2016 ars north america presentation · blue room, session 14 2016 ars north america begins at 2:20...

Blue Room, Session 142016 ARS North America

Begins at 2:20 PM, Thursday, June 23rd

Risk and Reliability Analysis Using Bivariate Weibull vs. General Log-Linear Models

Ken Yoon, GE Power

PRESENTATION SLIDESThe following presentation was delivered at the:

International Applied Reliability Symposium, North AmericaJune 21 - 23, 2016: San Diego, California

http://www.arsymposium.org/2016/

The International Applied Reliability Symposium (ARS) is intended to be a forum for reliability and maintainability practitioners within industry and government to discuss their success stories and lessons learned regarding the application of reliability techniques to meet real world challenges. Each year, the ARS issues an open

"Call for Presentations" at http://www.arsymposium.org/present.htm and the presentations delivered at the Symposium are selected on the basis of the presentation proposals received.

Although the ARS may edit the presentation materials as needed to make them ready to print, the content of the presentation is solely the responsibility of the author. Publication of these presentation materials in the

ARS Proceedings does not imply that the information and methods described in the presentation have been verified or endorsed by the ARS and/or its organizers.

The publication of these materials in the ARS presentation format is Copyright © 2016 by the ARS, All Rights Reserved.

Ken Yoon, GE Power Slide Number: 2Session 14App

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Copyright © 2016 General Electric Company. All rights reserved

GE Proprietary Notice

© 2016, General Electric Company.GE Proprietary Information - The information contained in this document isGeneral Electric Company (GE) proprietary information. It is the property ofGE and shall not be used, disclosed to others or reproduced without theexpress written consent of GE, including, but without limitation, in thecreation, manufacture, development, or derivation of any repairs,modifications, spare parts, or configuration changes or to obtaingovernment or regulatory approval to do so, if consent is given forreproduction in whole or in part, this notice and the notice set forth on eachpage of this document shall appear in any such reproduction in whole or inpart. The information contained in this document may also be controlled bythe US export control laws. Unauthorized export or re-export is prohibited.

All relative statements are with respect to GE technology unless otherwise noted.

Seek GE Counsel if a change is necessary


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Agenda

Introduction 10 minWeibull Models and MLE 7 min General Log Linear Models 8 min Bivariate Models 5 min Comparison of Models 15 min Summary 5 min Questions 10 min


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Power Requirement

2008

2035

Ref. 1: National Geographic

Ref. 2: BP Energy Outlook


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GE Gas Turbine Power Plant Overview

Ref. 3

7HA Gas turbine (60Hz)• Simple cycle net efficient: ~ 41.7%

Simple Cycle Output: ~ 330 MW• Start-up time: 10 min.• Ramp rate: 40 MW/min.• Turndown: ~ 30% of baseload

Compressor TurbineCombustor

Gas Turbineinlet

Steam Turbine HRSG

Multi-year Service Agreement• Comprehensive Warranty• Reliability & Availability Guarantees• Performance Guarantee Lifecycle Reliability Engineering

Generator


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Life Cycle Reliability Engineering Overview

Repair Data

Event Data

Cycle Data

Data Processing,

& Association

FMEA

Failure Mode

Models

System Models

Fleet Mgt.: RCA, Inspection Interval

Improvement.

Lifecycle Cost Evaluations

New Product : Design For Reliability

• Customers determine our success: using this process, we support various customers


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Key Steps for Reliability Analysis

1. Establish Failure Mode Definition and associated Aging Parameter Failure Mode Definition – Crack, Creep, Corrosion, Oxidation, Foreign

Object Damage, Trip, and so on Various Aging Parameters

2. Select the Prediction Methodology to represent failure rate distributions or damage accumulation Expert opinion or borrow from proxy models / products Physics–Based Models: Analytic Eq. & FEA Empirical Models: 1) gather field data for both failed parts and non-failed

parts and 2) correlate the data with HW Configuration, Vendor, Operator differences using survival models.

3. Draw useful conclusions from analyses, i.e., Help predict current and future risk & reliability to improve configuration

and outage plans & parts and services management

Weibull model has been popularly used in multiple industries


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Motivation Weibull models can take only one aging parameter, so it

requires a process to select the right aging parameter or expert opinions.

General Log Linear models can take additional factors but have limitation in accurately predicting risk of the whole space of the factors.

Bi-variate Weibull model can enable rapid or fully automated model development.

Multi-variate Weibull model can provide potential by taking more than two aging parameters and accurate risk prediction.


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Weibull Distribution• Weibull is so useful due to its flexibility in fitting different types of data,

and thus has been frequently used to model time-to-failure data.

Methods to Solve the Linear Equation:• Ranked Regression on X or Y a goodness of fit by Correlation

Coefficient• Maximum Likelihood Estimation a goodness of fit by Log-Likelihood

PDF of Failures

Ref. 4

exp

1 exp

ln

ln ln ln ln

CDF of Failures

Linear Equation with Parameters: Beta & Eta

Y X


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Weibull Parameter Estimation Using MLE

• Why MLE?• MLE estimation is one of the most robust parameter estimation

techniques due to its properties of asymptotic normality and consistency, and efficiency.

• It applies to every form of censored or multi-censored data to estimate life distribution parameters.

• MLE can estimate the parameters using data set of {X} only without the rank data of {Y}.

• How: MLE determines the parameters by maximizing the likelihood (or probability) of a set of observed data.

• Question: Which parameter (1) would you choose to maximize the probability of producing the observed data (ti)?

=1 =2 =3 =4distribution

Data points (or independent variables)Note MLE does not need a dependent variable or Y

Ref. 5


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Weibull Parameters

Weibull CDF, proportion that fail by t,

• , shape parameter, measures rate of occurrence of a SINGLE failure mode: It provides an indication of the physics of failure

− < 1, rate is decreasing (i.e., infant mortality)− = 1, rate is constant (i.e., random failures or mix of failure modes)− > 1, rate is increasing (wear out failures mode)

• , characteristic life, measures the age at which 63.2% of the units (components, functions, assemblies, etc.) will have failed due to a given failure mode.

1 exp

Weibull model needs to select only one aging parameter tH

azar

d ra

te:


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1 exp ∙ ∙

1 exp

General Log-Linear Model

Parametric Survival Models: • Exponential, Weibull, Lognormal, Loglogistic, and so on.

