Unpublish

2. i
PROCEEDING
SOUTH EAST ASIAN CONFERENCE ON MATHEMATICS
AND ITS APPLICATIONS
SEACMA 2013
“Mathematical Harmony in Science and Technology”
Published by:
MATHEMATICS DEPARTMENT
INSTITUT TEKNOLOGI SEPULUH NOPEMBER SURABAYA, INDONESIA

3. ii
PROCEEDING
SOUTH EAST ASIAN CONFERENCE ON MATHEMATICS AND ITS
APPLICATIONS
SEACMA 2013
Editor :
Prof. Dr. Basuki Widodo, M.Sc.
Prof. Dr. M. Isa Irawan, MT.
Dr. Subiono
Subchan, Ph.D
Dr. Darmaji
Dr. Imam Mukhlas
DR. Mahmud Yunus, M.Si
ISBN 978-979-96152-8-2
This Conference is held by cooperation with
Mathematics Department, ITS
Secretariat :
Mathematics Department
Kampus ITS Sukolilo Surabaya 60111, Indonesia
seacma@its.ac.id

4. iii
ORGANIZING COMMITTEE
PATRONS : Rector of ITS
STEERING : Dean Faculty of Mathematics and Natural Sciences ITS
INTERNATIONAL SCIENTIFIC COMMITTEE
Prof. Basuki Widodo (ITS - Indonesia)
Prof. M. Isa Irawan (ITS - Indonesia)
Dr. Erna Apriliani (ITS - Indonesia)
Dr. Subiono (ITS - Indonesia)
Subchan, Ph. D (ITS - Indonesia)
Dr. Abadi (Unesa-Indonesia)
Dr. Miswanto (Unair-Indonesia)
Dr. Eridani (Unair-Indonesia)
Prof. Marjono (Universitas Brawijaya Indonesia)
Prof. Toto Nusantara, M.Si (UM-Indonesia)
Dr. Said Munzir, M.EngSc
(Syiah Kuala University Banda Aceh-Indonesia)
Dr. Nguyen Van Sanh (Mahidol University-Thaiand)
Prof. dr. ir. Arnold W.Heemink
(Delft Institute Applied Mthemathics-Netherland)
COMMITEE
Chairman : Subchan Ph. D
Co-chairman : Dr. Imam Mukhlas
Secretary : Soleha, S.Si, M.Si
Tahyatul Asfihani S.Si, M.Si
Finance : Dian Winda Setyawati, S.Si, M.Si
Technical Programme :
Drs. Daryono Budi Utomo, M.Si.
Drs. Lukman Hanafi, M.Sc.
Drs. Bandung Arry Sanjoyo, M.T.
Drs. I. G. Rai Usadha, M.Si
Moh. Iqbal, S.Si, M.Si
Web and Publication :
Dr. Budi Setiyono, S.Si, MT.
Achmet Usman Ali
Transportation and Accommodation :
Dr. Darmaji, S.Si, MT.
Yunita HL

5. iv
Message
from the
Dean Faculty of Mathematics and Natural
Sciences
Institut Teknologi Sepuluh Nopember
On behalf of the Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh
Nopember, it is a great honor and sincere to welcome all participants to the second of South
East Asian Conference on Mathematics and Its Application (SEACMA 2013).
This year, Department of Mathematics, Institut Teknologi Sepuluh Nopember, have honor to
organize this meaningful conference. I believe that the purpose of this conference is not only
sharing knowledge among the mathematician and scholars in related fields but also to hearten
new generation of expertise in mathematics to realize the science and technology
advancement.
It is undeniable that there is mathematical harmony in science and technologies. Many
disciplines like engineering, computer science, information technology, operational research,
logistics management, risk management and many others are all the products of
mathematics. Thus, it is essential that we must hold this annual conference as a stage for all
scholars in finding new ideas and applications on Mathematics.
Greatly thank to all supportive session including organizing committee, keynote speakers,
invited speakers, paper reviewers, participants and sponsors. This event will not achieve
without you all. Finally, I hope that the outcome of SEACMA 2013 will be pleasing and most
useful to everybody.
Sincerely yours,
Prof. Dr. R.Y. Perry Burhan
Dean

