In the Name of Allah - Ferdowsi University of Mashhad · PDF fileIn the Name of Allah...
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In the Name of Allah
Abstracts of
The First Seminar on
Reliability Theory and itsApplications
Department of StatisticsUniversity of Isfahan, Isfahan, Iran
and
Ordered and Spatial Data Center of Excellence
Ferdowsi University of Mashhad, Iran
27-28 May, 2015
Contents
Estimating the Performance of Series System’s Production ProcessAhmadi Nadi, A., Sadeghpour Gildeh, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A Preventive Maintenance Model for Periodically Inspected Deteriorating SystemsAhmadi, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Estimation of Stress-Strength Reliability for Stable DistributionsAlizadeh Noughabi, R., Mohammadpour, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Prediction of Times to Failure of Censored Units in Progressive Hybrid CensoredSamples from Exponential Distribution
Ameli, S., Rezaie, M., Ahmadi, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Stochastic Comparisons of Parallel and Series Systems from Heterogeneous ScalePopulations
Amini-Seresht, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Baysian Estimation of Lifetime Performance Index Based on RSS SampleAsghari, S., Sadeghpour Gildeh, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Inference on Reliability Characteristics Based on Half-Logistic RecordsAsgharzadeh, A., Abdi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
On the Number of Failed Links in a Three-State NetworkAshrafi, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Bayesian Sensitivity Analysis for Competing Risks Data With Missing Cause ofFailure
Azizi, F., Eftekhari Mahabadi, S., Mosayebi, E. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Goodness-of-Fit Test Based on Kullback-Leibler Information for Progressively First-Failure Censored Data
Bitaraf, M. , Rezaei, M., Yousefzadeh, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
A Representation of the Residual Lifetime of a Repairable SystemChahkandi, M., Ahmadi, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
A Switch Model in Redundant SystemsChahkandi, M., Ahmadi, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
On Additive-Multiplicative Hazards ModelEsna-Ashari, M., Asadi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Stochastic Comparisons of Replacement PoliciesFathhi-Manesh, S., Khaledi, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Joint Modeling of Failure-Time and Linear Degradation Data with Multiple FailureModes Under Accelerated Testing
Haghighi, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Estimation with Non-Homogeneous Sequential K-out-of-N System LifetimesHashempour, M., Doostparast, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Bayesian Nonparametric Reliability Analysis from a Spatial PerspectiveHosseinpouri, M., Jafari Khaledi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Kaplan-Meier Estimator for Associated Random Variables Under Left Truncationand Right Censoring
Jabbari, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Reliability Estimation in Burr X Distribution Based on Fuzzy Lifetime DataJafari, A.A., Pak, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
A Non-Parametric Test Against Renewal Increasing Mean Residual Life Distribu-tions
Jamshidian, A.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Residual Lifetime of Coherent System with Dependent Identically Distributed Com-ponents
Kelkinnama, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Stochastic Comparicons of Generalized Residual Entropy of Order StatisticsKhammar, A. H., Baratpour, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
On the Effect of Dependent Components on the Mean Time To Failure (MTTF) ofthe System
Khanjari-Sadegh, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
On the Dynamic Proportional Odds ModelKharazmi, O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
On Properties of Log-Odds FunctionKhorashadizadeh, M., Mohtashami Borzadaran, G.R. . . . . . . . . . . . . . . . . . . . . . . . 25
Some Properties of Multivariate Skew-Normal Distribution, with Application toStrength-Stress model
Mehrali, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Nonparametric and Parametric Estimation of Survival FunctionMireh, S., Khodadadi, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Determining the Warranty Period Using Pitman Measure of ClosenessMirfarah, E., Ahmadi, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Bayesian Inference for the Rayleigh Distribution Based on Record Ranked SetSamples
MirMostafaee, S.M.T.K., Aminzadeh, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Estimation for the Exponential-Geometric Distribution Under Progressively Type-II Censoring with Binomial Removals
MirMostafaee, S.M.T.K., Azizi, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Estimation for the Weighted Exponential Distribution Using the Probability WeightedMoments Method
MirMostafaee, S.M.T.K., Khoshkhoo Amiri, Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Survival Modeling of Spatially Correlated DataMohammadzadeh, M., Motarjem, K., Abyar, A. . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Properties of Generalized Failure RateMohtashami Borzadaran, G.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Estimation of P (X > Y ) Using Imprecise Data in the Lindley DistributionPak, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Stress-Strength Reliability for Parallel System with Independent and Non-IdenticalComponents
Pakdaman, Z., Ahmadi, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
A New Investigation About Parallel (2, n− 2) System Using FGM CopulaParsa, M., Jabbari, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
On Mean Residual Life Ordering Among Weighted-k-out-of-n SystemsRahmani, R., Izadi, M., Khaledi, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Use Weibull Distribution in Accelerated Life Testing for Computing MTTF UnderNormal Operating Conditions
Ramezani, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
On Properties of Progressively Type-II Censored Conditionally N-ordered StatisticsArising from a Non-Identical and Dependent Random Vector
Rezapour, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Characterization of Bivariate Distribution by Mean Residual Life and QuantileResidual Life
Shafaei-Noughabi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Distribution-Free Comparison of Mean Residual Life Functions of Two PopulationsSharafi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
New Frontiers for Information MeasuresSoofi, E. S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Recent Advances in Comparisons of Coherent Systems Based on Inactivity TimesTavangar, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Some Results on Mean Vitality Function of Coherent SystemsToomaj, A., Hashempour, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
The Generalized Joint Signature for Systems with Shared ComponentsZarezadeh, S., Mohammadi, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Reliability Analysis of Multi-State k-out-of-n Systems with Components HavingRandom Weights
Zarezadeh, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Estimating the Performance of Series System’s ProductionProcess
Ahmadi Nadi, A. 1 Sadeghpour Gildeh, B. 2
1,2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In former Lifetime performance index CL studies, it is usually assume that quality characteristicis the lifetime of an electronic component, engine, camera or in special case lifetime of business. Inthis paper we suppose that the quality characteristic is the lifetime of a series system and underthe assumption of exponential distribution for component lifetime, we provide a maximum likelihoodestimator of CL and then this estimate used to develop testing procedure of CL. Finally, we give anexample to illustrate the use of the testing procedure.