Vital Input Parameters or X’s: • Continuous

• Scalar quantities such as temperature, voltage, environmental factors, or humidity

• Discrete• Non-scalar quantities such as configuration, vendor, or grouping

of the assets by regional or operational

Weibull Equation GLL Equation

Ref. 6


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GLL Contour Plots with Different Betas

1 1 exp1η

GLL values 12 45% 51% 55% 57% 60% 61% 63% 64% 65% 66% 67% 68%Beta 0.50 11 45% 51% 54% 57% 59% 60% 62% 63% 64% 65% 66% 67%

ao 10.00 10 44% 50% 53% 56% 58% 60% 61% 62% 63% 64% 65% 66%a1 0.50 9 43% 49% 52% 55% 57% 59% 60% 61% 62% 63% 64% 65%

8 42% 48% 51% 54% 56% 57% 59% 60% 61% 62% 63% 64%7 41% 47% 50% 53% 55% 56% 58% 59% 60% 61% 62% 63%6 40% 45% 49% 51% 53% 55% 56% 57% 59% 60% 60% 61%5 38% 44% 47% 50% 52% 53% 55% 56% 57% 58% 59% 60%4 37% 42% 45% 48% 50% 51% 53% 54% 55% 56% 57% 57%3 35% 40% 43% 45% 47% 49% 50% 51% 52% 53% 54% 55%2 32% 37% 40% 42% 44% 45% 47% 48% 49% 50% 51% 51%1 28% 32% 35% 37% 38% 40% 41% 42% 43% 44% 45% 45%

t2/t1 1 2 3 4 5 6 7 8 9 10 11 12

GLL values 12 31% 40% 47% 52% 56% 59% 62% 64% 67% 69% 70% 72%Beta 1.00 11 30% 39% 45% 50% 54% 58% 60% 63% 65% 67% 69% 70%

ao 10.00 10 28% 38% 44% 49% 53% 56% 59% 61% 63% 65% 67% 69%a1 0.50 9 27% 36% 42% 47% 51% 54% 57% 59% 61% 63% 65% 67%

8 26% 34% 40% 45% 49% 52% 55% 57% 59% 61% 63% 64%7 24% 33% 38% 43% 46% 50% 52% 55% 57% 59% 60% 62%6 23% 31% 36% 40% 44% 47% 50% 52% 54% 56% 58% 59%5 21% 28% 34% 38% 41% 44% 46% 49% 51% 53% 54% 56%4 19% 26% 31% 34% 38% 40% 43% 45% 47% 49% 50% 52%3 17% 23% 27% 31% 34% 36% 38% 40% 42% 44% 45% 47%2 14% 19% 23% 26% 28% 31% 33% 34% 36% 38% 39% 40%1 10% 14% 17% 19% 21% 23% 24% 26% 27% 28% 30% 31%

t2/t1 1 2 3 4 5 6 7 8 9 10 11 12

GLL values 12 5% 13% 22% 32% 42% 51% 60% 67% 73% 79% 83% 87%Beta 3.00 11 4% 11% 20% 29% 38% 47% 55% 62% 69% 74% 79% 83%

ao 10.00 10 4% 10% 18% 26% 34% 42% 50% 57% 63% 69% 74% 79%a1 0.50 9 3% 9% 15% 22% 30% 37% 44% 51% 58% 63% 69% 73%

8 3% 7% 13% 19% 26% 32% 39% 45% 51% 57% 62% 67%7 2% 6% 11% 16% 22% 27% 33% 39% 44% 50% 55% 60%6 2% 5% 9% 13% 18% 22% 27% 32% 37% 42% 47% 51%5 1% 4% 7% 10% 14% 18% 22% 26% 30% 34% 38% 42%4 1% 3% 5% 7% 10% 13% 16% 19% 22% 26% 29% 32%3 1% 2% 3% 5% 7% 9% 11% 13% 15% 18% 20% 22%2 0% 1% 2% 3% 4% 5% 6% 7% 9% 10% 11% 13%1 0% 0% 1% 1% 1% 2% 2% 3% 3% 4% 4% 5%

t2/t1 1 2 3 4 5 6 7 8 9 10 11 12

η exp ln12and

Beta =0.5

Beta =1

Beta =3

Observations:• Beta has no impact on

contour shape except the magnitude of risk

• Contour lines are all concave regardless of Betas


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1 0.32 0.45 0.55 0.63 0.71 0.77 0.84 0.89 0.95 1.000.9 0.30 0.42 0.52 0.60 0.67 0.73 0.79 0.85 0.90 0.950.8 0.28 0.40 0.49 0.57 0.63 0.69 0.75 0.80 0.85 0.890.7 0.26 0.37 0.46 0.53 0.59 0.65 0.70 0.75 0.79 0.840.6 0.24 0.35 0.42 0.49 0.55 0.60 0.65 0.69 0.73 0.770.5 0.22 0.32 0.39 0.45 0.50 0.55 0.59 0.63 0.67 0.710.4 0.20 0.28 0.35 0.40 0.45 0.49 0.53 0.57 0.60 0.630.3 0.17 0.24 0.30 0.35 0.39 0.42 0.46 0.49 0.52 0.550.2 0.14 0.20 0.24 0.28 0.32 0.35 0.37 0.40 0.42 0.450.1 0.10 0.14 0.17 0.20 0.22 0.24 0.26 0.28 0.30 0.32

FS/FH 1 2 3 4 5 6 7 8 9 10

GLL Contour Plots with Different a1’s

1 0.13 0.23 0.34 0.44 0.54 0.63 0.73 0.82 0.91 1.000.9 0.12 0.23 0.33 0.43 0.53 0.62 0.72 0.81 0.90 0.990.8 0.12 0.23 0.33 0.43 0.52 0.62 0.71 0.80 0.89 0.980.7 0.12 0.23 0.33 0.42 0.52 0.61 0.70 0.79 0.88 0.960.6 0.12 0.22 0.32 0.42 0.51 0.60 0.69 0.78 0.86 0.950.5 0.12 0.22 0.32 0.41 0.50 0.59 0.68 0.76 0.85 0.930.4 0.11 0.21 0.31 0.40 0.49 0.58 0.66 0.75 0.83 0.910.3 0.11 0.21 0.30 0.39 0.48 0.56 0.64 0.73 0.81 0.890.2 0.11 0.20 0.29 0.37 0.46 0.54 0.62 0.70 0.77 0.850.1 0.10 0.19 0.27 0.35 0.43 0.50 0.58 0.65 0.72 0.79

