49th European Organization for Quality Congress. Topic: Quality Improvement. Service Reliability in Electrical Distribution Networks
|
|
- Gyles Russell
- 5 years ago
- Views:
Transcription
1 49th European Organization for Quality Congress Topic: Quality Improvement Service Reliability in Electrical Distribution Networks José Mendonça Dias, Rogério Puga Leal and Zulema Lopes Pereira Department of Mechanical and Industrial Engineering, Faculty of Sciences and Technology, Universidade Nova de Lisboa, Quinta da Torre, CAPARICA, Portugal. ABSTRACT For the past few years, reliability has been assuming an increasingly important role in quality improvement and customer satisfaction. Reliability can be defined as the ability of an item to perform a required function under stated conditions for a certain period of time. The item can be a manufactured product or an assembly system such as an electrical process system. In this last example, the quality of the service provided by the system can significantly improve if appropriate reliability techniques are used to improve the overall performance. An electrical system usually comprises three different areas, namely the power generation, transmission and distribution. This paper characterises the reliability of the distribution subsystem (the so-called repartition network). Electrical shortages may be caused by several parameters, which include internal and external network factors or a failure of a key constituent of the system, such as a major distribution line or a substation plant. Furthermore, there are also failures associated with the energy generation and transmission which can be responsible for the blackouts in repartition networks. These faults are addressed as external to the distribution system. For the purpose of this study, the term service reliability denotes the extent to which the electrical needs of the community served by a local 60 kv substation can be met, regardless the set of available equipment at each distribution point. A procedure to determine the service reliability is suggested and is applied to a repartition network. The proportional hazard model (PHM) is used to model the service reliability and evaluate the network substations with high risk of failure. Keywords: Service Reliability; Service systems; Electrical Networks; PHM. INTRODUCTION It is generally accepted that customer s needs and requirements are continuously increasing. Quality is very often defined as conformity to specifications. However, this definition does not specifically address one of the most important features of a product, which is its performance over time. Therefore, a time based quality concept, such as reliability, becomes of extreme importance. Nowadays, reliability is one of the most important quality characteristics for customers and it is applied to products, systems, processes and components of systems as an interdisciplinary concept. Reliability efforts started in some critical areas, such as nuclear facilities and space vehicles, and have rapidly extended to several other areas, such as software reliability, human reliability,
2 structure reliability and service reliability. Nevertheless, applications of reliability analys is in services are relatively scarce in the available literature (Gunes and Deveci, 2002). Service quality associated to the supply of electrical energy is usually regulated. The regulations establish quality standards such as service continuity (number and duration of breakdowns) and the quality of the voltage wave (amplitude, frequency, wave shape and symmetry of the three phase system). Symmetry is monitored through indicators that are periodically established and assessed. The most used indicators are the SAIFI - System Average Interruption Frequency Index (the number of times a customer experiences a service interruption during one year) and the SAIDI - System Average Interruption Duration Index (the total amount of time a customer does not have power during one year). However, these indicators lead to a service quality analysis that is solely based in average values, which does not provide an integrated analysis of service reliability, making it impossible to assess the probability of an interruption of energy supply be experienced by a group of customers. The electrical shortages are generally originated by a complex set of factors, which may be internal or external to the repartition network. The most important external factor is related to breakdowns in the transmission network that cause significant perturbations in the distribution system. This study intends to assess the service reliability of a 60 kv repartition network in order to identify conditional probabilities of failure in the network substation and its influence on system failures. The term service reliability denotes the extent to which the electrical needs of the community served by a local 60 kv substation can be met. A procedure to determine the service reliability is suggested and is applied to a repartition network in the next sections. The proportional hazard model (PHM) is used to model the service reliability and evaluate the network substations with high risk of failure. METHODOLOGY There is a large group of factors that might cause failures in a repartition network, thus making it difficult to evaluate the reliability of a substation. Figure 1 shows a repartition network composed by several substations and inter-connections. They constitute a set that must be carefully managed to provide adequate service reliability levels. The proposed methodology assumes that each substation corresponds to an energy delivery point directly connected to an injection point of 150kV in the energy transmission network.
3 Figure 1 Repartition network Figure 2 depicts the repartition network constituted by the injection point (SE1502) of the transportation network and the substations that are supplied by it. Figure 2 Radial distribution of substations If the sequence of failures in each substation is known, it is possible to identify those with higher probability of failure and therefore with lower reliability. This approach assumes that all substations are equal, regardless the available equipments in each one. In fact, from a customer s standpoint, service reliability is what is perceived, no matter the number and condition of the equipments in each substation. Some other techniques have been applied to model service reliability (Gunawardane, 2004), but the PHM (Proportional Hazard Modelling), which is often utilised in maintenance management, seems to be a valuable tool for modelling the behaviour of each substation (Dias, 2002).