Keywords: Lifetime performance index , Series system, Capability analysis.
[email protected]@um.ac.ir
1
A Preventive Maintenance Model for Periodically InspectedDeteriorating Systems
Ahmadi, R. 1
1 School of Mathematics, Iran University of Science and Technology
Abstract
Using the repair alert model, this paper proposes a probabilistic model for the maintenancescheduling of periodically inspected systems whose state is described by a mean residual lifetime(MRL) process. Attention is restricted to the periodic inspection and perfect repair, but the modelprovides a framework for further developments.
Keywords: Maintenance, Inspection, Repair alert model, Scheduling function, Mean residual life-time process.
1re ahmadi [email protected]
2
Estimation of Stress-Strength Reliability for StableDistributions
Alizadeh Noughabi, R. 1 Mohammadpour, A. 2
1,2 Department of Statistics,Amirkabir University of Technology
Abstract
This paper deal with the estimation of Stress-Strength reliability parameter, R = P (X < Y ),when stress and strength are two independent stable distributions. The maximum likelihood estima-tor of stable distribution studied. Furthermore, we investigate the Rr,k = P (Xr:n1 < Yk:n2) for Levydistribution as a member of stable family. Using a Monte Carlo simulation, the MSE and Bayes riskestimators are computed and compared.
Keywords: Stable distributions, Stress-Strength, Maximum likelihood estimator, Lindley approxi-mation.
[email protected]@aut.ac.ir
3
Prediction of Times to Failure of Censored Units in ProgressiveHybrid Censored Samples from Exponential Distribution
Ameli, S. 1 Rezaie, M. 2 Ahmadi, J. 3
1,2 Department of Statistics, University of Birjand, Birjand3 Department of Statistics, Ferdowsi University of Mashhad
Abstract
Survival data often come in a form called ”censoring”. When exact survival times are known onlyfor a portion of the individuals or units under study censoring occurs. In this paper, we consider aprogressive hybrid censoring. The problem of predicting times to failure of units censored in multiplestages of progressively hybrid censored from exponentil distribution is discused. The best unbiasedpredictor (BUP), best linear unbiased predictor (BLUP) and maximum likelihood predictor are de-rived.
Keywords: Best linear unbiased predictor, Conditional median predictor, Maximum likelihood pre-dictor, Order statistics, Progressive hybrid censoring.
[email protected]@[email protected]
4
Stochastic Comparisons of Parallel and Series Systems fromHeterogeneous Scale Populations
Amini-Seresht, E. 1
1 Department of Statistics, Bu-Ali Sina University
Abstract
In this paper, we investigate stochastic comparisons of lifetimes of parallel and series systems withthe multiple-outlier independent components of the scale models with respect to likelihood ratio anddispersive orders.
Keywords: Likelihood ratio order, Dispersive order, p-larger order, Parallel system, Series system.
5
Baysian Estimation of Lifetime Performance Index Based onRSS Sample
Asghari, S. 1 Sadeghpour Gildeh, B. 2
1,2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
Lifetime performance index (CL) is a flexible and effective tool for evaluating product qualityand conforming rate. Ranked set sampling (RSS) scheme is applied for Baysian estimator of CL
based on square error loss. We assume that lifetimes of products follow a one-parameter exponentialdistribution. The simulation result for this scheme is compared with simple random sample (SRS)scheme based on bias, risk, pitman nearness, relative efficiency.
Keywords: Ranked set sampling, Lifetime performance index, Baysian estimation
[email protected]@um.ac.ir
6
Inference on Reliability Characteristics Based on Half-LogisticRecords
Asgharzadeh, A. 1 Abdi, M. 2
1 Department of Statistics, University of Mazandaran2 Department of Statistics, Higher Education Complex of Bam
Abstract
Based on record values, this paper investigates point estimation and confidence interval estima-tion for some reliability characteristics (reliability and hazard rate functions) as well as the unknownparameter of half logistic distribution. The maximum likelihood and Bayes estimators are discussed.Confidence intervals for the unknown parameter and reliability characteristics of interest are con-structed using pivotal quantities. We extend then the results for the stress-strength model involvingtwo half-logistic distributions with different parameter values. Finally, a numerical example is givento illustrate the application of the results and Monte Carlo simulations are performed to compare theperformances of the different methods.