FS/FH 1 2 3 4 5 6 7 8 9 10

1 0.79 0.85 0.89 0.91 0.93 0.95 0.96 0.98 0.99 1.000.9 0.72 0.77 0.81 0.83 0.85 0.86 0.88 0.89 0.90 0.910.8 0.65 0.70 0.73 0.75 0.76 0.78 0.79 0.80 0.81 0.820.7 0.58 0.62 0.64 0.66 0.68 0.69 0.70 0.71 0.72 0.730.6 0.50 0.54 0.56 0.58 0.59 0.60 0.61 0.62 0.62 0.630.5 0.43 0.46 0.48 0.49 0.50 0.51 0.52 0.52 0.53 0.540.4 0.35 0.37 0.39 0.40 0.41 0.42 0.42 0.43 0.43 0.440.3 0.27 0.29 0.30 0.31 0.32 0.32 0.33 0.33 0.33 0.340.2 0.19 0.20 0.21 0.21 0.22 0.22 0.23 0.23 0.23 0.230.1 0.10 0.11 0.11 0.11 0.12 0.12 0.12 0.12 0.12 0.13

FS/FH 1 2 3 4 5 6 7 8 9 10

a1 =0.1

a1 =-0.11 0.08 0.17 0.27 0.36 0.47 0.57 0.68 0.78 0.89 1.00

0.9 0.08 0.17 0.27 0.37 0.47 0.58 0.68 0.79 0.90 1.010.8 0.08 0.17 0.27 0.37 0.48 0.58 0.69 0.80 0.91 1.020.7 0.08 0.18 0.28 0.38 0.48 0.59 0.70 0.81 0.92 1.040.6 0.08 0.18 0.28 0.38 0.49 0.60 0.71 0.82 0.94 1.050.5 0.09 0.18 0.29 0.39 0.50 0.61 0.72 0.84 0.95 1.070.4 0.09 0.19 0.29 0.40 0.51 0.62 0.74 0.86 0.98 1.100.3 0.09 0.19 0.30 0.41 0.53 0.64 0.76 0.88 1.00 1.130.2 0.09 0.20 0.31 0.43 0.55 0.67 0.79 0.92 1.05 1.170.1 0.10 0.21 0.33 0.46 0.59 0.72 0.85 0.98 1.12 1.26

FS/FH 1 2 3 4 5 6 7 8 9 10

1 1.58 1.38 1.27 1.20 1.15 1.11 1.07 1.05 1.02 1.000.9 1.40 1.22 1.12 1.06 1.01 0.98 0.95 0.92 0.90 0.880.8 1.21 1.06 0.97 0.92 0.88 0.85 0.82 0.80 0.78 0.770.7 1.03 0.90 0.83 0.78 0.75 0.72 0.70 0.68 0.67 0.650.6 0.86 0.75 0.69 0.65 0.62 0.60 0.58 0.57 0.55 0.540.5 0.69 0.60 0.55 0.52 0.50 0.48 0.47 0.46 0.44 0.440.4 0.53 0.46 0.42 0.40 0.38 0.37 0.36 0.35 0.34 0.330.3 0.37 0.33 0.30 0.28 0.27 0.26 0.25 0.25 0.24 0.240.2 0.23 0.20 0.18 0.17 0.17 0.16 0.16 0.15 0.15 0.140.1 0.10 0.09 0.08 0.08 0.07 0.07 0.07 0.07 0.06 0.06

FS/FH 1 2 3 4 5 6 7 8 9 10

a1 =1.2

1 1 exp1

exp ln 12

plot

Greenline = equi-risk line

t2 / t1

t2 / t1

t2 / t1

t2 / t1

t2 / t1

All

Con

cave

• a1 is valid in a limited range and can be a measure for dominance of an aging parameter

a1 =0.9

a1 =0.5


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A Case Study with Parts Scrap Data

This plot shows artificially generated data to show a parts exposure in two aging parameters

• What would be a right model for this? Weibull, GLL• What would be a right aging parameter?

Non-scraps


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A Case Study with 2P-Weibull

The data is modified from an unplanned outage model datat1 based 2P-Weibull t2 based 2P-Weibull

2PW: 2P-Weibull

BIC = 813 BIC = 615

Bayesian Information Criterion: BIC = -2*Log-Likelihood + k*ln(n) where k is the number of estimated parameters in the model and n is the number of observations in the data set on Ref. 7


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A Case Study with GLL Model

BIC = 815


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A Case Study with BVW

t1

BVW valuesBeta 2.0Eta1 387605Eta2 17948

BVW on Ref. 8

Non-scraps

BIC = 819


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Comparison of the Models

t1

Non-scraps


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12 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%11 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%10 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%9 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%8 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%7 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%6 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%5 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%4 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%3 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%2 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%1 0.1% 0.5% 1.0% 1.7% 2.6% 3.6% 4.8% 6.1% 7.5% 9.1% 10.8% 12.6%

1 2 3 4 5 6 7 8 9 10 11 12

12 17.8% 17.8% 17.8% 17.8% 17.8% 17.8% 17.8% 17.8% 17.8% 17.8% 17.8% 17.8%11 16.1% 16.1% 16.1% 16.1% 16.1% 16.1% 16.1% 16.1% 16.1% 16.1% 16.1% 16.1%10 14.3% 14.3% 14.3% 14.3% 14.3% 14.3% 14.3% 14.3% 14.3% 14.3% 14.3% 14.3%9 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.6% 12.6%8 10.9% 10.9% 10.9% 10.9% 10.9% 10.9% 10.9% 10.9% 10.9% 10.9% 10.9% 10.9%7 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3% 9.3%6 7.7% 7.7% 7.7% 7.7% 7.7% 7.7% 7.7% 7.7% 7.7% 7.7% 7.7% 7.7%5 6.1% 6.1% 6.1% 6.1% 6.1% 6.1% 6.1% 6.1% 6.1% 6.1% 6.1% 6.1%4 4.6% 4.6% 4.6% 4.6% 4.6% 4.6% 4.6% 4.6% 4.6% 4.6% 4.6% 4.6%3 3.2% 3.2% 3.2% 3.2% 3.2% 3.2% 3.2% 3.2% 3.2% 3.2% 3.2% 3.2%2 1.9% 1.9% 1.9% 1.9% 1.9% 1.9% 1.9% 1.9% 1.9% 1.9% 1.9% 1.9%1 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8% 0.8%