4 PROPORTIONAL HAZARD MODEL Cox (1972) introduced a non-parametric free distribution model known as PHM (Proportional Hazards Model). The model was structured according to the traditional hazard function defined by h ( t z) ( t < T t + t T t, z ) P ; = lim (1) t 0 t or, generally, h ( t ; z ) = h0( t) g( z, ß) (2) The not specified baseline function ( t ) h 0 is multiplied by the effect of the covariates (load factors or others that can significantly influence the probability of failure of the system). The coefficients vector ß is estimated by maximising the maximum partial likelihood function. The hazard function is equal to the baseline function ( t ) h 0 when z = 0. The PHM constitutes a class of models in which different fixed covariates must have proportional hazard function, that is, the ratio h ( t; z1 ) h( t; z2 ) of the hazard functions is constant over time. Under these circumstances the PHM is given by ( t; z) = h0 ( t ) exp( z ß) h (3) T The model contains two unknown elements: the regression coefficients vector ß = ( β,..., β ) related to the p covariates considered in the model and the baseline hazard function ( t ) example, if the covariate corresponding to coefficient β 2 is significant, the value given by exp z β represents the hazard ratio relatively to the baseline covariate. ( ) 2 2 To estimate ß, Cox (1972) proposed the use of the maximum partial likelihood function L ( ) = k z e i ß i= 1 e z l ß l R( ) ß (4) t i where k is the observed number of failure times and R ( t i ) the number of elements at risk t, that is, in R ( t i ) = { i, ( i + 1),..., k }. immediately before i The estimate of ß maximum likelihood can be obtained from equations ln ( ) [ L( ß )] U j ß = (5.a) ß j and h 0 1 p. For
5 [ L( ß )] 2 ln Ihj ( ß ) = (5.b) ß h ß j by using the iterative procedure of Newton-Raphson (Kalbfleisch and Prentice, 1980). There are some software packages able to deal with the PHM. One of the most used is SAS (SAS Institute Inc.), which is employed to model the case study presented in this article. CASE STUDY The repartition network presented in Figure 2, where 247 failures had occurred, will be modelled by PHM. The injection network SE1502 is constituted by eight substations and seven of them (SE210, SE212, SE213, SE214, SE215, SE216 e SE217) are considered to be the covariates of the model. Substation SE211 is excluded because it is very recent and the record of failures is not available. Table 1 presents the estimates of the coefficients for the seven covariates. The elimination through the backward procedure (Table 2) reveals as significant the covariates corresponding to substations SE210, SE212 and SE215. The data show that substation SE212, on its own, increases the network s failure risk by 73%, while substation SE 210 raises it by 62%. Table 1. Model with SE1502 substations as covariates Covariate Test Without With Covariates Covariates Chi-Square Pr > ChiSq -2LnL( b ) Statist score Wald test w/ 7 d.f w/ 7 d.f w/ 7 d.f. d.f. Testing Global Null Hypothesis: BETA=0 Analysis of Maximum Likelihood Estimates Parameter Standard Wald Hazard Pr > ChiSq Estimate Error Chi-Square Ratio SE SE SE SE SE SE SE
6 Covariate Test d.f. Table 2. Final model for SE1502 substations Testing Global Null Hypothesis: BETA=0 Without Covariates Covariates -2LnL( b ) c/ 3 g.l. Score Estatístico c/ 3 g.l. Teste de Wald c/ 3 g.l. Pr > ChiSq Parameter Standard Wald Hazard Pr > ChiSq Estimate Error Chi-Square Ratio SE SE SE With Analysis of Maximum Likelihood Estimates Chi-Square SERVICE RELIABILITY As mentioned before, the analysis here made considers that the reliability of the electrical energy distribution only depends of the breakouts sequence and does not take into account their duration. The previous section led to the important conclusion that only SE210, SE212 and SE215 are significant, so the assessment will just focus on these substations. Figure 3 depicts the service reliability of the three substations. SE210 SE212 SE215 BASE 1.0 Service Reliability Time since last failure (Days) Figure 3 Service reliability by substation The baseline is obtained for the entire set of significant covariates, revealing a 70% reliability value for a forty day period of energy supply. The reliability of substations SE210 and SE212 is about 60% for the same period. However, the most relevant situation occurs in substation SE215 with a negative coefficient corresponding to a decrease of about 61% in its hazard function. This situation is revealed by an increase in reliability of approximately 90% for the aforementioned
