
Conclusion: Data Pattern follow the Power Law
Process. By applying the Formula of intensity
function and appropriate formula of Reliability the
Reliability at different time intervals are calculated.
and it is shown graphically in the figure 13
mentioned below
Plot of cumulative T.B.F. verses cumulative failures of
Generator failure data
60000
cumulative T.B.F.
2000
(i-1)th T.B.F.
Figure 10: Reliability at different intervals of combustion chamber
system.
Generator:
The Cumulative TBF verses
cumulative failures data are drawn in a plot and
the plot is shown below in figure 11. Similarly
the failure Data of I th failure verses (i-1) th
failure data are plotted in figure 12. The result
shows that Failure data line has slight deviation
from straight line. and the points are randomly
scattered and not in straight line in the serial
Series1
3000
2000
1000
0
0
0
5000
4000
50000
Reliability at different operating intervals of
Generator
40000
30000
20000
1
10000
0.8
0
6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81
Reliability
1
cumulative failures
Figure 11:-Cumulative failure vs. Cumulative T.B.F of Generators
used in GTPPS system
0.6
0.4
0.2
0
100
200-
300
400
500
600
700
800
900
1000
Operating time
Figure: 13 Reliability at different intervals of Generator system
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Turbine: The Cumulative TBF verses cumulative
failures data are drawn in a plot and the plot is
shown below in figure 14. Similarly the failure Data
of ith failure verses (i-1) th failure data are plotted
in figure 15. The result shows that Failure data line
has slight deviation from straight line. and the
points are randomly scattered and not in straight
line in the serial correlation test.
On the other hand, if the failure data of a system
rejects the null hypothesis of Military Handbook
test, the data follows the power law model. Since
Turbine failure Data rejects the Null hypothesis in
Laplace test the failure Data follows Log Lineaer
model. The result of Laplace Test is as follows
Plot of cumulative failures verses cumulative T.B.F. of
Turbine system failure
Com
pone
nt
Laplu
s
Statist
ics
LC>0
LC< 0
Turb
ine
111.9
3
LC<0,
decreasing
trend
80000
Cumulative T.B.F.
70000
60000
50000
Series1
40000
Series2
30000
20000
0
26 51 76 101 126 151 176 201 226
cumulative failures
Figure 14:-Cumulative failure vs. Cumulative T.B.F of Turbines
used in GTPPS system
1000
2000
3000
Reliability
Ith TBF
Series1
0
Reject
ed
Reliability at different time intervals of Turbine
system of GTPPS
Serial corelation test of Turbine system failure data
3500
3000
2500
2000
1500
1000
500
0
Null
Hypot
hesis
Table: 5 Result of Laplace test of Turbine unit
system.
Conclusion: Data Pattern follow the Log linear
model.By applying the Formula of intensity
function and appropriate formula of Reliability the
Reliability at different time intervals are calculated.
and it is shown graphically shown in the figure 16
as mentioned below
10000
1
or Laplace
Statistics>
<chi
square
statistics
Χ2N,,0.5
> Χ2N,,0.5
1
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0
4000
100
200
300
400
500
600
700
1000
Operating time
(i-1)th TBF
Figure16: Reliability at different intervals of Turbine system
Figure: 15 Serial correlation test of Turbine units of GTPPS.
Electrical System: The Cumulative TBF verses
cumulative failures datas are drawn in a plot and the
plot is shown below in figure 17. Similarly the
failure Data of ith failure verses (i-1) th failure
data are plotted in figure 18. The condition is
Deviations from straight line: trend is absent No
deviations – trend present, Points are randomly
scattered and not in straight line .
Data are independent and identically distributed. In
straight line = Data have correlation and
dependence.
Conclusion: data is modeled by NHPP.and data are
independently and identically distributed. Now to
select the model for Log linear or Power law
process the data are further processed by carrying
out military Handbook Test and Laplace test.. The
result of Military Handbook Test is Null hypothesis
is accepted It is mentioned that if the failure data of
a system rejects the null hypothesis of Laplace‘s
Test, the data is considered to follow the log-linear
model.
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Cumulative T.B.F. verses cumulative failure data of electrical
system failures
600000
cumulative T.B.F.
500000
400000
300000
200000
100000
0
1
14
27
40
53
66
79
92
105 118 131 144 157 170
cumulative failures
Figure 17: Cumulative failure vs. Cumulative T.B.F of electrical
system used in GTPPS system
Serial corelation test of electrical system failure
data
Reliability analysis in system level:Estimation of Reliability of systems by using the
Reliability of components.