1 2 3 4 5 6 7 8 9 10 11 12

Comparison of Contour Plots2P-Weibull hours vs. Starts models

t2/t1

t2/t1

2PW on t1 valuesBeta 1.9

Eta 420000

2PW on t2 valuesBeta 1.3

Eta 18900


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12 1.8% 4.6% 7.8% 11.4% 15.2% 19.1% 23.1% 27.1% 31.0% 34.9% 38.7% 42.4%11 1.7% 4.3% 7.3% 10.7% 14.2% 17.9% 21.7% 25.4% 29.2% 32.9% 36.6% 40.1%10 1.5% 3.9% 6.8% 9.9% 13.2% 16.7% 20.2% 23.7% 27.3% 30.8% 34.3% 37.7%9 1.4% 3.6% 6.2% 9.1% 12.2% 15.4% 18.7% 22.0% 25.3% 28.6% 31.9% 35.2%8 1.3% 3.3% 5.7% 8.3% 11.1% 14.0% 17.1% 20.1% 23.2% 26.4% 29.4% 32.5%7 1.1% 2.9% 5.1% 7.4% 10.0% 12.7% 15.4% 18.2% 21.1% 23.9% 26.8% 29.7%6 1.0% 2.6% 4.5% 6.6% 8.8% 11.2% 13.7% 16.2% 18.8% 21.4% 24.0% 26.6%5 0.9% 2.2% 3.9% 5.7% 7.6% 9.7% 11.9% 14.1% 16.4% 18.7% 21.0% 23.3%4 0.7% 1.8% 3.2% 4.7% 6.4% 8.1% 10.0% 11.9% 13.8% 15.8% 17.8% 19.8%3 0.6% 1.5% 2.5% 3.7% 5.1% 6.5% 7.9% 9.4% 11.0% 12.6% 14.3% 15.9%2 0.4% 1.0% 1.8% 2.7% 3.6% 4.6% 5.7% 6.8% 8.0% 9.2% 10.4% 11.6%1 0.2% 0.6% 1.0% 1.5% 2.1% 2.6% 3.2% 3.9% 4.6% 5.3% 6.0% 6.7%

1 2 3 4 5 6 7 8 9 10 11 12

12 8.8% 9.0% 9.5% 10.1% 10.8% 11.8% 12.9% 14.1% 15.5% 17.0% 18.7% 20.5%11 7.4% 7.7% 8.1% 8.8% 9.5% 10.5% 11.6% 12.9% 14.3% 15.8% 17.5% 19.3%10 6.2% 6.5% 6.9% 7.5% 8.3% 9.3% 10.4% 11.7% 13.1% 14.7% 16.4% 18.2%9 5.1% 5.3% 5.8% 6.4% 7.2% 8.2% 9.3% 10.6% 12.1% 13.7% 15.4% 17.2%8 4.0% 4.3% 4.8% 5.4% 6.2% 7.2% 8.4% 9.7% 11.1% 12.7% 14.5% 16.4%7 3.1% 3.4% 3.9% 4.5% 5.3% 6.3% 7.5% 8.8% 10.3% 11.9% 13.7% 15.6%6 2.3% 2.6% 3.1% 3.7% 4.6% 5.6% 6.7% 8.1% 9.6% 11.2% 13.0% 14.9%5 1.7% 1.9% 2.4% 3.1% 3.9% 4.9% 6.1% 7.4% 8.9% 10.6% 12.4% 14.3%4 1.1% 1.4% 1.9% 2.5% 3.4% 4.4% 5.6% 6.9% 8.4% 10.1% 11.9% 13.8%3 0.7% 0.9% 1.4% 2.1% 2.9% 3.9% 5.1% 6.5% 8.0% 9.7% 11.5% 13.4%2 0.3% 0.6% 1.1% 1.8% 2.6% 3.6% 4.8% 6.2% 7.7% 9.4% 11.2% 13.1%1 0.2% 0.4% 0.9% 1.6% 2.4% 3.5% 4.7% 6.0% 7.5% 9.2% 11.0% 13.0%

1 2 3 4 5 6 7 8 9 10 11 12

Comparison of Contour PlotsGLL vs. BVW models

t2/t1

t2/t1

GLL valuesBeta 2.2

ao 10.9a1 0.4

BVW valuesBeta 2.0Eta1 387605Eta2 17948


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Data Generation for 2-D Space Study

• Define two Weibull models based on t1 & t2 and fleet exposure• Generate outage times randomly from two models independent each other:

• Generate unit operation times randomly on t1 & t2 up to the fleet leader exposure

• Compare the outage times with the unit operation times and generate data for the BVW and GLL models

1 1 exp 1 ∙/

2 1 exp 2 ∙/

t1

Suspension at t1=83 & t2=5

Exposure time

Outage point on t1

t2

40 100 12090838550

10

12

7

543

Suspension at t1=40 & t2=7

Outage at t1=85 & t2=10

Outage at t1=100 & t2=3

Outage point on t2

Input Models Analysis Data

B50 Life_t1 96000Beta1 2Eta1 115308Fleet Leader t1 96000Fleet Leader Bx t1 50%B50 Life_t2 4800Beta2 2Eta2 5765Fleet Leader t2 4800Fleet Leader Bx t2 50%


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Exposure Plot Case I: Same Betas on t1 & t2


F: FailureS: Suspension


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Model Comparison Case I: Same Betas on t1 & t2

• BVW accurately estimates the original Beta and Etas• BVW more accurately estimates at a longer exposure than

GLL, but shows more scatters in an early exposure

Model AP Beta a0 / Eta1

a1 / Eta2

BIC

2PW t1 1.27 99123 88432PW t2 1.40 4632 6719GLL t1 1.64 9.42 0.60 8637BVW t1,t2 2.00 119064 5556 8537

t1 2.00 115308t2 2.00 5765

Input data


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Contour Plots Case I: Same Betas on t1 & t2