7 period. So, a deep study should be conducted to compare this last substation with the others and determine the best way to explore the substations with lower reliability values. MODEL VALIDATION Models similar to PHM can be validated through the analysis of different sorts of residuals (Collett, 1994). The Cox-Snell s residuals, which are quite useful and widely applied, are defined by eˆ i = ln Rˆ t i ( z ) i (6) The ê i must have an exponential distribution withλ = 1 (if t i is a censored o bservation, then ê i is also considered as censored) if the model is correctly adjusted. The graphical representation of ln [ R( ˆ )] e i (which are obtained through the Kaplan-Meier method) against ê i must be adjusted to a straight line of unitary slope (Figure 4). ) lnr e i [ ( )] ,0 Observed residuals Figure 4 - Cox-Snell residuals The residual analysis reflects an adequate behaviour of the model, despite the deviation of some observations, which is justified by the censored data (9%). CONCLUSION This article makes use of the Proportional hazards Model to assess the reliability of electrical energy distribution service. A general conclusion is that it is possible to make use of modelling techniques usually associated to product reliability. The model identified the three more significant substations among the seven initially considered, regardless the local atmospheric
8 conditio ns and the equipment used by each one. The SE215 substatio n was found to be the one with higher reliability, thus assuring a better service quality to the customers. As regards substations SE210 and SE212, one can see from Figure 1 that their configurations are quite distinctive. Therefore, it is advisable to carry out a detailed study of each substation, so that the critical points may be identified and a revision of the maintenance programme and/or the equipment replacement can be undertaken. REFERENCES Collett, D. (1994), Modelling Survival Data in Medical Research, Chapman & Hall, London. Cox, D.R. (1972), Regression Models and Life Tables (with Discussion), Journal of the Royal Statistical Society (B), Vol.34, No.1, pp Dias, J.M. (2002), Fiabilidade em Redes de Distribuição de Energia Eléctrica (Reliability of Distribution Electrical Networks), PhD thesis, FCT/Universidade Nova de Lisboa, Portugal. Five-Year Electric Service Reliability Study Electrical Safety and Reliability Section. Oregon Public Utility Commission. Gunawardane, G. (2004), Measuring reliability of service systems using failure rates: variations and extensions, International Journal of Quality & Reliability Management, Vol. 21 No. 5, 2004, pp Gunes, M. and Deveci, I. (2002), Reliability of service systems and an application in student office, International Journal of Quality and Reliability, Vol. 19 No. 2, pp Kalbfleisch, J. D. and Prentice, R. L. (1980), The Statistical Analysis of Failure Time Data, John Wiley & Sons, Inc., New York. Lawless, J.F. (1982), Statistical Models and Methods for Lifetime Data, John Wiley & Sons, Inc., New York.
TMA 4275 Lifetime Analysis June 2004 Solution
TMA 4275 Lifetime Analysis June 2004 Solution Problem 1 a) Observation of the outcome is censored, if the time of the outcome is not known exactly and only the last time when it was observed being intact,
More informationInterval Estimation for Parameters of a Bivariate Time Varying Covariate Model
Pertanika J. Sci. & Technol. 17 (2): 313 323 (2009) ISSN: 0128-7680 Universiti Putra Malaysia Press Interval Estimation for Parameters of a Bivariate Time Varying Covariate Model Jayanthi Arasan Department
More informationThe Proportional Hazard Model and the Modelling of Recurrent Failure Data: Analysis of a Disconnector Population in Sweden. Sweden
PS1 Life Cycle Asset Management The Proportional Hazard Model and the Modelling of Recurrent Failure Data: Analysis of a Disconnector Population in Sweden J. H. Jürgensen 1, A.L. Brodersson 2, P. Hilber
More informationSemiparametric Regression
Semiparametric Regression Patrick Breheny October 22 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/23 Introduction Over the past few weeks, we ve introduced a variety of regression models under
More informationSurvival Analysis Math 434 Fall 2011
Survival Analysis Math 434 Fall 2011 Part IV: Chap. 8,9.2,9.3,11: Semiparametric Proportional Hazards Regression Jimin Ding Math Dept. www.math.wustl.edu/ jmding/math434/fall09/index.html Basic Model Setup
More informationN.B. When citing this work, cite the original published paper.
http://www.diva-portal.org This is the published version of a paper presented at 2018 Power Systems Computation Conference (PSCC). Citation for the original published paper: Jürgensen, J H., Nordström,
More informationSurvival Regression Models
Survival Regression Models David M. Rocke May 18, 2017 David M. Rocke Survival Regression Models May 18, 2017 1 / 32 Background on the Proportional Hazards Model The exponential distribution has constant
More informationUNIVERSITY OF CALIFORNIA, SAN DIEGO
UNIVERSITY OF CALIFORNIA, SAN DIEGO Estimation of the primary hazard ratio in the presence of a secondary covariate with non-proportional hazards An undergraduate honors thesis submitted to the Department
More informationAbstract. 1. Introduction
Abstract Repairable system reliability: recent developments in CBM optimization A.K.S. Jardine, D. Banjevic, N. Montgomery, A. Pak Department of Mechanical and Industrial Engineering, University of Toronto,
More informationAnalysis of Time-to-Event Data: Chapter 6 - Regression diagnostics
Analysis of Time-to-Event Data: Chapter 6 - Regression diagnostics Steffen Unkel Department of Medical Statistics University Medical Center Göttingen, Germany Winter term 2018/19 1/25 Residuals for the
More informationLecture 22 Survival Analysis: An Introduction