Keywords: Half-Logistic Model, Reliability Function, Hazard rate function, Record values.
[email protected]@bam.ac.ir
7
On the Number of Failed Links in a Three-State Network
Ashrafi, S. 1
1 Department of Statistics, University of Isfahan
Abstract
In this paper, we consider a single-step network consists of n links and assume that the linksare subject to failure. It is assumed that the network can be in three states, up (K = 2), partialperformance (K = 1) and down (K = 0). Under different scenarios on the states of the network andusing the concept of two-dimensional signature, we obtain the probabilities that i links fail at timet1 and j links fail at time t . Several stochastic and aging properties of the proposed probabilities arestudied.
Keywords: Signature matrix, Bivariate increasing failure rate, Total positive of order 2, Stochasticorder.
8
Bayesian Sensitivity Analysis for Competing Risks Data WithMissing Cause of Failure
Azizi, F. 1 Eftekhari Mahabadi, S. 2 Mosayebi, E. 3
1,2,3 Department of Mathematics, University of Tehran
Abstract
Competing risks data are often summarized using a failure time and an indicator of cause offailure that may not be observed for some subjects. In such case, standard analysis through completecase may lead to biased inferences when the missing mechanism is not ignorable. In this paper, wepropose a Bayesian Index of local Sensitivity to Non-ignorability (ISNI) for modeling competing risksdata in the presence of hybrid censoring when the competing risks have Weibull distribution with thesame shape parameter, but different scale parameters. The results of applying the above index ona set of real data show that the model could have potential sensitivity to non-ignorability for scaleparameters but not for the common shape parameter.
Keywords: Competing risks, Missing data, Sensitivity analysis, Type-I Hybrid censoring, Weibulldistribution.
[email protected]@khayam.ut.ac.ir3elham [email protected]
9
Goodness-of-Fit Test Based on Kullback-Leibler Information forProgressively First-Failure Censored Data
Bitaraf, M. 1 Rezaei, M. 2 Yousefzadeh, F. 3
1,2,3 Department of Statistics, University of Birjand
Abstract
In this article, We constructed a goodness-of-fit test statistic based on Kullback-Leibler informa-tion for exponential distribution by using maximum likelihood estimate of the model parameter. AMonte Carlo simulation is performed to evaluate the power of the proposed test for several alterna-tives under different sample sizes and progressive first-failure censoring schemes.
Keywords: Entropy, Goodness-of-fit test, Kullback-Leibler information, Monte Carlo simulation,Progressively frist-failure censored data.
[email protected]@[email protected]
10
A Representation of the Residual Lifetime of a RepairableSystem
Chahkandi, M. 1 Ahmadi, J. 2
1 Department of Statistics, University of Birjand2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In this paper, the residual lifetime of a repairable system is studied when the failure status ofthe system is known. A mixture representation of the reliability function of the conditional residuallifetime of a repairable system in terms of the reliability function of residual records is provided.Some stochastic properties of the conditional probabilities and the residual lifetimes also are given.
Keywords: Aging properties, Minimal repair, Residual lifetime, Stochastic ordering.
[email protected]@um.ac.ir
11
A Switch Model in Redundant Systems
Chahkandi, M. 1 Ahmadi, J. 2
1 Department of Statistics, University of Birjand2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
Redundancy is a technique that has been widely applied to improve the system reliability andits availability. In this paper, a new switching model is proposed to increase the reliability of a unit(system) with a cold standby backup. It is assumed that the switch over to the standby unit is notfailure-free, contrary to what we have in standby redundancy. The optimal time to switch betweenthe key unit and its cold standby backup is find such that the mean lifetime of the system to bemaximized. Finally, an example is presented to compare the mean lifetime of the proposed switchingmodel and a system with parallel redundancy.
Keywords: Parallel system, Redundancy, Survival function, Switching.
[email protected]@um.ac.ir
12
On Additive-Multiplicative Hazards Model
Esna-Ashari, M. 1 Asadi, M. 2
1,2 Department of Statistics, University of Isfahan
Abstract
A fundamental problem in reliability theory and survival analysis is the study of lifetime prop-erties of a live organism or system. In this regard, several models based on different concepts ofaging such as hazard rate and mean residual life have been considered. In this paper, we consider anadditive-multiplicative hazard model (AMHM) and study some of reliability and aging properties ofthe proposed model. We then specify a bivariate model whose conditionals satisfy AMHM. Severalproperties of the proposed bivariate model are investigated and adequacy of the model is evaluatedbased on a real data set.
Keywords: Conditionally specified distributions, Bivariate Pareto distribution, Additive hazard,Multiplicative hazard.