12 58.9% 60.2% 62.3% 65.0% 68.3% 71.8% 75.5% 79.2% 82.7% 85.9% 88.8% 91.3%11 52.7% 54.2% 56.6% 59.8% 63.5% 67.6% 71.9% 76.1% 80.1% 83.8% 87.1% 89.9%10 46.2% 47.9% 50.7% 54.3% 58.5% 63.2% 68.0% 72.8% 77.4% 81.6% 85.3% 88.6%9 39.6% 41.5% 44.6% 48.7% 53.4% 58.7% 64.1% 69.5% 74.6% 79.3% 83.5% 87.2%8 33.0% 35.2% 38.6% 43.1% 48.3% 54.1% 60.2% 66.1% 71.8% 77.1% 81.7% 85.8%7 26.6% 29.0% 32.7% 37.6% 43.4% 49.8% 56.4% 62.9% 69.1% 74.9% 80.0% 84.4%6 20.6% 23.1% 27.2% 32.5% 38.7% 45.6% 52.8% 59.8% 66.6% 72.8% 78.3% 83.1%5 15.1% 17.8% 22.1% 27.8% 34.5% 41.9% 49.5% 57.1% 64.3% 70.9% 76.8% 81.9%4 10.3% 13.1% 17.7% 23.7% 30.8% 38.6% 46.6% 54.6% 62.3% 69.3% 75.5% 80.9%3 6.4% 9.3% 14.1% 20.4% 27.8% 35.9% 44.3% 52.7% 60.6% 67.9% 74.5% 80.1%2 3.5% 6.5% 11.5% 17.9% 25.6% 33.9% 42.6% 51.2% 59.4% 67.0% 73.7% 79.5%1 1.7% 4.8% 9.8% 16.4% 24.2% 32.7% 41.5% 50.3% 58.7% 66.3% 73.2% 79.1%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 35.4% 49.6% 59.1% 66.0% 71.2% 75.4% 78.8% 81.6% 83.9% 85.9% 87.5% 89.0%11 33.0% 46.7% 56.0% 62.8% 68.1% 72.4% 75.9% 78.8% 81.3% 83.4% 85.2% 86.8%10 30.6% 43.6% 52.6% 59.3% 64.7% 69.0% 72.6% 75.7% 78.3% 80.5% 82.4% 84.1%9 28.0% 40.3% 49.0% 55.6% 60.9% 65.2% 68.9% 72.0% 74.7% 77.1% 79.1% 81.0%8 25.4% 36.9% 45.0% 51.4% 56.6% 61.0% 64.6% 67.8% 70.6% 73.1% 75.2% 77.2%7 22.6% 33.2% 40.8% 46.9% 51.9% 56.1% 59.8% 63.0% 65.8% 68.3% 70.6% 72.6%6 19.8% 29.3% 36.3% 41.9% 46.7% 50.7% 54.3% 57.4% 60.2% 62.7% 65.0% 67.1%5 16.8% 25.1% 31.4% 36.5% 40.8% 44.6% 48.0% 51.0% 53.7% 56.2% 58.4% 60.5%4 13.7% 20.7% 26.1% 30.5% 34.4% 37.8% 40.8% 43.6% 46.1% 48.4% 50.5% 52.5%3 10.5% 16.0% 20.3% 24.0% 27.2% 30.0% 32.6% 35.0% 37.2% 39.2% 41.1% 42.9%2 7.2% 11.0% 14.1% 16.8% 19.1% 21.3% 23.2% 25.1% 26.8% 28.4% 29.9% 31.3%1 3.7% 5.7% 7.4% 8.9% 10.2% 11.4% 12.5% 13.6% 14.5% 15.5% 16.4% 17.3%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 61.5% 62.7% 64.5% 66.9% 69.8% 73.0% 76.3% 79.7% 82.9% 85.9% 88.6% 91.0%11 55.2% 56.6% 58.7% 61.5% 64.9% 68.6% 72.5% 76.4% 80.1% 83.6% 86.8% 89.5%10 48.6% 50.1% 52.6% 55.8% 59.7% 63.9% 68.4% 72.9% 77.2% 81.2% 84.8% 88.0%9 41.8% 43.5% 46.3% 50.0% 54.3% 59.2% 64.2% 69.3% 74.2% 78.7% 82.8% 86.4%8 34.9% 36.8% 39.9% 44.1% 48.9% 54.3% 60.0% 65.6% 71.1% 76.2% 80.8% 84.8%7 28.2% 30.3% 33.7% 38.3% 43.7% 49.6% 55.8% 62.1% 68.1% 73.7% 78.8% 83.2%6 21.8% 24.1% 27.8% 32.8% 38.6% 45.1% 51.9% 58.7% 65.3% 71.4% 76.9% 81.7%5 15.9% 18.4% 22.4% 27.8% 34.1% 41.0% 48.3% 55.6% 62.7% 69.2% 75.2% 80.4%4 10.8% 13.5% 17.7% 23.4% 30.1% 37.4% 45.2% 52.9% 60.4% 67.4% 73.7% 79.2%3 6.6% 9.4% 13.9% 19.8% 26.8% 34.5% 42.6% 50.7% 58.6% 65.9% 72.4% 78.2%2 3.5% 6.4% 11.0% 17.1% 24.4% 32.3% 40.7% 49.1% 57.2% 64.7% 71.5% 77.5%1 1.6% 4.6% 9.3% 15.5% 22.9% 31.0% 39.6% 48.1% 56.3% 64.0% 71.0% 77.0%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

• Original Model

• GLL

• BVW

• BVW accurately estimates the risks within 2-3% error

• GLL shows huge errors and needs to define an effective range of the model

12 -23.5% -10.5% -3.2% 0.9% 3.0% 3.6% 3.3% 2.4% 1.2% 0.0% -1.2% -2.3%11 -19.6% -7.5% -0.6% 3.0% 4.6% 4.8% 4.1% 2.8% 1.2% -0.4% -1.9% -3.2%10 -15.6% -4.3% 1.9% 5.1% 6.2% 5.8% 4.6% 2.9% 0.9% -1.1% -2.9% -4.4%9 -11.6% -1.2% 4.3% 6.9% 7.4% 6.6% 4.8% 2.6% 0.1% -2.2% -4.4% -6.2%8 -7.6% 1.7% 6.5% 8.4% 8.3% 6.8% 4.5% 1.7% -1.2% -4.0% -6.5% -8.6%7 -4.0% 4.2% 8.1% 9.3% 8.5% 6.4% 3.4% 0.1% -3.3% -6.6% -9.4% -11.8%6 -0.8% 6.2% 9.1% 9.5% 7.9% 5.1% 1.5% -2.4% -6.4% -10.1% -13.3% -16.0%5 1.8% 7.3% 9.3% 8.7% 6.4% 2.8% -1.5% -6.1% -10.6% -14.8% -18.4% -21.5%4 3.5% 7.6% 8.4% 6.8% 3.6% -0.8% -5.8% -11.1% -16.2% -20.9% -25.0% -28.4%3 4.2% 6.7% 6.2% 3.6% -0.6% -5.9% -11.7% -17.7% -23.4% -28.7% -33.3% -37.2%2 3.7% 4.5% 2.7% -1.1% -6.4% -12.6% -19.3% -26.1% -32.6% -38.6% -43.8% -48.2%1 2.0% 0.9% -2.4% -7.6% -14.0% -21.3% -29.0% -36.8% -44.1% -50.9% -56.8% -61.8%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 2.6% 2.5% 2.2% 1.9% 1.5% 1.2% 0.8% 0.5% 0.2% 0.0% -0.2% -0.2%11 2.6% 2.4% 2.1% 1.8% 1.4% 1.0% 0.6% 0.3% 0.0% -0.2% -0.3% -0.4%10 2.4% 2.2% 1.9% 1.6% 1.2% 0.8% 0.4% 0.1% -0.2% -0.4% -0.5% -0.6%9 2.2% 2.0% 1.7% 1.3% 0.9% 0.5% 0.1% -0.2% -0.5% -0.6% -0.7% -0.8%8 1.9% 1.7% 1.4% 1.0% 0.6% 0.2% -0.2% -0.5% -0.7% -0.9% -1.0% -1.0%7 1.5% 1.3% 1.0% 0.7% 0.2% -0.2% -0.5% -0.8% -1.0% -1.2% -1.2% -1.2%6 1.2% 1.0% 0.7% 0.3% -0.1% -0.5% -0.8% -1.1% -1.3% -1.4% -1.4% -1.4%5 0.9% 0.7% 0.3% 0.0% -0.4% -0.8% -1.2% -1.4% -1.6% -1.7% -1.7% -1.6%4 0.5% 0.3% 0.0% -0.3% -0.7% -1.1% -1.5% -1.7% -1.9% -1.9% -1.9% -1.8%3 0.3% 0.1% -0.2% -0.6% -1.0% -1.4% -1.7% -1.9% -2.1% -2.1% -2.0% -1.9%2 0.1% -0.1% -0.4% -0.8% -1.2% -1.6% -1.9% -2.1% -2.2% -2.2% -2.2% -2.0%1 0.0% -0.2% -0.6% -0.9% -1.3% -1.7% -2.0% -2.2% -2.3% -2.3% -2.2% -2.1%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