University of Illinois Department of Economics Spring 2017 Econ 574 Roger Koenker Lecture 22 Survival Analysis: An Introduction There is considerable interest among economists in models of durations, which
More informationLogistic regression model for survival time analysis using time-varying coefficients
Logistic regression model for survival time analysis using time-varying coefficients Accepted in American Journal of Mathematical and Management Sciences, 2016 Kenichi SATOH ksatoh@hiroshima-u.ac.jp Research
More informationExtensions of Cox Model for Non-Proportional Hazards Purpose
PhUSE 2013 Paper SP07 Extensions of Cox Model for Non-Proportional Hazards Purpose Jadwiga Borucka, PAREXEL, Warsaw, Poland ABSTRACT Cox proportional hazard model is one of the most common methods used
More informationADVANCED STATISTICAL ANALYSIS OF EPIDEMIOLOGICAL STUDIES. Cox s regression analysis Time dependent explanatory variables
ADVANCED STATISTICAL ANALYSIS OF EPIDEMIOLOGICAL STUDIES Cox s regression analysis Time dependent explanatory variables Henrik Ravn Bandim Health Project, Statens Serum Institut 4 November 2011 1 / 53
More informationIntroduction to Statistical Analysis
Introduction to Statistical Analysis Changyu Shen Richard A. and Susan F. Smith Center for Outcomes Research in Cardiology Beth Israel Deaconess Medical Center Harvard Medical School Objectives Descriptive
More informationTypical Survival Data Arising From a Clinical Trial. Censoring. The Survivor Function. Mathematical Definitions Introduction
Outline CHL 5225H Advanced Statistical Methods for Clinical Trials: Survival Analysis Prof. Kevin E. Thorpe Defining Survival Data Mathematical Definitions Non-parametric Estimates of Survival Comparing
More informationFULL LIKELIHOOD INFERENCES IN THE COX MODEL
October 20, 2007 FULL LIKELIHOOD INFERENCES IN THE COX MODEL BY JIAN-JIAN REN 1 AND MAI ZHOU 2 University of Central Florida and University of Kentucky Abstract We use the empirical likelihood approach
More informationIntroduction to Reliability Theory (part 2)
Introduction to Reliability Theory (part 2) Frank Coolen UTOPIAE Training School II, Durham University 3 July 2018 (UTOPIAE) Introduction to Reliability Theory 1 / 21 Outline Statistical issues Software
More informationLongitudinal Modeling with Logistic Regression
Newsom 1 Longitudinal Modeling with Logistic Regression Longitudinal designs involve repeated measurements of the same individuals over time There are two general classes of analyses that correspond to
More informationReliability Engineering I
Happiness is taking the reliability final exam. Reliability Engineering I ENM/MSC 565 Review for the Final Exam Vital Statistics What R&M concepts covered in the course When Monday April 29 from 4:30 6:00
More informationNotes largely based on Statistical Methods for Reliability Data by W.Q. Meeker and L. A. Escobar, Wiley, 1998 and on their class notes.
Unit 2: Models, Censoring, and Likelihood for Failure-Time Data Notes largely based on Statistical Methods for Reliability Data by W.Q. Meeker and L. A. Escobar, Wiley, 1998 and on their class notes. Ramón
More informationH-LIKELIHOOD ESTIMATION METHOOD FOR VARYING CLUSTERED BINARY MIXED EFFECTS MODEL
H-LIKELIHOOD ESTIMATION METHOOD FOR VARYING CLUSTERED BINARY MIXED EFFECTS MODEL Intesar N. El-Saeiti Department of Statistics, Faculty of Science, University of Bengahzi-Libya. entesar.el-saeiti@uob.edu.ly
More information1 Introduction. 2 Residuals in PH model
Supplementary Material for Diagnostic Plotting Methods for Proportional Hazards Models With Time-dependent Covariates or Time-varying Regression Coefficients BY QIQING YU, JUNYI DONG Department of Mathematical
More informationPrerequisite: STATS 7 or STATS 8 or AP90 or (STATS 120A and STATS 120B and STATS 120C). AP90 with a minimum score of 3
University of California, Irvine 2017-2018 1 Statistics (STATS) Courses STATS 5. Seminar in Data Science. 1 Unit. An introduction to the field of Data Science; intended for entering freshman and transfers.
More informationExtensions of Cox Model for Non-Proportional Hazards Purpose
PhUSE Annual Conference 2013 Paper SP07 Extensions of Cox Model for Non-Proportional Hazards Purpose Author: Jadwiga Borucka PAREXEL, Warsaw, Poland Brussels 13 th - 16 th October 2013 Presentation Plan
More informationStatistical Inference on Constant Stress Accelerated Life Tests Under Generalized Gamma Lifetime Distributions
Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session CPS040) p.4828 Statistical Inference on Constant Stress Accelerated Life Tests Under Generalized Gamma Lifetime Distributions
More informationPENALIZED LIKELIHOOD PARAMETER ESTIMATION FOR ADDITIVE HAZARD MODELS WITH INTERVAL CENSORED DATA
PENALIZED LIKELIHOOD PARAMETER ESTIMATION FOR ADDITIVE HAZARD MODELS WITH INTERVAL CENSORED DATA Kasun Rathnayake ; A/Prof Jun Ma Department of Statistics Faculty of Science and Engineering Macquarie University
More informationSTAT331. Cox s Proportional Hazards Model
STAT331 Cox s Proportional Hazards Model In this unit we introduce Cox s proportional hazards (Cox s PH) model, give a heuristic development of the partial likelihood function, and discuss adaptations
More informationPart [1.0] Measures of Classification Accuracy for the Prediction of Survival Times