6. v
Message from the
Chairman
Organizing Committee
On behalf of the organizing committee it is my pleasure to welcome you to the
South East Asian Conference on Mathematics and Its Applications. The conference aims
to provide a forum for academics, researchers, and practitioners to exchange ideas and
recent developments on mathematics. The conference is expected to faster networking,
collaboration and joint effort among the conference participants to advance the theory
and practice as well as to identify major trends in mathematics.
We are also very pleased to welcome keynote speakers of the conference: Prof.
Dr. Ir. Arnold W. Heemink, from Delft Institute of Applied Mathematics, Netherlands,
Prof. Dr. Muhammad Isa Irawan, MT, from Institut Teknologi Sepuluh Nopember,
Surabaya, Indonesia, and Dr. Said Munzir, M.EngSc, from Syiah Kuala University,
Indonesia, Dr. Nguyen Van Sanh, from Department of Mathematics, Faculty of Science,
Mahidol University, Thailand.
We will spend about a day together for the conference. This conference is
attended delegates and contributors from Indonesia, Malaysia, Thailand, and Netherlands
Such a spread of participation from around the world confirms the appropriateness of the
“National” label of this conference. There are 35 papers to be presented orally. Papers
presented in the conference will be included in the conference proceeding to be published
at the conference.
The organizing committee would like to express our deepest appreciation to ITS
Rector, keynote speakers, head of departments of Mathematics of ITS, and sponsors for
the support, without all mentioned this conference may not be happened. Furthermore,
my appreciation goes to the members of the committee for their hard work and
cooperative teamwork in the preparation of the conference. Finally, we wish all
participants enjoy a fruitful scientific and human discussion.
Subchan, PhD
Conference Chairman

7. vi
CONTENTS
Cover i
Organizing Committee iii
Message from Dean Faculty of Mathematics and Natural Sciences iv
Message from Chairman of Organizing Committee v
Contents vi
Tentative Schedule ix
Abstract of Keynote Speaker
1. Model Reduced Variational Data Assimilation: An Ensemble Approach To Model
Calibration (A.W. Heemink)
2. Computational Optimal Control: Past, Current and Future Trends
(Said Munzir)
3. An Introduction to Some Kinds of Radicals for Module Theory (Nguyen Van Sanh)
4. Optimization Combination of Number, Dimension, and Mooring Time of the Ships
in PT. (Persero) Pelabuhan Indonesia III Gresik Harbor Using Genetic Algorithms
(M. Isa Irawan)
Mathematics Papers
PM1 Partial Ordered Bilinear Form Semigroups in Term of Their Fuzzy Right
and Fuzzy Left Ideals (Karyati, Dhoriva Uwatul Wutsqa)
PM2 ᶯ-Dual of Some New Double Sequence
(Sumardyono, Soepama D.W. and Supama)
PM6 Construction Of Suboptimal Solution of the Stick and Rope Problem Using
Sequence of Semicircle (Abrari Noor Hasmi and Iwan Pranoto)
PM7 A Laplace Transform DRBEM for Time-Dependent Infiltration from
Periodic Flat Channels (Imam Solekhudin)
PM10 On The Total Irregularity Strength Of Gears
(R. Ramdani, A.N.M. Salman and H. Assiyatun)
PM11 Construction Of Cone Difference Space-c0
(Sadjidon and Sunarsini)
PM12 The Star Partition Dimention Of Corona Product Graph
(Darmaji)
AM1 Measuring and Optimizing Conditional Value at Risk Using Copula
Simulation (Komang Dharmawan)
AM4 Biomass Feedstock Optimization for the Production of Methane Gas from
Water Hyacinth, Elephant Grass and Rice Straw Waste
(Suharmadi and Sumarno)
AM5 Application of Disturbance Compensating Model Predictive Control
(DC-MPC) On Ship Control System (Sari Cahyaningtias, Tahiyatul
Asfihani, Subchan)