GLL - Original Model

BVW – Original Model


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Exposure Plot Case II: Different Betas on t1 & t2



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Model Comparison Case II: Different Betas on t1 & t2

• BVW more accurately estimates at a longer exposure than GLL, but shows more scatters in an early exposure


a1 / Eta2

BIC


t1 1.00 138499t2 3.00 5424

Input data


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12 65.8% 68.7% 71.3% 73.6% 75.8% 77.8% 79.7% 81.4% 82.9% 84.3% 85.6% 86.8%11 57.1% 60.7% 63.9% 66.9% 69.7% 72.2% 74.5% 76.6% 78.6% 80.3% 82.0% 83.5%10 48.2% 52.5% 56.4% 60.1% 63.4% 66.4% 69.2% 71.8% 74.1% 76.2% 78.2% 80.0%9 39.5% 44.5% 49.1% 53.4% 57.2% 60.8% 64.0% 67.0% 69.8% 72.3% 74.6% 76.7%8 31.5% 37.2% 42.4% 47.2% 51.6% 55.6% 59.3% 62.7% 65.8% 68.6% 71.2% 73.6%7 24.6% 30.9% 36.6% 41.9% 46.7% 51.1% 55.2% 58.9% 62.3% 65.4% 68.3% 70.9%6 18.9% 25.7% 31.8% 37.5% 42.7% 47.4% 51.8% 55.8% 59.5% 62.8% 65.9% 68.7%5 14.6% 21.7% 28.2% 34.2% 39.6% 44.6% 49.2% 53.4% 57.3% 60.9% 64.1% 67.1%4 11.6% 18.9% 25.7% 31.8% 37.5% 42.7% 47.4% 51.8% 55.8% 59.5% 62.8% 65.9%3 9.7% 17.2% 24.1% 30.4% 36.2% 41.4% 46.3% 50.8% 54.9% 58.6% 62.0% 65.2%2 8.7% 16.3% 23.2% 29.6% 35.5% 40.8% 45.7% 50.2% 54.4% 58.1% 61.6% 64.8%1 8.4% 16.0% 22.9% 29.3% 35.2% 40.6% 45.5% 50.0% 54.2% 58.0% 61.5% 64.7%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 25.2% 38.2% 47.6% 54.9% 60.8% 65.7% 69.8% 73.3% 76.2% 78.8% 81.1% 83.0%11 24.4% 37.0% 46.3% 53.5% 59.4% 64.3% 68.4% 71.9% 74.9% 77.6% 79.9% 81.9%10 23.5% 35.9% 44.9% 52.1% 57.9% 62.8% 66.9% 70.5% 73.5% 76.2% 78.5% 80.6%9 22.6% 34.6% 43.5% 50.5% 56.3% 61.1% 65.2% 68.8% 71.9% 74.6% 77.0% 79.1%8 21.6% 33.2% 41.8% 48.7% 54.4% 59.2% 63.4% 66.9% 70.1% 72.8% 75.2% 77.4%7 20.5% 31.7% 40.0% 46.8% 52.4% 57.1% 61.2% 64.8% 68.0% 70.7% 73.2% 75.4%6 19.3% 30.0% 38.0% 44.6% 50.0% 54.7% 58.8% 62.4% 65.5% 68.3% 70.8% 73.1%5 18.0% 28.0% 35.7% 42.0% 47.3% 51.9% 55.9% 59.5% 62.6% 65.4% 68.0% 70.3%4 16.5% 25.8% 33.1% 39.0% 44.1% 48.6% 52.5% 56.0% 59.1% 61.9% 64.5% 66.8%3 14.7% 23.2% 29.8% 35.4% 40.2% 44.4% 48.2% 51.5% 54.6% 57.3% 59.9% 62.2%2 12.5% 19.9% 25.7% 30.7% 35.0% 38.9% 42.4% 45.5% 48.4% 51.1% 53.5% 55.8%1 9.4% 15.1% 19.8% 23.8% 27.4% 30.6% 33.5% 36.3% 38.8% 41.1% 43.3% 45.4%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 47.4% 50.8% 54.4% 58.2% 61.9% 65.5% 69.0% 72.2% 75.2% 77.9% 80.5% 82.7%11 43.9% 47.5% 51.4% 55.4% 59.4% 63.2% 66.9% 70.3% 73.5% 76.5% 79.1% 81.6%10 40.3% 44.1% 48.3% 52.5% 56.8% 60.9% 64.7% 68.4% 71.8% 74.9% 77.8% 80.4%9 36.5% 40.6% 45.0% 49.6% 54.1% 58.4% 62.5% 66.4% 70.0% 73.4% 76.4% 79.2%8 32.7% 37.0% 41.7% 46.5% 51.3% 55.9% 60.3% 64.4% 68.2% 71.7% 75.0% 77.9%7 28.8% 33.3% 38.3% 43.4% 48.4% 53.3% 58.0% 62.3% 66.4% 70.1% 73.5% 76.6%6 24.8% 29.6% 34.9% 40.3% 45.6% 50.7% 55.6% 60.2% 64.5% 68.5% 72.1% 75.3%5 20.9% 25.9% 31.5% 37.1% 42.7% 48.1% 53.3% 58.1% 62.6% 66.8% 70.6% 74.0%4 17.0% 22.3% 28.1% 34.0% 39.9% 45.6% 51.0% 56.1% 60.8% 65.2% 69.1% 72.8%3 13.2% 18.7% 24.8% 31.0% 37.2% 43.1% 48.8% 54.1% 59.0% 63.6% 67.7% 71.5%2 9.7% 15.4% 21.7% 28.2% 34.6% 40.8% 46.7% 52.2% 57.3% 62.1% 66.4% 70.4%1 6.5% 12.5% 19.0% 25.7% 32.3% 38.7% 44.8% 50.5% 55.9% 60.8% 65.3% 69.3%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