[email protected]@sci.ui.ac.ir
13
Stochastic Comparisons of Replacement Policies
Fathhi-Manesh, S. 1 Khaledi, B. 2
1,2 Department of Statistics, Razi University,
Abstract
Consider a system that has one component in operation and n − 1 components as standby,for which the probability of the failure at the time of switching is zero. To improve the relia-bility of the system, we use the preventative maintenance (PM) with block replacement policya = (a1, . . . an) such that
∑ni=1 ai = a. That is, we replace the ith component by the (i + 1)th
component at the time Tai = (Xi ∧ ai), where Xi, i = 1, . . . , n, is the lifetime of the ith componentand (Xi ∧ ai) = min(Xi, ai). Then, the lifetime of this standby system is T =
∑ni=1 Tai . The aim of
this talk is to present some new results about the optimum and the worst allocations of (a1, . . . , an).
Keywords: Arrangement increasing density function, Log concave density function, Majorization,Preventative maintenance, Schur convcave function, Standby system, Stochastic orderings.
14
Joint Modeling of Failure-Time and Linear Degradation Datawith Multiple Failure Modes Under Accelerated Testing
Haghighi, F. 1
1 Department of Statistics, University of Tehran
Abstract
The paper surveys an approach to model the relationship between failure-time and degradationdata under accelerated testings . We focus on a senario where the degradation of product is describedby a linear model and multiple failure modes can occur during product’s degradation. The failure ratecorresponding to each failure mode is influenced by the degradation level of product, no assumptionsare made about the failure-time distribution and a Cumulative Exposure (CE) model type is hold.A joint model is constructed for the statistically dependent degradation level and time to failure ofdifferent failure modes. This model is used for estimating the failure rates and then for estimatingthe reliability of products.
Keywords: Accelerated life tests, Cumulative exposure model, Degradation process, Joint mod-eling, Multiple failure modes.
15
Estimation with Non-Homogeneous Sequential K-out-of-NSystem Lifetimes
Hashempour, M. 1 Doostparast, M. 2
1,2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In this paper, sequential k-out-of-n systems with coming non- homogeneous exponential compo-nent lifetimes are considered. Point estimates of parameters as well as equal-tail and approximateconfidence intervals and Fisher Information are derived on the basis of observed multiply systemlifetimes.
Keywords: Bayesian approach, Estimation, Maximum likelihood, Sequential order statistics.
[email protected]@um.ac.ir
16
Bayesian Nonparametric Reliability Analysis from a SpatialPerspective
Hosseinpouri, M. 1 Jafari Khaledi, M. 2
1,2 Department of Statistics, Tarbiat Modares University
Abstract
In the reliability analysis, appropriate specification of time-of-failure density function is significant.In cases where the functional form is not parametrically specified, full inference is not obtained. Inaddition, when failure times are collected from a system where its components are subject to spatialvariability, it is known that assuming the non-spatial prior for parameters of time-of-failure densitycan lead to loss of efficiency and/or bias. This paper proposes a flexible Bayesian nonparametricapproach via spatial stick-breaking prior to capture both spatial variability and uncertainty in theparametric form of time-of-failure density function. It takes into account inference for parameters oftime-of-failure density functions where they follow spatial stick-breaking prior.
Keywords: Spatial variability, Reliability modeling, Bayesian nonparametric approach, Spatial stickbreaking prior.
[email protected]@modares.ac.ir
17
Kaplan-Meier Estimator for Associated Random VariablesUnder Left Truncation and Right Censoring
Jabbari, H. 1
1 Department of Statistics, Ferdowsi University of Mashhad
Abstract
It is assumed that in long term studies the lifetimes are positively (negatively) associated randomvariables. Under some regular conditions, the strong convergence rates of Kaplan-Meier estimatorof marginal distribution function F and cumulative hazard function Λ are obtained. In order todemonstrate the empirical performance of the results, simulation studies are done.
Keywords: Censored data, Kaplan-Meier estimator, Negative association, Positive association,Strong consistency, Truncation.
18
Reliability Estimation in Burr X Distribution Based on FuzzyLifetime Data
Jafari, A.A. 1 Pak, A. 2
1 Department of Statistics, Yazd University, Yazd, Iran2 Department of Computer Sciences, Shahrekord University
Abstract
In this paper we consider estimation of the reliability characteristics of Burr type X distributionbased on fuzzy lifetime data. The Bayes estimates of the parameter and reliability function of theBurr type X model are obtained using a Markov Chain Monte Carlo method. Simulation studies areconducted to demonstrate the efficiency of the proposed method.
Keywords: Fuzzy lifetime data, Reliability estimation, Bayesian estimation, Markov Chain MonteCarlo method.
[email protected]@gmail.com
19
A Non-Parametric Test Against Renewal Increasing MeanResidual Life Distributions
Jamshidian, A.R. 1
1 Department of Mathematics and Computer, Sheikh Bahaee University
Abstract
In this paper we introduce a new aging class of life distributions when a device is operating ina realistic environment. We study the behavior of such life distributions through the mean residuallife notion, when a device is experiencing number of shocks. Due to these shocks the lifetime of suchdevice has become shortened or prolonged. These tempered events are governed by a homogenousPoisson process. A moment inequality which characterizes this new aging class, namely renewal in-creasing mean residual life, is derived. We propose a new U-statistic test procedure to address theproblem of testing exponentiality against such class of life distributions. It is shown that the proposedtest enjoys a superior power for some commonly used alternative.