8. vii
AM6 The Application of Ensemble Kalman Filter to Estimate the Debris Flow
Distribution ( Ngatini, Erna Apriliani, Imam Mukhlash, Lukman Hanafi,and
Soleha)
AM7 Modeling Consumer Prices Index Data in Yogyakarta using Truncated
Polynomial Spline Regression
( Dhoriva Urwatul Wutsqa and Yudhistirangga )
AM8 Flow Patterns Characteristics in Agitated Tank with Side Entering Impeller
( Sugeng Winardi, Tantular Nurtono, Widiyastuti, Siti Machmudah and Eka
Lutfi Septiani)
AM10 Flood Gate Control of Barrage Using Ensemble Kalman Filter Based On
Nonlinier Model Predictive Control (NMPC)
(Evita Purnaningrum and Erna Apriliani)
AM15 Calculation of Moving Vehicles with Video Using Expectation Maximization
Algorithm
( Budi Setiyono, R. Arif Firdaus Lazuardi and Shofwan Ali Fauji )
AM16 Application of fitting and Probabilistic Method to Characterize Physical
&Mechanical Rock Properties Distribution
( S.A. Pramuditya, M.A. Azizi , S. Kramadibrata and R.K. Wattimena)
AM17 Testing Proportion for Portfolio Profit of CAPM and LCAPM
( Retno Subekt, Rosita Kusumawati)
AM18 Numerical Simulation of Linear Water Waves Using Smoothed Particle
Hydrodynamics (Rizal Dwi Prayogo and Leo Hari Wiryanto)
AM19 Mathematical Model of Drag Coeficient of Tandem Configuration on Re =
100 (Chairul Imorn, Suhariningsih, Basuki Widodo, and Triyogi Yuwono)
AM20 Performance Evaluation of Two-Microphone Separation with Convolutive
Speech Mixtures ( Irwansyah and Dhany Arifianto)
AM22 Bayesian Analysis for Smoothing Spline in Semiparametric Multivariable
Regression Model Using WinBUGS
( Rita Diana, I. Nyoman Budiantara, Purhadi and Satwiko Darmesto)
AM23 Simulated Annealing Based Approach for the Dynamic Portfolio Selection of
Stocks ( Novriana Sumarti, Agung Laksono and Viony A. Jantoro)
AM24 On the Text Documents Pattern Recognition Using Latent Semantic Analysis
and Kolmogorov-Smirnov Test
( Soehardjoepri, Nur Iriawan, Brodjol Sutijo SU, Irhamah)
AM25 Study of Comparation Between Finite Difference and Crank- Nicholson
Method in Heat Transfer (Lukman Hanafi and Durmin)
AM27 Multi-level Stock Investment Evaluation Using Fuzzy Logic
(Mahmod Bin Othman)
AM28 The Relationship Between Parvate-Gangal Mean Value Theorems and Holder
Continuous Function of Order 𝜶𝜶 ∈ (0,1) on The Cantor Set
( Supriyadi Wibowo and Pangadi)
AM29 Calibration Of Rainfall Data by Using Ensemble Model Output Statistic
(EMOS) ( Dian Anggraeni, Heri Kuswanto, Irhamah and Waskitho Wibisono)
AM30 Full Conditional Distributions of Bayesian Poisson-Lognormal 2-Level
Spatio-Temporal Extension for DHF Risk Analysis
( Mukhsar, Iriawan, N, Ulama, B. S. S, Sutikno and Kuswanto, H)
AM31 Fuzzy Inference System Implementation On Rainfall Events Prediction At
North Surabaya (Farida Agustini Widjajati and Dynes Rizky Navianti)