Unit Level Reliability: Assuming the total System
has identical units and all the 5 units are parallally
connected keeping two standby units as shown in
the operational Diagram of GTPPS. The unit and
System level Reliability is calculated. Unit level
Reliability: Since all the components are in series
the series system reliability is Rs= R1x R2x R3x R4x
R5 [34] the system level reliability is calculated by
applying the series level formula. The Calculated
Reliability is shown in the Graph of figure 20.
Reliability of Parallel unit from unit 1,4,5,6,8 units in
GTPPS
6000
4000
1
3000
0.8
Reliability
ith T.B.F.
5000
2000
1000
0.6
0.4
0.2
0
0
1000
2000
3000
4000
5000
6000
0
(i-1) th T.B.F.
0
100 200- 300
400
500
600
700
800
900 1000
Operating Time
Figure18: Serial correlation tests of Electricals system units of
GTPPS.
Figure 20: Reliability at different intervals of identical units in
series system.
Conclusion:
Trend is absent Hence it is
Homogeneous Process Since correlation and
dependence is absent Datas are independently and
identically distributed. So next condition is after
repair it is as good as new. Yes it is as good as new
.
so this is a case of Renewal Process By applying
the Formula of intensity function and appropriate
formula of Reliability the Reliability at different
time intervals are calculated and it is shown
graphically shown in the figure 19 as mentioned
below
Determination of Parallel system Reliability:
Parallel Using the Formula Rp=1-Qp 1-[1-e(-λt))]n
[36]of Parallel system Reliability we get
the
Reliability of Parallel system at different time
intervals. The Reliability at different time intervals
and is shown in Figure 21.
Reliability Pattern of the GTPP s ys tem having all units
in parallel
1
0.9
Reliability at different intervals of electrical system
0.8
0.7
Reliability
1
0.6
0.6
0.5
0.4
0.3
0.4
0.2
0.1
0.2
900
1000
900 1000
800
700 800
700
500 600
600
400
500
200 300
400
100
300
0
0
200-
0
0
100
Reliability
0.8
Operating Tim e
Operating Time
Figure19: Reliability at different intervals of Electrical system
Figure 21: Reliability Pattern of Parallel system unit failure Dataˆˇ
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Determination of standby system Reliability
The formula used here is
,Rs(t) =
λ1t
λ1t +
In serial correlation test it is proved that Data
pattern
are independently and identically
distributed. So
Data are modeled by Non
Homogeneous Poison Process Now for deciding
whether Data Pattern follow the Power l;aw process
or Log Linear model Data are again tested by
Military Handbook test. It is Proved that the Data
Pattern follow the Power law Process as Null
hypothesis is rejected in Military Handbook test. By
setting the Parameters of Power law Process the
Reliability at different time interval are shown in
figure 7. The Reliability from 0th hour to 100 th
hour is drastically changing in the Diagram.
Combustion Chamber: The trend test shows that
there is little deviations from straight line. So it can
be concluded that Data Pattern of TBF data have
trend. In serial correlation test it is proved that Data
pattern
are independently and identically
distributed. So
Data are modeled by Non
Homogeneous Poison Process Now for deciding
whether Data Pattern follow the Power l;aw process
or Log Linear model Data are again tested by
Military Handbook test. It is Proved that the Data
Pattern follow the Power law Process as Null
hypothesis is rejected in Military Handbook test. By
setting the Parameters of Power law Process the
Reliability at different time interval are shown in
figure 10. Here the Reliability is almost constant fro
0 th hour to 200 hour and from 700 hour to 900
hour which requires further investigation as
Reliability pattern does not show a constant Path.
Generator: The trend test shows that there is little
deviations from straight line. So it can be concluded
that Data Pattern of TBF data have trend. In serial
correlation test it is proved that Data pattern are
independently and identically distributed. So Data
are modeled by Non Homogeneous Poison Process
Now for deciding whether Data Pattern follow the
Power l;aw process or Log Linear model Data are
again tested by Military Handbook test. It is
Proved that the Data Pattern follow the Power law
Process as Null hypothesis is rejected in Military
Handbook test. By setting the Parameters of Power
law Process the Reliability at different time interval
are shown in figure 13. Here the Reliability Pattern
shows a decreasing trend with constant rate. It is
almost acceptable..
Turbine: The trend test shows that there is little
deviations from straight line. So it can be concluded
that Data Pattern of TBF data have trend.