Keywords: Poisson Shock model, Increasing mean residual life, Exponential distribution, Mo-ment inequalities, U-statistics.
20
Residual Lifetime of Coherent System with DependentIdentically Distributed Components
Kelkinnama, M. 1
1 Department of Mathematical Sciences, Isfahan University of Technology
Abstract
In this paper, we study the residual lifetime of coherent system with possibly dependent identicallydistributed component lifetimes. These results are based on the representation of system reliabilityfunction as a distorted function of common reliability function of components.
Keywords: Coherent systems, Residual lifetime, Survival copula, Distorted function, Stochasticorders.
21
Stochastic Comparicons of Generalized Residual Entropy ofOrder Statistics
Khammar, A. H. 1 Baratpour, S. 2
1,2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In modeling of biological and engineering systems often requires use of concepts of informationtheory, and in particular of entropy. The concept of residual entropy is applicable to a system whichhas survived for some units of time. In this paper, we propose a generalized residual entropy basedon order statistics and obtain some results on the stochastic comparisons of it.
Keywords: Generalized residual entropy, Hazard rate function, Order statistics, Stochastic com-paricons.
[email protected]@um.ac.ir
22
On the Effect of Dependent Components on the Mean Time ToFailure (MTTF) of the System
Khanjari-Sadegh, M. 1
1 Department of Statistics, University of Birjand
Abstract
In many practical applications in system reliability, the assumption that the component lifetimesare independent is not valid and realistic.In this talk we Consider the effect of dependency between system components on MTTF of the sys-tem. For example if we increase (decrease) the degree of dependency between system componentswether the MTTF of the system has the same behavior or not? We see that the answer of thisquestion depends on the structure of the system (it also may depend on the structure of dependencybetween system components).
Keywords: Quadrant Dependency, Mean Time To Failure, Diagonally Dependency, System Re-liability, Stochastic Ordering.
23
On the Dynamic Proportional Odds Model
Kharazmi, O. 1
1 Department of Statistics, Vli-e-Asr University of Rafsanjan
Abstract
The proportional odds model plays an important role in analyzing survival data.This note de-velops the definition of dynamic proportional odds (DPO) model and its properties including someresults on stochastic comparisons. One application of DPO model is considerd as Marshall and Olkinfamily of distribution in dynamic situation.
Keywords: Proportional odd model , Survival analysis, Marshall and olkin distribution.
24
On Properties of Log-Odds Function
Khorashadizadeh, M. 1 Mohtashami Borzadaran, G.R. 2
1 Department of Statistics, University of Birjand2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In this paper, first we introduce the log-odds (LO) and log-odds ratio (LOR) functions and theirrelations with reliability concepts such as hazard and reversed hazard rate. Then, we proposed anew measure of skewness based on LO function in discrete and continuous lifetime distributions andcompare it with Pearson’s moment coefficient of skewness and also Groeneveld-Meeden measure ofskewness via some examples. Also some results due to bivariate log-odds are discussed.
Keywords: Log-odds rate, Hazard rate, Reversed hazard rate, Second hazard rate, Second reversedrate of failure.
[email protected]@um.ac.ir
25
Some Properties of Multivariate Skew-Normal Distribution,with Application to Strength-Stress model
Mehrali, Y. 1
1 Department of Statistics, University of Isfahan
Abstract
In recent years, a large number of research works are appeared in the literature dealing with theproperties and applications of the skew distributions. Skew distributions are shown to be flexible mod-els for describing different kind of data. In the present study, we consider multivariate skew-normaldistribution, and obtain some of its properties. These properties help us to explore the stress-strengthmodel based on the multivariate skew-normal distribution.
Keywords: Linear combination, Multivariate skew-normal distribution, Skew-normal distribution,Stress-strength model.
26
Nonparametric and Parametric Estimation of Survival Function
Mireh, S. 1 Khodadadi, A. 2
1,2 Department of Statistics, University of Shahid Beheshti
Abstract
This paper considers a general degradation path model and failure time data with traumaticfailure mode. It provides a review of the nonparametric estimator of survival function, studied byBagdonavicius, and considers the parametric estimation of survival function of failure times with ahazard rate in the degradation space. In addition, we discuss the comparison of both parametric andnonparametric methods according to simulated and real data.
Keywords: Degradation models, Failure times, Hazard rate, Nonparametric and parametric es-timation, Survival function.
1s [email protected]@sbu.ac.ir
27
Determining the Warranty Period Using Pitman Measure ofCloseness
Mirfarah, E. 1 Ahmadi, J. 2
1,2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In this paper, we study the determination of the warranty period in view of a warranty policywhere the manufacture accept to minimally repaired the failure product. To do this, the problem ofpredicting the time of minimal repair based on a progressive Type-II censored sample is considered.We utilize the property of Pitman measure of closeness and propose a method to find the closestpredictor. Since, over-predication may be more important in a warranty problem, asymmetry loss isalso considered in the probability of closeness.