Contour Plots Case II: Different Betas on t1 & t2

• Original Model

• GLL

• BVW

12 -40.6% -30.5% -23.7% -18.8% -15.0% -12.1% -9.9% -8.1% -6.7% -5.5% -4.6% -3.8%11 -32.8% -23.6% -17.6% -13.4% -10.3% -7.9% -6.1% -4.7% -3.6% -2.8% -2.1% -1.6%10 -24.7% -16.6% -11.5% -8.0% -5.4% -3.6% -2.3% -1.3% -0.6% -0.1% 0.3% 0.5%9 -16.9% -10.0% -5.7% -2.9% -1.0% 0.3% 1.2% 1.8% 2.1% 2.3% 2.4% 2.4%8 -9.9% -4.0% -0.6% 1.5% 2.8% 3.6% 4.1% 4.3% 4.3% 4.2% 4.0% 3.8%7 -4.1% 0.8% 3.4% 4.9% 5.7% 6.0% 6.1% 5.9% 5.7% 5.3% 4.9% 4.5%6 0.4% 4.3% 6.2% 7.1% 7.4% 7.3% 7.0% 6.6% 6.1% 5.5% 4.9% 4.4%5 3.4% 6.3% 7.5% 7.9% 7.7% 7.3% 6.7% 6.0% 5.3% 4.6% 3.9% 3.2%4 4.9% 6.9% 7.4% 7.2% 6.7% 5.9% 5.1% 4.2% 3.3% 2.4% 1.6% 0.9%3 5.0% 6.0% 5.8% 5.0% 4.1% 3.0% 1.9% 0.8% -0.3% -1.3% -2.2% -3.0%2 3.8% 3.6% 2.5% 1.1% -0.4% -1.9% -3.3% -4.7% -5.9% -7.1% -8.1% -9.0%1 1.1% -0.8% -3.2% -5.5% -7.8% -10.0% -12.0% -13.8% -15.4% -16.9% -18.1% -19.3%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 -18.4% -17.9% -16.8% -15.4% -13.9% -12.3% -10.7% -9.2% -7.7% -6.4% -5.2% -4.1%11 -13.2% -13.2% -12.5% -11.5% -10.3% -9.0% -7.6% -6.3% -5.1% -3.9% -2.8% -1.9%10 -7.9% -8.4% -8.2% -7.5% -6.6% -5.6% -4.5% -3.4% -2.3% -1.3% -0.4% 0.4%9 -3.0% -4.0% -4.1% -3.8% -3.2% -2.4% -1.5% -0.6% 0.3% 1.1% 1.8% 2.5%8 1.1% -0.2% -0.7% -0.7% -0.3% 0.3% 1.0% 1.7% 2.4% 3.1% 3.8% 4.3%7 4.2% 2.5% 1.7% 1.5% 1.8% 2.2% 2.8% 3.4% 4.1% 4.7% 5.2% 5.7%6 5.9% 4.0% 3.0% 2.8% 2.9% 3.3% 3.8% 4.4% 5.0% 5.6% 6.1% 6.6%5 6.3% 4.2% 3.3% 3.0% 3.1% 3.5% 4.1% 4.7% 5.3% 5.9% 6.5% 7.0%4 5.4% 3.4% 2.4% 2.2% 2.4% 2.9% 3.6% 4.3% 5.0% 5.7% 6.3% 6.9%3 3.5% 1.5% 0.7% 0.7% 1.0% 1.7% 2.5% 3.3% 4.2% 5.0% 5.7% 6.3%2 0.9% -0.9% -1.5% -1.4% -0.9% 0.0% 0.9% 2.0% 3.0% 3.9% 4.8% 5.6%1 -1.8% -3.5% -3.9% -3.6% -2.9% -1.8% -0.7% 0.5% 1.7% 2.8% 3.8% 4.7%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12



• BVW shows some errors at high t2 region

• GLL shows huge errors at both extreme exposure regions


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Exposure Plot Case III: Very Different Betas on t1 & t2

B50 Life_Ft1 96000Beta1 0.5Eta1 199811Fleet Leader Ft1 96000Fleet Leader Bx t1 50%B50 Life_t2 4800Beta2 3.5Eta2 5330Fleet Leader Ft2 4800Fleet Leader Bx t2 50%


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Model Comparison Case III: Very Different Betas on t1 & t2

• BVW more accurately estimates at a longer exposure than GLL, but shows more scatters in an early exposure


a1 / Eta2

BIC


t1 0.50 199811t2 3.50 5330

Input data


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Contour Plots Case III: Very Different Betas on t1 & t2

12 72.5% 75.2% 77.0% 78.5% 79.7% 80.7% 81.6% 82.4% 83.2% 83.8% 84.4% 85.0%11 63.8% 67.3% 69.8% 71.7% 73.3% 74.6% 75.8% 76.9% 77.8% 78.7% 79.5% 80.2%10 55.0% 59.3% 62.4% 64.8% 66.7% 68.4% 69.9% 71.2% 72.4% 73.5% 74.5% 75.4%9 46.6% 51.8% 55.4% 58.2% 60.6% 62.6% 64.3% 65.9% 67.3% 68.6% 69.7% 70.8%8 39.2% 45.1% 49.2% 52.4% 55.1% 57.4% 59.4% 61.2% 62.8% 64.2% 65.6% 66.8%7 33.2% 39.7% 44.2% 47.7% 50.7% 53.2% 55.4% 57.3% 59.1% 60.7% 62.1% 63.5%6 28.7% 35.5% 40.4% 44.2% 47.3% 50.0% 52.3% 54.4% 56.3% 58.0% 59.6% 61.0%5 25.5% 32.7% 37.7% 41.7% 44.9% 47.8% 50.2% 52.4% 54.3% 56.1% 57.8% 59.3%4 23.5% 30.9% 36.0% 40.1% 43.5% 46.3% 48.9% 51.1% 53.1% 54.9% 56.6% 58.2%3 22.4% 29.9% 35.1% 39.2% 42.7% 45.6% 48.1% 50.4% 52.4% 54.3% 56.0% 57.6%2 21.9% 29.4% 34.7% 38.9% 42.3% 45.2% 47.8% 50.1% 52.2% 54.0% 55.7% 57.3%1 21.7% 29.3% 34.6% 38.8% 42.2% 45.1% 47.7% 50.0% 52.1% 53.9% 55.6% 57.2%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 38.2% 46.7% 52.0% 56.0% 59.1% 61.6% 63.8% 65.7% 67.4% 68.8% 70.2% 71.4%11 37.7% 46.0% 51.4% 55.3% 58.4% 61.0% 63.1% 65.0% 66.7% 68.2% 69.5% 70.7%10 37.1% 45.4% 50.7% 54.6% 57.7% 60.2% 62.4% 64.3% 66.0% 67.4% 68.8% 70.0%9 36.5% 44.7% 49.9% 53.8% 56.9% 59.4% 61.6% 63.5% 65.2% 66.6% 68.0% 69.2%8 35.8% 43.9% 49.1% 52.9% 56.0% 58.5% 60.7% 62.6% 64.3% 65.8% 67.1% 68.3%7 35.0% 43.0% 48.1% 52.0% 55.0% 57.5% 59.7% 61.6% 63.2% 64.7% 66.1% 67.3%6 34.1% 42.0% 47.0% 50.8% 53.9% 56.4% 58.5% 60.4% 62.1% 63.6% 64.9% 66.1%5 33.1% 40.8% 45.8% 49.5% 52.5% 55.0% 57.2% 59.0% 60.7% 62.2% 63.5% 64.7%4 31.8% 39.4% 44.3% 47.9% 50.9% 53.4% 55.5% 57.3% 59.0% 60.5% 61.8% 63.0%3 30.3% 37.6% 42.3% 45.9% 48.8% 51.2% 53.3% 55.2% 56.8% 58.3% 59.6% 60.8%2 28.2% 35.2% 39.7% 43.2% 46.0% 48.3% 50.4% 52.2% 53.8% 55.2% 56.5% 57.8%1 25.0% 31.3% 35.5% 38.7% 41.3% 43.6% 45.5% 47.2% 48.7% 50.1% 51.4% 52.6%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