Part [1.0] Measures of Classification Accuracy for the Prediction of Survival Times Patrick J. Heagerty PhD Department of Biostatistics University of Washington 1 Biomarkers Review: Cox Regression Model
More informationLogistic Regression: Regression with a Binary Dependent Variable
Logistic Regression: Regression with a Binary Dependent Variable LEARNING OBJECTIVES Upon completing this chapter, you should be able to do the following: State the circumstances under which logistic regression
More informationAccelerated Failure Time Models
Accelerated Failure Time Models Patrick Breheny October 12 Patrick Breheny University of Iowa Survival Data Analysis (BIOS 7210) 1 / 29 The AFT model framework Last time, we introduced the Weibull distribution
More informationField data reliability analysis of highly reliable item
Field data reliability analysis of highly reliable item David Vališ & Zdeněk Vintr Faculty of Military Technologies University of Defence 612 00 Brno Czech Republic david.valis@unob.cz Miroslav Koucký
More informationA comparison of inverse transform and composition methods of data simulation from the Lindley distribution
Communications for Statistical Applications and Methods 2016, Vol. 23, No. 6, 517 529 http://dx.doi.org/10.5351/csam.2016.23.6.517 Print ISSN 2287-7843 / Online ISSN 2383-4757 A comparison of inverse transform
More informationDISTRIBUTION SYSTEM ELECTRIC INFRASTRUCTURE RELIABILITY PERFORMANCE INDICATORS
EB-- Exhibit D Page of DISTRIBUTION SYSTEM ELECTRIC INFRASTRUCTURE RELIABILITY PERFORMANCE INDICATORS FIVE-YEAR HISTORICAL RELIABILITY PERFORMANCE THESL tracks System Average Interruption Frequency Index
More informationComparative Distributions of Hazard Modeling Analysis
Comparative s of Hazard Modeling Analysis Rana Abdul Wajid Professor and Director Center for Statistics Lahore School of Economics Lahore E-mail: drrana@lse.edu.pk M. Shuaib Khan Department of Statistics
More informationPractical Applications of Reliability Theory
Practical Applications of Reliability Theory George Dodson Spallation Neutron Source Managed by UT-Battelle Topics Reliability Terms and Definitions Reliability Modeling as a tool for evaluating system
More informationMAS3301 / MAS8311 Biostatistics Part II: Survival
MAS3301 / MAS8311 Biostatistics Part II: Survival M. Farrow School of Mathematics and Statistics Newcastle University Semester 2, 2009-10 1 13 The Cox proportional hazards model 13.1 Introduction In the
More informationMeei Pyng Ng 1 and Ray Watson 1
Aust N Z J Stat 444), 2002, 467 478 DEALING WITH TIES IN FAILURE TIME DATA Meei Pyng Ng 1 and Ray Watson 1 University of Melbourne Summary In dealing with ties in failure time data the mechanism by which
More informationLOGISTIC REGRESSION Joseph M. Hilbe
LOGISTIC REGRESSION Joseph M. Hilbe Arizona State University Logistic regression is the most common method used to model binary response data. When the response is binary, it typically takes the form of
More informationSigmaplot di Systat Software
Sigmaplot di Systat Software SigmaPlot Has Extensive Statistical Analysis Features SigmaPlot is now bundled with SigmaStat as an easy-to-use package for complete graphing and data analysis. The statistical
More informationVALIDATION OF AN INTEGRATED METHODOLOGY FOR DESIGN OF GROUNDING SYSTEMS THROUGH FIELD MEASUREMENTS
VALIDATION OF AN INTEGRATED METHODOLOGY FOR DESIGN OF GROUNDING SYSTEMS THROUGH FIELD MEASUREMENTS Carlos CARDOSO Luís ROCHA Andreia LEIRIA Pedro TEIXEIRA EDP Labelec - Portugal EDP Labelec - Portugal
More informationTime-varying failure rate for system reliability analysis in large-scale railway risk assessment simulation
Time-varying failure rate for system reliability analysis in large-scale railway risk assessment simulation H. Zhang, E. Cutright & T. Giras Center of Rail Safety-Critical Excellence, University of Virginia,
More informationAnalysis of Time-to-Event Data: Chapter 4 - Parametric regression models
Analysis of Time-to-Event Data: Chapter 4 - Parametric regression models Steffen Unkel Department of Medical Statistics University Medical Center Göttingen, Germany Winter term 2018/19 1/25 Right censored
More informationModel Estimation Example
Ronald H. Heck 1 EDEP 606: Multivariate Methods (S2013) April 7, 2013 Model Estimation Example As we have moved through the course this semester, we have encountered the concept of model estimation. Discussions
More informationLecture 7. Proportional Hazards Model - Handling Ties and Survival Estimation Statistics Survival Analysis. Presented February 4, 2016
Proportional Hazards Model - Handling Ties and Survival Estimation Statistics 255 - Survival Analysis Presented February 4, 2016 likelihood - Discrete Dan Gillen Department of Statistics University of
More informationSTAT 6350 Analysis of Lifetime Data. Failure-time Regression Analysis
STAT 6350 Analysis of Lifetime Data Failure-time Regression Analysis Explanatory Variables for Failure Times Usually explanatory variables explain/predict why some units fail quickly and some units survive
More informationStatistical inference for Markov deterioration models of bridge conditions in the Netherlands