Keywords: Pitman measure of closeness, Prediction, Warranty period, Progressively Type-II cen-sored order statistics, Minimal repair.
1elham−[email protected]@um.ac.ir
28
Bayesian Inference for the Rayleigh Distribution Based onRecord Ranked Set Samples
MirMostafaee, S.M.T.K. 1 Aminzadeh, M. 2
1,2 Department of Statistics, University of Mazandaran
Abstract
In this paper, we discuss the Bayesian estimation problem for the Rayleigh distribution based onupper record ranked set samples. The Bayes estimators are obtained with respect to two differentloss functions. We also obtain the Bayes confidence intervals for the parameter of the Rayleigh dis-tribution. Finally, we present a simulation study for the purpose of numerical comparison.
Keywords: General entropy loss function, Maximum likelihood estimator, Simulation.
[email protected]@yahoo.com
29
Estimation for the Exponential-Geometric Distribution UnderProgressively Type-II Censoring with Binomial Removals
MirMostafaee, S.M.T.K. 1 Azizi, E. 2
1,2 Department of Statistics, University of Mazandaran
Abstract
In this paper, we study the estimation problem for the exponential-geometric distribution undertype II progressive censoring with binomial removals. The maximum likelihood estimators as well asthe asymptotic confidence intervals for the parameters are derived. Finally, a real data example ispresented to illustrate the results of the paper.
Keywords: Asymptotic confidence interval, Binomial censoring scheme, Type II progressive cen-soring.
[email protected]@yahoo.com
30
Estimation for the Weighted Exponential Distribution Usingthe Probability Weighted Moments Method
MirMostafaee, S.M.T.K. 1 Khoshkhoo Amiri, Z. 2
1,2 Department of Statistics, University of Mazandaran
Abstract
In this paper, we focus on the problem of estimation for the scale and shape parameters of theweighted exponential distribution. The probability weighted moments method has been developedfor estimating the parameters. A real data example ends the paper.
Keywords: Maximum likelihood estimator, Probability weighted moment method, Weighted ex-ponential distribution.
[email protected]@stu.umz.ac.ir
31
Survival Modeling of Spatially Correlated Data
Mohammadzadeh, M. 1 Motarjem, K. 2 Abyar, A. 3
1,2,3 Department of Statistics, Tarbiat Modares University
Abstract
Identifying risk sources of survival data are given special emphasis in survival analysis. Identifiablerisk factors can be modeled by available covariates using some models like Cox proportional hazardsmodel. However some risk factors are often unidentifiable or immeasurable. The spatial correlation ofdata is one of these factors that is rarely noticed. In this paper a spatial survival model is introducedfor such data. A simulation study is performed to show the high performance of the model parameterestimations for the proposed model. Results validate our approach.
Keywords: Proportional hazards model, Unknown risk factors, Spatial random effect, Spatial sur-vival model.
[email protected]@[email protected]
32
Properties of Generalized Failure Rate
Mohtashami Borzadaran, G.R. 1
1 Department of Statistics, Ferdowsi University of Mashhad
Abstract
The concept of a failure function initially deal with state changes such as death or product failure(Steffensen, 1930). In the product reliability context, failure corresponds to the proportion of thesurviving items that fail at x, and the state change is the transition from a good product to a productfailure. Because many problems can be regarded as a state change, failure functions have been usedin many disciplines. This interpretation and some other properties such as increasing failure rate(IFR) of an object is an ageing of some kind, which is an important property in various applications.The reasons of decreasing failure rate, that is, a system improving as time goes by are less intuitive.Suppose the distribution of a continuous random variable X has the probability density functionf (pdf) and cumulative density function F (cdf), the survival function is given by S(x) = P (X >x) = F (x) which is monotonically decreasing. The hazard (failure) rate function of X is given by
r(x) = f(x)
F (x). If r(x) is monotonically increasing (decreasing), then the distribution of X has an in-
creasing (decreasing) failure rate, denoted IFR (DFR). The generalized failure rate (GFR) of the
random variable X with pdf f and cdf F as h(x) = xr(x) = xf(x)
F (x)which leads to interesting ideas.
It is easy to check that all IFR distributions are IGFR, but the reverse is not true. Recent inter-est has focused on IGFR distributions, see Lariviere and Porteus (2001); Paul (2005) or Colomboand Labrecciosa (2012). Some of the results and notes due to GFR and IGFR with aspects aboutinteractions between the probabilistic model for lifetimes and considerations of an economic kind isreviewed. Extended known results and characterizations on IFR (DFR) to IGFR (DGFR) with theirclosure properties with respect to convolution, mixing, ordering and also some implications of theseresults in economics aspects such as elasticity of survival function, demands and supply chain. Usingrepresentation of weighted distributions for GFR class and importance of them is the last part of thiswork.
Keywords: Elasticity function, Failure rate, Increasing failure rate, Generalized failure rate, In-creasing generalized failure rate, Weighted distributions.