12 44.5% 49.4% 53.0% 56.0% 58.5% 60.7% 62.7% 64.4% 66.0% 67.5% 68.9% 70.1%11 43.3% 48.3% 52.0% 55.0% 57.6% 59.9% 61.9% 63.7% 65.3% 66.8% 68.2% 69.5%10 42.0% 47.1% 50.9% 54.0% 56.7% 59.0% 61.0% 62.9% 64.5% 66.1% 67.5% 68.8%9 40.7% 45.9% 49.8% 52.9% 55.6% 58.0% 60.1% 62.0% 63.7% 65.3% 66.7% 68.1%8 39.2% 44.6% 48.5% 51.8% 54.6% 57.0% 59.1% 61.1% 62.8% 64.4% 65.9% 67.3%7 37.7% 43.1% 47.2% 50.6% 53.4% 55.9% 58.1% 60.1% 61.9% 63.5% 65.0% 66.4%6 36.0% 41.6% 45.8% 49.2% 52.1% 54.7% 56.9% 59.0% 60.8% 62.5% 64.1% 65.5%5 34.1% 39.9% 44.2% 47.7% 50.7% 53.4% 55.7% 57.8% 59.7% 61.4% 63.0% 64.5%4 32.1% 38.0% 42.5% 46.1% 49.2% 51.9% 54.3% 56.5% 58.4% 60.2% 61.9% 63.4%3 29.7% 35.9% 40.5% 44.2% 47.4% 50.2% 52.7% 54.9% 57.0% 58.8% 60.5% 62.1%2 26.9% 33.3% 38.1% 42.0% 45.3% 48.2% 50.8% 53.1% 55.3% 57.2% 59.0% 60.6%1 23.3% 30.0% 35.0% 39.2% 42.6% 45.7% 48.4% 50.8% 53.1% 55.1% 57.0% 58.7%

t2/ t1 1 2 3 4 5 6 7 8 9 10 11 12

• Original Model

• GLL

• BVW

• Both GLL & BVW show huge errors especially at extreme t2 exposure regions




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Summary Introduced to GE Power Services, Lifecycle

Reliability Engineering. Overviewed Weibull & GLL models. Compared BVW model with other survival models. BVW models showed superior risk estimation

performance than GLL models with a limited range of the shape parameter.

BVW models have potential to support for simplification and automation of models update.


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Questions

Thank you for your attention.

Do you have any questions?

Appendix


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References1. http://environment.nationalgeographic.com/environment/energy/great-

energy-challenge/world-electricity-mix/ 2. http://www.bp.com/content/dam/bp/pdf/energy-economics/energy-outlook-

2016/bp-energy-outlook-2015.pdf3. https://powergen.gepower.com/applications/utility-power-generation.html4. http://reliawiki.org/index.php/Parameter_Estimation5. https://en.wikipedia.org/wiki/Maximum_likelihood6. http://www.ReliaSoft.com/newsletter/2q2001/general_loglinear.htm7. https://en.wikipedia.org/wiki/Bayesian_information_criterion8. Johnson, Richard A.; Evans, James W.; Green, David W., Some bivariate

distributions for modeling the strength properties of lumber, Research Paper FPL, RP-575 : http://www.fpl.fs.fed.us/documnts/fplrp/fplrp575.pdf


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Acronym HRSG: Heat Recovery Steam Generator RCA: Root Cause Analysis RAM: Reliability, Availability & Maintenance CBM: Condition Based Maintenance MSA: Multi-year Services Agreement FEA: Finite Element Analysis PDF: Probability Density Function CDF: Cumulative Distribution Function GLL: General Log Linear IPL: Inverse Power Law 2-P Weibull: Two Parameter Weibull BVW: Bivariate Weibull AP: Aging Parameter


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Ken Yoon

IAM&D, Korea (1997-1998)• Research Scientist: induction motor heat

transfer using telemetry• Lecturer: Engr. Mathematics, Heat Power

GE P&W (2013-2015)• Senior Reliability Engineer, Risk

& Reliability, UOM & Fallout models, RAMDeck & RAM Analysis & DFR, & online CBM

SD School of Mines & Technology (2005-2010)• Assistant Professor: mechatronics, CAD-CAM, fluid

mechanics, thermal systems design, & advanced engineering analysis, etc.

Education• BS Mechanical Engineering, Seoul

National University (SNU), Korea, 1990

• MS Mech. Engr., SNU, Korea, 1992• PhD Mech. Engr., SNU, Korea, 1997

Certification• GE Reliability Practitioner Program

Lecturer • GE Certified Analytics Engr., • ASQ Certified Reliability Engr.

GE Energy (2011-2013)• Lead Engineer, ATO-WS & WFE-S:

Program manager for NPI’s (FSA models & CMS) & NTI’s

CCM, Univ. of Delaware (1998-2005)• Research Associate: composite materials, structures,

and manufacturing processes, health monitoring system

GE Power (Oct. 2015~)• Intelligent Fleet & Parts Forecasting

Leader• [email protected]

2016 ars north america presentation · blue room, session 14 2016 ars north america begins at 2:20...

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