9. viii
AM32 Monochromatic wave propagating over a step
(L.H. Wiryanto and M. Jamhuri)
AM33 The Normal Form For The Integral Of 3-Dimensional Maps Derived From A
Sine-Gordon Equation (Zakaria L, Tuwankotta J.M., and Budhi M.W.S)
AM34 Stability Analisis of Lotka-Volterra Model with Holling Type II Functional
Response ( Abadi, Dian Savitri, and Choirotul Ummah)
AM35 On The Construction of Prediction Interval for Double Seasonal Holt-Winters
: a Simulation Study
(Arinda R. Lailiya, Heri Kuswanto , Suhartono and Mutiah Salamah)
AM36 Bayesian Neural Networks for Time Series Modeling
(Fithriasari, K, Iriawan, N, Ulama, B. S and Sutikno)
AM37 Upper Bound And Upper Limit of The Optimum Interpolation Function of
Filter Bank (Dhany Arifianto)

10. ix
Tentative schedule
Thursday, 14 November 2013
07.30 – 08.00 : Registration
08.00 – 08.30 : Opening Ceremony
08.30 – 09.00 : Keynote Session 1 by Prof. dr. ir. Arnold W.Heemink (Netherland)
09.00 – 09.30 : Keynote Session 2 by Dr. Said Munzir, M.EngSc (Indonesia)
09.30 – 10.00 : Discussion Session
10.00 – 10.15 : Break
10.15 – 10.45 : Keynote Session 3 by Dr. Nguyen Van Sanh(Thailand)
10.45 – 11.15 : Keynote Session 4 by Prof. M. Isa Irawan(Indonesia)
11.15 – 11.45 : Discussion Session
11.45 – 13.00 : Break
13.00 – 16.00 : Parallel Session

11. 1 INTRODUCTION
Slope design has over the years become the domain of geotechnical engineers.
While this has benefited the technology of theslope design processes, it has
also separated the the mine design engineers from the responsibility of the risk
versus reward relationship.
Given the uncertainties that prevail within the geotechnical discipline, there
always exists a probability that a slope may not perform aspredicted, and in the
worst case can result in a catastrophic failure.
The rock slope stability analysis affected by the random input parameters such
as internal friction angle, cohesion, water pressure, seismic acceleration and
density, which cannot be properly represented by a single value as input
parameters in slope stability analysis. The uncertainty in the values of rock
mass properties is a major factor in slope stability analysis.
Each input parameter has a certain distribution function. There are several
methods used in characterizing a data distribution, namely: Chi-SquareMethod,
Kolmogorov-Smirnov method, and the method of Anderson Darling. This
paper uses the Kolmogorov-Smirnov method. The principle of this method is
based on a comparison between the experimental cumulative distribution
function and cumulative distribution theoretical assumptions.
The 4 assumptions of the cumulative distribution function will be compared
with the empirical distribution functions, namely: normal, lognormal, beta,
gamma.
The results of the characterization process will be used for the calculation of
the safety factor and failure probability of slopes, and the distribution data are
obtained from Tutupan Coal Mine, South Kalimantan, Indonesia.
2 BASIC THEORY
2.1 Probability Distribution Function
Probability distribution function describes the spread of a random variable that
is used to estimate the probability of the occurrence of a parameter value. It has
Application of fitting and Probabilistic Method to Characterize
Physical &Mechanical Rock Properties Distribution
S.A. Pramuditya1
, M.A. Azizi 2
, S. Kramadibrata3
and R.K. Wattimena4
1
Universitas Swadaya Gunung Jati, Indonesia
amamisurya@gmail.com,
2
Institut Teknologi Bandung, Indonesia
3
Institut Teknologi Bandung, Indonesia
4
Institut Teknologi Bandung, Indonesia
Abstract: Uncertainties of factors that influence slope stability have been acknowledged by many geotechnical engi-
neers, and these are drawn from the characterization of the geotechnical parameters of the slope. The characterization
is associated with a process of identifying the distribution of random variable values used in the design of a single
slope of an open mine, and also part of the probabilistic method which is an alternative approach in estimating the
stability of a slope with a failure probability value (FP). This paper explains the characterization process using the
Kolmogorov-Smirnov (K-S) method, which will determine the most appropriate function for the distribution of the
random variable. The characterization results can be used in determining the Safety Factor including the level of con-
fidence and Probability of Failure based on the best fitting function.
Keyword: uncertainties, failure probability, slope stability, safety factor
Proceeding South East Asian Conference
on Mathematics and its Application (SEACMA 2013) ISBN 978-979-96152-8-2
AM-16