Statistical inference for Markov deterioration models of bridge conditions in the Netherlands M.J.Kallen & J.M. van Noortwijk HKV Consultants, Lelystad, and Delft University of Technology, Delft, Netherlands
More informationSurvival Analysis I (CHL5209H)
Survival Analysis Dalla Lana School of Public Health University of Toronto olli.saarela@utoronto.ca January 7, 2015 31-1 Literature Clayton D & Hills M (1993): Statistical Models in Epidemiology. Not really
More informationResiduals and model diagnostics
Residuals and model diagnostics Patrick Breheny November 10 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/42 Introduction Residuals Many assumptions go into regression models, and the Cox proportional
More informationTied survival times; estimation of survival probabilities
Tied survival times; estimation of survival probabilities Patrick Breheny November 5 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/22 Introduction Tied survival times Introduction Breslow approximation
More informationReliability Analysis of Tampered Failure Rate Load-Sharing k-out-of-n:g Systems
Reliability Analysis of Tampered Failure Rate Load-Sharing k-out-of-n:g Systems Suprasad V. Amari Relex Software Corporation 540 Pellis Road Greensburg, PA 15601 USA Krishna B. Misra RAMS Consultants 71
More informationMultistate Modeling and Applications
Multistate Modeling and Applications Yang Yang Department of Statistics University of Michigan, Ann Arbor IBM Research Graduate Student Workshop: Statistics for a Smarter Planet Yang Yang (UM, Ann Arbor)
More informationProportional hazards regression
Proportional hazards regression Patrick Breheny October 8 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/28 Introduction The model Solving for the MLE Inference Today we will begin discussing regression
More informationApplication of Time-to-Event Methods in the Assessment of Safety in Clinical Trials
Application of Time-to-Event Methods in the Assessment of Safety in Clinical Trials Progress, Updates, Problems William Jen Hoe Koh May 9, 2013 Overview Marginal vs Conditional What is TMLE? Key Estimation
More informatione 4β e 4β + e β ˆβ =0.765
SIMPLE EXAMPLE COX-REGRESSION i Y i x i δ i 1 5 12 0 2 10 10 1 3 40 3 0 4 80 5 0 5 120 3 1 6 400 4 1 7 600 1 0 Model: z(t x) =z 0 (t) exp{βx} Partial likelihood: L(β) = e 10β e 10β + e 3β + e 5β + e 3β
More informationLecture 3. Truncation, length-bias and prevalence sampling
Lecture 3. Truncation, length-bias and prevalence sampling 3.1 Prevalent sampling Statistical techniques for truncated data have been integrated into survival analysis in last two decades. Truncation in
More informationn =10,220 observations. Smaller samples analyzed here to illustrate sample size effect.
Chapter 7 Parametric Likelihood Fitting Concepts: Chapter 7 Parametric Likelihood Fitting Concepts: Objectives Show how to compute a likelihood for a parametric model using discrete data. Show how to compute
More informationRegularization in Cox Frailty Models
Regularization in Cox Frailty Models Andreas Groll 1, Trevor Hastie 2, Gerhard Tutz 3 1 Ludwig-Maximilians-Universität Munich, Department of Mathematics, Theresienstraße 39, 80333 Munich, Germany 2 University
More informationMultistate models and recurrent event models
and recurrent event models Patrick Breheny December 6 Patrick Breheny University of Iowa Survival Data Analysis (BIOS:7210) 1 / 22 Introduction In this final lecture, we will briefly look at two other
More information7. Assumes that there is little or no multicollinearity (however, SPSS will not assess this in the [binary] Logistic Regression procedure).
1 Neuendorf Logistic Regression The Model: Y Assumptions: 1. Metric (interval/ratio) data for 2+ IVs, and dichotomous (binomial; 2-value), categorical/nominal data for a single DV... bear in mind that
More informationAnalysis of Gamma and Weibull Lifetime Data under a General Censoring Scheme and in the presence of Covariates
Communications in Statistics - Theory and Methods ISSN: 0361-0926 (Print) 1532-415X (Online) Journal homepage: http://www.tandfonline.com/loi/lsta20 Analysis of Gamma and Weibull Lifetime Data under a
More informationGeneralized Linear Models (GLZ)
Generalized Linear Models (GLZ) Generalized Linear Models (GLZ) are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the
More informationSimple logistic regression
Simple logistic regression Biometry 755 Spring 2009 Simple logistic regression p. 1/47 Model assumptions 1. The observed data are independent realizations of a binary response variable Y that follows a
More informationLecture 7 Time-dependent Covariates in Cox Regression
Lecture 7 Time-dependent Covariates in Cox Regression So far, we ve been considering the following Cox PH model: λ(t Z) = λ 0 (t) exp(β Z) = λ 0 (t) exp( β j Z j ) where β j is the parameter for the the
More informationEconometric Analysis of Cross Section and Panel Data
Econometric Analysis of Cross Section and Panel Data Jeffrey M. Wooldridge / The MIT Press Cambridge, Massachusetts London, England Contents Preface Acknowledgments xvii xxiii I INTRODUCTION AND BACKGROUND
More informationKey Words: Lifetime Data Analysis (LDA), Probability Density Function (PDF), Goodness of fit methods, Chi-square method.