33
Estimation of P (X > Y ) Using Imprecise Data in the LindleyDistribution
Pak, A. 1
1 Department of Computer Sciences, Shahrekord University
Abstract
Classical estimation procedures of the stress-strength parameter R = Pr(X > Y ) are based onprecise data. However, in real world situations, some collected data might be imprecise and are rep-resented in the form of fuzzy numbers. In this paper, we obtain the maximum likelihood estimationof the parameter R when X and Y are independent Lindley random variables, and the available dataare reported in the form of fuzzy numbers. A Monte Carlo simulation study is carried out in orderto assess the accuracy of the proposed method.
Keywords: Stress-Strength model, Fuzzy data analysis, Maximum likelihood estimation.
34
Stress-Strength Reliability for Parallel System withIndependent and Non-Identical Components
Pakdaman, Z. 1 Ahmadi, J. 2
1,2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
The estimation problem of the multicomponent stress-strength reliability parameter is considered,while the stress and the strength system has n1 and n2 independent and non-identical parallel compo-nents. It is assumed that the stress and the strength components have Fi = (F )α(i) and Gi = (G)ν(j)
distributions for i = 1, . . . n1 and j = 1, . . . n2, respectively where α(i) and ν(j) are unknown positivereal values. We study in more detail the case where F and G are exponential distributions. Frequen-tist estimators are obtained and compared.
Keywords: Stress-strength reliability, Uniformly minimum variance unbiased estimator, Maximumlikelihood estimator
[email protected]@um.ac.ir
35
A New Investigation About Parallel (2, n− 2) System UsingFGM Copula
Parsa, M. 1 Jabbari, H. 2
1,2 Depertment of Statistics, Ferdowsi University of Mashhad
Abstract
Redundancy is a highly used technique to increase the systems lifetimes and availability. Recently,employing standby units in systems has received great attention. Here, parallel system of n unitsand two-unit parallel system supported by (n− 2) cold standbys are considered where units lifetimesare assumed to be dependent in terms of Farlie-Gumbel-Morgenstern copula structure. Applicableformulas of mean time to system failure are given and the impact of dependence parameter on systemslifetimes are investigated.
Keywords: Cold standby FGM copula Mean time to system failure Parallel system.
36
On Mean Residual Life Ordering Among Weighted-k-out-of-nSystems
Rahmani, R. 1 Izadi, M. 2 Khaledi, B. 3
1,2,3 Department of Statistics, Razi University
Abstract
Consider a system consisting of n binary components with different contributions (weights) ondetermining the state of the system. The system is known as weighted-k-out-of-n system when itworks iff the total weight of working components are greater than a pre-specified value k. Supposethat this system has the property that, with probability 1, operates as long as at least n − s + 1components operate (s ≤ n). In this paper, we compare two such systems with respect to their meanresidual life function under the condition that n−r+1 components (r ≤ s) of the systems are workingat time t.
Keywords: Weighted-k-out-of-n system, Mean residual life, Usual stochastic order.
[email protected]@[email protected]
37
Use Weibull Distribution in Accelerated Life Testing forComputing MTTF Under Normal Operating Conditions
Ramezani, R. 1
1 Department of Statistics, University of Damghan
Abstract
The intensity of the global competition for the development of new products in a short time. Test-ing under normal operating conditions for compute reliability quatities, requires a very long time.This has led to the development of accelerated life testing (ALT). In this article, We compute MTTFof Bourdon tubes (used as a part of pressure sensors in avionics) in stress conditiion. The failureis leak in the tube. Base on Anderson-Darling test weibull distribution is appropriate for fittingdata under stress condition. We determine MTTF of Bourdon tubes in operating condition base onarrhenius model and mean of weibull distributions.
Keywords: acceleration test , arrheinus model, mean time to failure , Anderson-Darling test, weibulldistribution.
38
On Properties of Progressively Type-II Censored ConditionallyN-Ordered Statistics Arising from a Non-Identical and
Dependent Random Vector
Rezapour, M. 1
1 Department of Statistics, Shahid Bahonar University of Kerman
Abstract
In this paper, we investigate progressively Type-II censored conditionally N-ordered statistics aris-ing from a system with identical as well as non-identical but dependent components, jointly distributedaccording to an Archimedean copula with completely monotone generator (PCCOSDNARCM-N).Our results generalized the results in Bairamov (2006) and is more flexible than those in practice,because of considering the dependency between components that is a common fact for real data.
Keywords: Archimedean copula, Order statistics, Progressive censoring, Progressively Type-II cen-sored order statistics, Reliability systems.
39
Characterization of Bivariate Distribution by Mean ResidualLife and Quantile Residual Life
Shafaei-Noughabi, M. 1
1 Department of Mathematics and Statistics, University of Gonnabad
Abstract
Nair and Nair (1989) showed that bivariate mean residual life function characterizes the distri-bution uniquely. The subject of this paper is to verify how closely the bivariate quantile residuallife function determines the distribution. It has been shown that like univariate case, two suitablebivariate quantile residual life can characterize the underlying distribution uniquely.