12. typical and unique properties of distribution that make one function different
from others. But this does not rule out the possibility that a distribution
function is a derivative from another function. For example, the exponential
distribution function is a special form of the gamma distribution function
withshape parameter (a) is 1. Likewise,a uniform distribution function is a
special form of the beta distribution function with shape parameter values α = 1
and β = 1. A triangular distribution function is also a special form of the beta
distribution function with shape parameter values α1 = 1 and α2 = 2.
This paper employs 4 assumed continuous distribution functions, i.e.
normal, lognormal, beta, and gamma. These are considered to represent the
properties of the distribution of the random variables (see Table 1).
Table 1. Assumed Probability Density Function [8]
Distribution Probability Density Function Mean&Varians
Normal
fx(x)=
1
σ√2π
e-
1
2
�
x-μ
σ
�
2
−∞ < 𝑥 < ∞
Μ
σ2
Lognormal
fx(x)=
1
xσ√2π
e-
1
2
�
ln x-μ
σ
�
2
x>0
eμ+
1
2
σ2
e2μ+σ2
�eσ2-1
�
Beta
f(x)=
xα1-1(1-x)α2-1
Β(α1,α2)
;0≤x≤1
f(x)=0, x others
α1
α1+α2
α1α2
(α1+α2)2(α1+α2+1)2
Gamma
f(x) =
xα-1e-x/β
βα
Γ(α)
; x > 0
f(x)=0, x others
αβ
αβ2
Probability Density
Function
Cumulative Distribution
Function
Figure 1. Probability Distribution Function

13. Figure 1 describes a Probability Density Function (PDF) and Cumulative
Distribution Function (CDF). Probability density functionsexplains the area in
which the relative probability of a random number can be assumed to be a
unique value compared to the other value. Failure probability (FP) is
determined from the distribution of the safety factor. The area under the curve
(FK <1) is defined as a failure probability value.
2.2 Fitting Distribution Function
If a theoretical distribution has been assumed, then the validity of the assumed
distribution could be confirmed or refuted by a statistical test with goodness of
fit. There are several methods to test the goodness of fit of some assumed
distribution functions, i.e. Chi Square method, Kolmogrov-Smirnov (K-S)
method, and Anderson-Darling method. This paper only discusses the K-S
method. The basic procedure of this method includes a comparison between
experimental and theoretical cumulative frequency distribution of the types of
assumed distributions. If the difference of both frequencies is higher than
those of a certain sample size, the assumed theoretical distribution will be
rejected. The equation of this cumulative distribution function is as follows:
Sn(𝑥) = �
0 𝑥 < 𝑥1
k
n
𝑥 𝑘 ≤ 𝑥 < 𝑥 𝑘+1
1 𝑥 ≥ 𝑥 𝑛
(1)
𝑥1, 𝑥2, . . . . , 𝑥 𝑛R are the values of the sample data that is already set, and n is the
sample size.
In the K-S test, the maximum difference between the Sn(𝑥)and 𝐹(𝑥) for all
ranges of 𝑥 is a measure of the difference between assumed theoretical
distributions and experimental data distribution. The maximum difference of
both distributions can be written as follows:
𝐷 𝑛 = 𝑚𝑎𝑥 𝑥|𝐹(𝑥) − 𝑆 𝑛(𝑥)| (2)
Theoretically Dn is a random variable whose distribution depends on n. To a
certain significance level α, K-S test compares the maximum difference of the
observations in above equation with the critical value Dn
α
. Table 2 describes the
critical value with a particular significance level α. Thus with a significance
level α, the null hypothesis is rejected if Dn is higher than the critical value. To
facilitate this method assisted with Matlab software Ver.7.12.0.
Table 2. Critical Value (Tse, 2009)
Significance level α 0.10 0.05 0.01