λ2t
-
)+ λ1 λ2
X[
+
+
] [35]-----------------------------------
---------------------[27]
Where
λ1 = Failure rate of the Parallel units
λ2 = Failure rate of the standby unit
λ3 = Failure rate of the second standby unit
Using the appropriate formula we got the Parallel
system reliability with two unit standby. The
Reliability at different time interval is shown in
figure 22
System Reliability at different time interval with 2
unit standby of Rukhia Gasthermal Power Plant
1
Reliability
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
800
900 1000
Operating Time
Figure 22: Reliability Pattern of whole plant unit if two stand by
unit is kept
6.0 Discussion:-The selection of model for
calculation of Reliability shows that the turbine unit
follows Log Linear model and compressor unit,
Generator and combustion chamber units follows
Power law model and electrical system follow
Renewal Process. The Reliability of different
components of Rukhia Gas Power Plant is analyzed
by taking the failure data of different operating units
and consultation with Plant operating Personnel and
management People about the arrangement of units
in winter and summer season, It is known that in
winter less Power is supplied to Grid and two units
are kept as standby system. In Summer the demand
is more and only one unit is kept as standby system.
In both cases Reliability is determined by taking
one and two units as stand by. Initially the
component level Reliability is discussed one by one.
Compressor: The trend test shows that there is little
deviations from straight line. So it can be concluded
that Data Pattern of TBF data have trend.
570
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
In serial correlation test it is proved that Data
pattern
are independently and identically
distributed. So
Data are modeled by Non
Homogeneous Poison Process Now for deciding
whether Data Pattern follow the Power l;aw process
or Log Linear model Data are again tested by
Laplace test as Military handbook test is not
applicable. In the Military Handbook test. Data
pattern shows that Null hypothesis is accepted. So it
is further tested by Laplace test and Null hypothesis
is rejected. It is Proved that the Data Pattern follow
the Log Linear Process as Null hypothesis is
rejected in Laplace test and is in decreasing nature
as Lc <0 By setting the Parameters of Log linear
Process the Reliability at different time interval are
calculated and shown in figure 16. Here trend is
not satisfactory from 0 to 100 hour and from 200
hour to 300 it is almost constant. The pattern
requires further investigation.
Electrical system: The trend test shows that there
are
deviations from straight line. So it can be
concluded that Data Pattern of TBF data have no
trend. In serial correlation test it is proved that Data
pattern
are independently and identically
distributed So Trend is absent Hence it is
Homogeneous Process Since correlation and
dependence is absent Data are independently and
identically distributed. So next condition is After
repair it is as good as new. Yes it is as good as new
because after failure all the components are repaired
and it is as good as new. So Renewal Process is
followed here and Parameter and Reliability
function is applicable here.. By setting the
Parameters of Renewal function the reliability
Patterns are estimated here and are shown in figure
19. The reliability Pattern is drastically changing
from 0 th hour to 100 th hour. Which requires
further investigation?
Reliability of units :Since all the units are identical
Reliability of the unit is the product of component
Reliability. The Reliability of the units at different
operating intervals are shown in figure 20
Reliability of Parallel units: After setting the
component Reliability Pattern the Reliability at unit
level is calculated at different time interval by
multiplying the Reliability of component in series
and by applying the Parallel combination Reliability
formula. The Unit 1 and Unit 8 are kept in standby
system and unit 3, 4,5,6,7 are kept in Parallel
system. The unit level Reliability in Parallel system
are calculated and shown in figure 21 and
components in series of all units are shown in figure
20. Sharp fall in trend is observed from 0th hour to
700 hour which requires further investigation
.Reliability of system with two standby units: After
setting the Parallel system Reliability Pattern the
Reliability of system with two standby units is
calculated at different time interval by applying the
appropriate formula discussed in section 4. The Unit
1 and Unit 8 are kept in standby system and unit 3,
4,5,6,7, are kept in Parallel. The Reliability at
different intervals are shown in figure 22. Here
Reliability pattern is deviating from straight line in
200 and 500 hours which is required to be
investigated? Here the management of Power Plant
has option either to keep one unit as stand by or two
units as stand by or running all the units Parallaly.
The component Performances are also determined
by this way and one can have option how to run the
way in most efficient way. When this will be
compared by cost analysis this will give a
operational schedule to an optimized cost.
Conclusions:
In this paper the important Reliability trend test and
serial correlation tests are incorporated to conduct
the analysis of failures. A reliability logic diagram
is incorporated to plan the whole work in a logical
way. The field failure Data of Turbine, compressor,
Generator and combustion chamber were further
analyzed by placing the Data points in a suitable
reliability model, either Log Linear Process, or
Power law model or renewal process. On the basis
of this aforesaid tests the appropriate Reliability
model is incorporated to find out the Reliability at
different time intervals. After determining the
component Reliability the system level Reliability
of the Plant are estimated in different time intervals.
The operational diagram of the plant is incorporated
to understand the relation between the components,
relation between units and above all the clear
Picture of the system .. The standby mode injects
the further boost of reliability improvement. The
Reliability Pattern at different time intervals
application wise represent the failure behavior of
the system. Some practical problems that one may
encounter when analyzing reliability data are also
briefly discussed and references are given in each
case for further review.
571
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
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