Reliability prediction based on lifetime data analysis methodology: The pump case study Abstract: The business case aims to demonstrate the lifetime data analysis methodology application from the historical
More informationSurvival Analysis. 732G34 Statistisk analys av komplexa data. Krzysztof Bartoszek
Survival Analysis 732G34 Statistisk analys av komplexa data Krzysztof Bartoszek (krzysztof.bartoszek@liu.se) 10, 11 I 2018 Department of Computer and Information Science Linköping University Survival analysis
More informationCIMAT Taller de Modelos de Capture y Recaptura Known Fate Survival Analysis
CIMAT Taller de Modelos de Capture y Recaptura 2010 Known Fate urvival Analysis B D BALANCE MODEL implest population model N = λ t+ 1 N t Deeper understanding of dynamics can be gained by identifying variation
More informationPASS Sample Size Software. Poisson Regression
Chapter 870 Introduction Poisson regression is used when the dependent variable is a count. Following the results of Signorini (99), this procedure calculates power and sample size for testing the hypothesis
More informationβ j = coefficient of x j in the model; β = ( β1, β2,
Regression Modeling of Survival Time Data Why regression models? Groups similar except for the treatment under study use the nonparametric methods discussed earlier. Groups differ in variables (covariates)
More informationSurvival Analysis for Case-Cohort Studies
Survival Analysis for ase-ohort Studies Petr Klášterecký Dept. of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, harles University, Prague, zech Republic e-mail: petr.klasterecky@matfyz.cz
More informationApproaches to the calculation of losses in power networks Study and test of different approximate methods to the calculation of losses
Approaches to the calculation of losses in power networks Study and test of different approximate methods to the calculation of losses João Tiago Abelho dos Santos Calheiros Andrade Department of Electrical
More informationDebbie Lee, Communications and Public Affairs Officer. Update on Southern California Edison s Capital Improvement Projects
Information Item Date: June 22, 2015 To: From: Subject: Mayor and City Council Debbie Lee, Communications and Public Affairs Officer Update on Southern California Edison s Capital Improvement Projects
More informationObjective Experiments Glossary of Statistical Terms
Objective Experiments Glossary of Statistical Terms This glossary is intended to provide friendly definitions for terms used commonly in engineering and science. It is not intended to be absolutely precise.
More informationLoad-strength Dynamic Interaction Principle and Failure Rate Model
International Journal of Performability Engineering Vol. 6, No. 3, May 21, pp. 25-214. RAMS Consultants Printed in India Load-strength Dynamic Interaction Principle and Failure Rate Model LIYANG XIE and
More informationUniversity of California, Berkeley
University of California, Berkeley U.C. Berkeley Division of Biostatistics Working Paper Series Year 24 Paper 153 A Note on Empirical Likelihood Inference of Residual Life Regression Ying Qing Chen Yichuan
More informationA Survival Analysis of GMO vs Non-GMO Corn Hybrid Persistence Using Simulated Time Dependent Covariates in SAS
Western Kentucky University From the SelectedWorks of Matt Bogard 2012 A Survival Analysis of GMO vs Non-GMO Corn Hybrid Persistence Using Simulated Time Dependent Covariates in SAS Matt Bogard, Western
More informationA Recursive Formula for the Kaplan-Meier Estimator with Mean Constraints
Noname manuscript No. (will be inserted by the editor) A Recursive Formula for the Kaplan-Meier Estimator with Mean Constraints Mai Zhou Yifan Yang Received: date / Accepted: date Abstract In this note
More informationLogistic Regression. Fitting the Logistic Regression Model BAL040-A.A.-10-MAJ
Logistic Regression The goal of a logistic regression analysis is to find the best fitting and most parsimonious, yet biologically reasonable, model to describe the relationship between an outcome (dependent
More informationSubject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study
Subject-specific observed profiles of log(fev1) vs age First 50 subjects in Six Cities Study 1.4 0.0-6 7 8 9 10 11 12 13 14 15 16 17 18 19 age Model 1: A simple broken stick model with knot at 14 fit with
More informationTEST POWER IN COMPARISON DIFFERENCE BETWEEN TWO INDEPENDENT PROPORTIONS
TEST POWER IN COMPARISON DIFFERENCE BETWEEN TWO INDEPENDENT PROPORTIONS Mehmet MENDES PhD, Associate Professor, Canakkale Onsekiz Mart University, Agriculture Faculty, Animal Science Department, Biometry
More informationConfirmatory Factor Analysis: Model comparison, respecification, and more. Psychology 588: Covariance structure and factor models
Confirmatory Factor Analysis: Model comparison, respecification, and more Psychology 588: Covariance structure and factor models Model comparison 2 Essentially all goodness of fit indices are descriptive,
More informationESTIMATION OF RELIABILITY CHARACTERISTICS OF POWER OIL TRANSFORMERS