14. Critical value
1.22
√n
1.36
√n
1.63
√n
When two non-nested models are compared, the larger model with more pa-
rameters have the advantage of being able to fit the in-sample data with more
flexible function and thus possibly a larger log-likelihood. To compare models
on more equal terms, penalized log-likelihood may be adopted. The Akaike
information criterion, denoted by AIC, proposes to penalize large models by
subtracting the number of parameters in the model from its log-likelihood.
Thus, AIC is defined as:
AIC = log L�θ�;x� -p (3)
Wherelog 𝐿�𝜃�; 𝒙�is the log-likelihood and p is thenumber of estimated pa-
rameters in the model. Based on this approach the model with the largest AIC
is selected.
The above problem of the AIC can be corrected by imposing a different
penalty on the log-likelihood. The Schwarz information criterion, also called
the Bayesian information criterion, denoted by BIC, is defined as:
BIC = log L�θ�;x� -
p
2
log n (4)
The details of these methods can be seen in [8].
2.3 Monte Carlo Simulation
This method effectively simulates the response of the SF performance function
to randomly select discrete values of the component variables. The process is
repeated many times to obtain an approximate discrete PDF of the resulting SF
values. The component random variables for each calculation are selected from
a sample of random values that are based on the selected PDF of the random
variables. Although the PDFs can take on any shape, the normal, lognormal,
beta and gamma distributions are among the most favored for the analysis.
It should be noted that each Monte Carlo simulation will use a different
sequence of random values, and the resulting probabilities, means, variances,
and histograms will be slightly different. As the number of trials increases, the
differences will become smaller.
Because the Monte Carlo simulation requires a large number of calculations,
it often has been viewed as a less desirable option than the Taylor series or
point estimation method. However, with the general availability of faster
desktop computers, the Monte Carlo approach has gained wider acceptance due
to its inherent simplicity and the ability to use existing computer programs with
only minor modifications. Details of this method can be read in [1,3,8].

15. 3 DATA COLLECTION & METHODOLOGY
Data gathering of the physical and mechanical properties of the lithology (coal,
mudstone and sandstone) of Tutupan coal mines, South Kalimantan, Indonesia
was carefully conducted. These properties include unit weight, cohesion, and
internal friction angle.The number of data from each lithology consists of 10,
33 and 16for coal properties data, mudstone properties data, and
sandstoneproperties data respectively.
Furthermore,the fitting test of K-S method was done using Matlab software
Ver.7.12.0. By using equation [1], the empirical data representation can be
done by sorting the data from smallest to highest value, which produces a
histogram in the form of CDF (See Figure 2).
In the K-S method, the empirical distribution function was compared with
the 4 assumptions in the theoretical distribution function,i.e. normal,
lognormal, beta, and gamma. If the distribution function of the data is not
actually Sn(x), then Dn has a considerable value. Thus, with a significance
level α = 5%, the null hypothesis is rejected if Dn is greater than the critical
value. The critical value for α = 5% is 1.36/√ 𝑛. For example, a fitting test was
conducted on the cohesion distribution of mudstone (see Figure 3). The amount
of data is 33 and α = 5%, the critical value is 0.237. To declare the assumptions
of the functions fit and the hypothesis is accepted, the Dnvaluemust be smaller
than the critical value. The results of the fitting test on cohesion distribution of
mudstone indicates that the 4 assumed theoritical distribution functions have a
Dn value smaller than the critical value, the hypothesis is then accepted.
Figure 2. EmpricalCDF
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Data
Cumulativeprobability
KohMs data