Keywords: Bivariate distribution function, Bivariate α-quantile residual life, Bivariate mean resid-ual life
40
Distribution-Free Comparison of Mean Residual Life Functionsof Two Populations
Sharafi, M. 1
1 Department of Statistics, Razi University
Abstract
At any age the mean residual life function gives the expected remaining life at that age. Thisfunction can be useful in life-testing experiments in biological as well as industrial settings. In thispaper, we first propose a nonparametric test to compare mean residual life functions based on twoindependent samples. Next, in order to assess the power properties of the proposal test statistic,we examine its empirical power properties, through a Monte Carlo simulation study under differentlifetime distributions.
Keywords: Empirical distribution function, Mean residual life ordering, Power.
41
New Frontiers for Information Measures
Soofi, E. S. 1
1 Lubar School of Business, University of Wisconsin-Milwaukee
Abstract
This presentation shows formulations that lead to new interpretations of familiar informationmeasures in two seemingly unrelated areas in statistics: forecast evaluation, and kernel estimation.Some challenging topics for future research will be posed. The stochastic error distance (SED) rep-resentation of the mean absolute error and its weighted versions have recently been introduced byDiebold and Shin (2014). In a current project (Ardakani, Ebrahimi, and Soofi 2015), we show thatthe SED facilitates identifying conditions under which the mean absolute error ranks the forecastsequivalently with the variance and Shannon entropy. We also introduce a new weighted SED whichincludes a forecast error tolerance threshold. This measure is a representation of the mean residualfunction of the absolute error. We explore conditions under which it ranks the forecasts equivalentlywith Shannon entropy. The risk of this measure over all thresholds is the survival information of theabsolute error. Estimates of the risk provide Survival Information Criteria (SIC) for ranking forecastmodels.Nonparametric kernel estimation has been used for estimating information measures such as entropyand mutual information. Kullback-Leibler information has been used for bandwidth selection, a keycomponent in kernel estimation. However, an unanswered question is how much information the ker-nel function and the bandwidth provide for kernel estimation? In another current project (Beheshti,Racine, and Soofi 2015), we address this question. We show that kernel estimation of a cumulativedistribution function (CDF) is an information processing procedure for transforming the empiricalcumulative distribution function (ECDF) into a smooth estimate. The information processing chan-nel is the kernel function itself, which is a conditional distribution with a data point as its locationparameter and a bandwidth as its scale parameter. The output of the information processing proce-dure is the kernel estimate of the CDF which is a marginal distribution constructed as the sampleaverage of each of the kernel functions for each data point. This framework provides a lower boundfor the entropy of the kernel estimate of the distribution in terms of the entropy of the kernel functionalong with an information measure of sample information for kernel smoothing.
Keywords: Sochastic error distance, Survival information criteria, Kullback-Leibler information.
42
Recent Advances in Comparisons of Coherent Systems Basedon Inactivity Times
Tavangar, M. 1
1 Department of Statistics, University of Isfahan
Abstract
The purpose of the talk is to study the inactivity time of failed components of a coherent systemconsisting of n identical components with statistically independent lifetimes. Different aging andstochastic properties of this conditional random variable are obtained. Also we investigate stochasticproperties of the inactivity time in the case where the component lifetimes are dependent randomvariables. Some results are extended to the case where the system has an arbitrary coherent structurewith exchangeable components.
Keywords: Exchangeability, Joint reliability function, Signature, Likelihood ratio order.
43
Some Results on Mean Vitality Function of Coherent Systems
Toomaj, A. 1 Hashempour, M. 2
1 Department of Statistics, Gonbad Kavous University2 Department of Statistics, Ferdowsi University of Mashhad
Abstract
In this paper, we present some results on applications of mean vitality function to comparisons ofcoherent systems. We also obtain an upper bound for the mean vitality function of coherent systemwhen the lifetimes of components are independent and identically distributed.
Keywords: Coherent System, IFRA, MVF, Stochastic Orders, System Signature.
[email protected]@stu.um.ac.ir
44
The Generalized Joint Signature for Systems with SharedComponents
Zarezadeh, S. 1 Mohammadi, L. 2
1,2 Department of Statistics, Shiraz University
Abstract
The concept of joint signatures which first defined by Navarro et al. [?] are useful tools for inves-tigating the reliability of two systems with shared components. When several coherent systems sharesome components and the components have independent and identically distributed (i.i.d.) lifetimes,we obtain a pseudo-mixture representation for the joint distribution of the lifetimes of the systemsbased on a general notion of joint signatures. We present an R program to find the mentioned jointsignature for any number of systems and components.
Keywords: Coherent system, Order statistic, Signature.
[email protected]@yahoo.com
45
Reliability Analysis of Multi-State k-out-of-n Systems withComponents Having Random Weights
Zarezadeh, S. 1
1 Department of Statistics, Shiraz University
Abstract
This paper is concerned with reliability modeling of multi-state k-out-of-n systems consisting ofmulti-state components. It is also assumed that each component of the system has an integer-valuedrandom weight (capacity). A recursive algorithm is presented for reliability evaluation of this model.Some illustrative examples are also provided.
Keywords: Multi-state system, k-out-of-n system, Recursive algorithm.
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