Engineering MECHANICS, Vol. 19, 2012, No. 1, p. 61 73 61 ESTIMATION OF RELIABILITY CHARACTERISTICS OF POWER OIL TRANSFORMERS Miloš Hammer*, Jakub Ertl*, Ondřej Janda* At present days, the requirements
More informationHazard Function, Failure Rate, and A Rule of Thumb for Calculating Empirical Hazard Function of Continuous-Time Failure Data
Hazard Function, Failure Rate, and A Rule of Thumb for Calculating Empirical Hazard Function of Continuous-Time Failure Data Feng-feng Li,2, Gang Xie,2, Yong Sun,2, Lin Ma,2 CRC for Infrastructure and
More informationNON-STATIONARY QUEUE SIMULATION ANALYSIS USING TIME SERIES
Proceedings of the 2003 Winter Simulation Conference S. Chick, P. J. Sánchez, D. Ferrin, and D. J. Morrice, eds. NON-STATIONARY QUEUE SIMULATION ANALYSIS USING TIME SERIES Rita Marques Brandão Departamento
More informationCOMPLEMENTARY LOG-LOG MODEL
COMPLEMENTARY LOG-LOG MODEL Under the assumption of binary response, there are two alternatives to logit model: probit model and complementary-log-log model. They all follow the same form π ( x) =Φ ( α
More informationThe coxvc_1-1-1 package
Appendix A The coxvc_1-1-1 package A.1 Introduction The coxvc_1-1-1 package is a set of functions for survival analysis that run under R2.1.1 [81]. This package contains a set of routines to fit Cox models
More informationQuantitative Trendspotting. Rex Yuxing Du and Wagner A. Kamakura. Web Appendix A Inferring and Projecting the Latent Dynamic Factors
1 Quantitative Trendspotting Rex Yuxing Du and Wagner A. Kamakura Web Appendix A Inferring and Projecting the Latent Dynamic Factors The procedure for inferring the latent state variables (i.e., [ ] ),
More informationMultistate models and recurrent event models
Multistate models Multistate models and recurrent event models Patrick Breheny December 10 Patrick Breheny Survival Data Analysis (BIOS 7210) 1/22 Introduction Multistate models In this final lecture,
More informationUNIVERSITY OF MASSACHUSETTS Department of Mathematics and Statistics Applied Statistics Friday, January 15, 2016
UNIVERSITY OF MASSACHUSETTS Department of Mathematics and Statistics Applied Statistics Friday, January 15, 2016 Work all problems. 60 points are needed to pass at the Masters Level and 75 to pass at the
More informationAvailability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility
International Journal of Systems Science and Applied Mathematics 2018; 3(1): 10-15 http://www.sciencepublishinggroup.com/j/ijssam doi: 10.11648/j.ijssam.20180301.12 ISSN: 2575-5838 (Print); ISSN: 2575-5803
More informationFault Location in Distribution Feeders with Distributed Generation using Positive Sequence Apparent Impedance
Fault Location in Distribution Feeders with Distributed Generation using Positive Sequence Apparent Impedance ARTURO SUMAN BRETAS Federal University of Rio Grande do Sul Department of Electrical Engineering
More informationEvaluation of the risk of failure due to switching overvoltages of a phase to phase insulation
Evaluation of the risk of failure due to switching overvoltages of a phase to phase insulation A. Xemard, J. Michaud, A. Guerrier, I. Uglesic, G. Levacic, M. Mesic Abstract-- The upgrade of an overhead
More informationMAS3301 / MAS8311 Biostatistics Part II: Survival
MAS330 / MAS83 Biostatistics Part II: Survival M. Farrow School of Mathematics and Statistics Newcastle University Semester 2, 2009-0 8 Parametric models 8. Introduction In the last few sections (the KM
More informationMahdi karbasian* & Zoubi Ibrahim
International Journal of Industrial Engineering & Production Research (010) pp. 105-110 September 010, Volume 1, Number International Journal of Industrial Engineering & Production Research ISSN: 008-4889
More informationFailure Prognostics with Missing Data Using Extended Kalman Filter
Failure Prognostics with Missing Data Using Extended Kalman Filter Wlamir Olivares Loesch Vianna 1, and Takashi Yoneyama 2 1 EMBRAER S.A., São José dos Campos, São Paulo, 12227 901, Brazil wlamir.vianna@embraer.com.br
More informationA conceptual interpretation of the renewal theorem with applications
Risk, Reliability and Societal Safety Aven & Vinnem (eds) 2007 Taylor & Francis Group, London, ISBN 978-0-415-44786-7 A conceptual interpretation of the renewal theorem with applications J.A.M. van der
More informationSurvival analysis in R
Survival analysis in R Niels Richard Hansen This note describes a few elementary aspects of practical analysis of survival data in R. For further information we refer to the book Introductory Statistics
More informationOptimal Cusum Control Chart for Censored Reliability Data with Log-logistic Distribution
CMST 21(4) 221-227 (2015) DOI:10.12921/cmst.2015.21.04.006 Optimal Cusum Control Chart for Censored Reliability Data with Log-logistic Distribution B. Sadeghpour Gildeh, M. Taghizadeh Ashkavaey Department
More informationInvestigation of goodness-of-fit test statistic distributions by random censored samples
d samples Investigation of goodness-of-fit test statistic distributions by random censored samples Novosibirsk State Technical University November 22, 2010 d samples Outline 1 Nonparametric goodness-of-fit
More information