16. 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Data
Cumulativeprobability
KohMs data
Normal
Lognormal
Beta
Gamma
Figure 3. Overlay Emprical and Assumed Theoritical CDF
Besides that, we also have to see the AIC and BIC values of the 4 assumed
theoretical distribution functions. By using equation [3] and [4], AIC and BIC
values can be determined. The largest value of that distribution is normal
distribution, i.e. respectively 44.111 and 44.593.Thus, it can be said that the
most appropriate distribution function is the normal distribution (see Table 2).
Table 3 presents the summary of the characterization test of rock properties
distribution on 3 lithology of rock. Only the cohesion of coalthat has gamma
distribution, while others have normal distribution.
Table 2. The results of Fitting Test on Cohesion of mudstone
Statistical
Parameter
Normal Lognormal Beta Gamma
Mean 0.191 0.193 0.191 0.191
Dn 0.096 0.118 0.095 0.096
Critical value 0.237 0.237 0.237 0.237
Log-likelihood 46.111 42.632 45.543 45.147
AIC 44.111 40.632 43.543 43.147
BIC 44.593 41.113 44.024 43.629
Table 3. The result of Fitting Test in Rock Properties of Tutupan Coal Mine
Mudstone
Statistical
Parameter
c
(MPa)
φ
(Deg.)
γ
(kN/m2
)
Mean 0.169 23.6 22.68
Variance 0.004 23.5 0.38

17. Std.Deviation 0.061 4.8 0.62
Dn 0.096 0.090 0.324
Critical Value 0.237 0.237 0.237
Log-likelihood 46.11 -98.38 -30.42
AIC 44.11 -100.38 -32.42
BIC 44.59 -99.82 -31.93
Distribution Normal Normal Normal
Sandstone
Mean 0.191 27.8 21.48
Variance 0.003 33.1 -
Std.Deviation 0.057 5.8 -
Dn 0.144 0.121 -
Critical Value 0.340 0.340 -
Log-likelihood 23.54 -50.20 -
AIC 21.54 -52.20 -
BIC 22.34 -51.40 -
Distribution Normal Normal -
Coal
Mean 0.241 34.1 12.36
Variance 0.003 5.4 -
Std.Deviation 0.051 2.3 -
Dn 0.190 0.120 -
Critical Value 0.430 0.430 -
Log-likelihood 15.77 -22.13 -
AIC 13.77 -24.13 -
BIC 14.77 -23.13 -
Distribution Gamma Normal -
4 DISCUSSION
Based on the characterization results using K-S method, each fitted distribution
was included in the calculation of the safety factor. Given any variation in the
random variable that is used in the determination of SF, then FPwas also be
generated.
Characterization data can also be used to predict failure probability when
the slope failed. This is possible when there is a strength decrease (see Table
4).
Table 4. The results of Failure Probability
Lithology Coal Mudstone Sandstone
Slope Height (m) 15 15 15

18. Slope Angle (deg.) 70 70 70
SF Deterministic 5.5 2.4 2.8
SF Mean 5.5 2.5 2.8
Cohesion (kPa) 241 169 191
Cohesion (kPa)
Back Analysis
57 68 66
Deterioration (%) 76.3 59.8 65.4
FP (%) 0 3.0 0
FP (%)
Back Analysis
56.5 46.2 49.8
5 CONCLUSIONS
Several points can be concluded from the results of this study, and is as fol-
lows:
 KS method is the most practical method to obtain the most suitable
distribution.
 The results of the characterization of the properties of 3 rock lithology
produce all types of variables tested had a normal distribution, except for the
cohesion of coal that has a gamma distribution.
 Characterization results are used to estimate the value of the safety factor
following the data distribution, which would further strengthen the
confidence level of the FK value.
6 AKNOWLEDGMENT
The authors would like to thank the committee which gives the opportunity to
present this paper, and PT Adaro Indonesia for the support in providing data.
REFERENCES
1. Abramson, L.W., Lee, T.S., Sharma, S., and Boyce, G.M., 2002, Slope Stability and Stabi-
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2. Ang, A.H-S., and Tang, W.H., 1984, Probability Concepts in Engineering Planning and
Design – Vol.II Decision, Risk and ReliabilityJohn Wiley &Sons.
3. Baecher, G.B., and J.T. Christian. 2003. Reliability and statistics in geotechnical engineer-
ing. Wiley, Chichester, U.K.
4. Hoek E., Factor of Safety and Probability of Failure, Chapter 8 - Rock Engineering.
5. M.A. Azizi, S.Kramadibrata, R.K. Wattimena, and I.Arif, 2010, Application of
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