Optimum Accelerated Life Testing Models With Time-

PRZEDMIOTEM OFERTY JEST KOD DOSTĘPOWY DO KSIĄŻKI ELEKTRONICZNEJ (EBOOK)

KSIĄŻKA JEST DOSTĘPNA NA ZEWNĘTRZNEJ PLATFORMIE. KSIĄŻKA NIE JEST W POSTACI PLIKU.

Today's manufacturers are under tremendous pressure to develop new technological and high reliability products in record time. This has motivated reliability engineers to evaluate the reliabilities of such products. Reliability testing under accelerated environment accelerated life testing helps to meet this challenge.This comprehensive and must-have edition provides a broad coverage of the optimal design of Accelerated Life Test Plans under time-varying stress loadings. It also focuses on the formulation of Accelerated Life Test Sampling Plans (ALTSPs) which integrate accelerated life tests with quality control technique of acceptance sampling plans. These plans help to determine optimal experimental variables such as appropriate stress levels, optimal allocation at each stress levels, stress change points, etc, depending on the stress loading scheme. ALTSPs determine optimal plans such that the producers' and consumers' risks are safeguarded.

• Autorzy: Preeti Wanti Srivastava
• Wydawnictwo: World Scientific Publishing
• Data wydania: 2017
• Wydanie:
• Liczba stron:
• Forma publikacji: ePub (online)
• Język publikacji: angielski
• ISBN: 9789813141278

• Cover Page
• Title
• Copyright
• Contents
• Preface
• Acronyms
• List of Figures
• List of Tables
• About the Author
• 1. Different Aspects of ALT Models
• 1.1 Introduction
• 1.1.1 Difference between ALT and ADT
• 1.1.2 Fully and Partially Accelerated Tests
• 1.1.3 Inspection Modes in Accelerated Testing
• 1.2 Types of Stress Loadings
• 1.2.1 Constant-Stress Loading
• 1.2.2 Step-Stress Loading
• 1.2.3 Progressive-Stress Loading
• 1.2.4 Cyclic-Stress Loading
• 1.2.5 Random-Stress Loading
• 1.2.6 Ramp-Constant Stress Loading
• 1.2.7 Ramp-Step Stress Loading
• 1.3 Types of Stresses
• 1.3.1 Mechanical Stresses
• 1.3.2 Electrical Stresses
• 1.3.3 Environmental Stresses
• 1.3.4 Usage Rate Acceleration
• 1.4 A Product’s Life Distribution
• 1.4.1 Reliability Metrics
• 1.4.2 Life Distribution Models
• 1.4.2.1 Exponential Distribution
• 1.4.2.2 Normal Distribution
• 1.4.2.3 Lognormal Distribution
• 1.4.2.4 Weibull Distribution
• 1.4.2.5 Extreme Value Distribution
• 1.4.2.6 Logistic Distribution
• 1.4.2.7 Log-Logistic Distribution
• 1.4.2.8 Truncated Logistic Distribution
• 1.4.2.9 Burr Type-XII Distribution
• 1.5 Fully ALT Models
• 1.5.1 Life-Stress Relationship
• 1.5.1.1 Arrhenius Relationship
• 1.5.1.2 Inverse Power Law Relationship
• 1.5.1.3 Eyring Relationship
• 1.5.1.4 Temperature–Humidity Relationship
• 1.5.1.5 Temperature–Nonthermal Relationship
• 1.5.1.6 Multivariable Relationship
• 1.6 Constant-Stress ALT Models
• 1.7 Proportional Hazards Based ALT Models
• 1.8 Proportional Odds (PO) Based ALT Models
• 1.9 ALT Models under Time-Varying Stress
• 1.9.1 Step-Stress ALT Model
• 1.9.2 Progressive-Stress ALT Model
• 1.10 Time-Varying Stress ALT Models with Log-Location-Scale Distribution
• 1.11 Relationship Between Constant-Stress, Step-Stress, and Progressive-Stress Loadings
• 1.12 PALT Models
• 1.12.1 Constant-Stress PALT Models
• 1.12.2 Time-varying Stress PALT Models: Step-Stress Set-Up
• 1.12.2.1 Tampered Failure Rate (TFR) Model: Step-Stress Set-Up
• 1.13 Data Types
• 1.14 Data Analysis Methods
• 1.15 Optimum Test Plans
• 1.15.1 Variance Optimality
• 1.15.2 D-Optimality
• 1.15.3 A-Optimality
• 1.16 Likelihood Function Formulation
• 1.16.1 Formulation of Likelihood Function with Time-Censored Data
• 1.16.2 Formulation of Likelihood Function with Failure-Censored Data
• 1.17 Sensitivity Analysis
• 1.18 Design of Fully ALT Models Under Continuous Inspection: A Review
• 1.18.1 Constant-Stress ALT Models
• 1.18.2 Step-Stress ALT Models
• 1.18.3 Progressive-Stress ALT Models
• 1.18.4 Modified-Stress ALT Models
• 1.18.5 ALT Models with Competing Causes of Failure
• 1.19 Design of PALT Models: A Review
• 1.19.1 Constant-Stress PALT Models
• 1.19.2 Step-Stress PALT Models
• 1.20 Design of ALT Models Under Periodic Inspection: A Review
• 2. Optimum Step-Stress Accelerated Life Test Models
• 2.1 Introduction
• 2.1.1 Notation
• 2.2 An Optimum Simple Log-Logistic Step-Stress ALT Model for Complete Data Set
• 2.2.1 Assumptions
• 2.2.2 Test Procedure
• 2.2.3 Life Distribution under Step-Stress
• 2.2.4 Maximum Likelihood Estimation
• 2.2.5 Fisher Information Matrix
• 2.2.6 Optimality Criterion
• 2.3 An Optimum Simple Log-Logistic Step-Stress ALT Model for Type-I Censored Data Set
• 2.3.1 Assumptions
• 2.3.2 Test Procedure
• 2.3.3 Life Distribution under Step-Stress
• 2.3.4 Maximum likelihood Estimation
• 2.3.5 Fisher Information Matrix
• 2.3.6 Optimum Plan
• 2.4 Testing of Hypotheses
• 2.4.1 For Complete Data Set
• 2.4.2 For Time-Censored Data Set
• 2.5 Numerical Examples
• 2.5.1 For Complete Data Set
• 2.5.2 For Time-Censored Data Set
• 2.6 Sensitivity Analysis
• 2.7 Summary
• 3. Optimum Step-Stress Partially Accelerated Life Test Plans with Type-I and Type-II Censoring
• 3.1 Introduction
• 3.1.1 Notation
• 3.1.2 Truncated Logistic Distribution under Step-Stress PALT
• 3.2 Optimum Time-Censored Step-Stress PALT Model
• 3.2.1 Assumptions
• 3.2.2 Test Procedure
• 3.2.3 Log-Likelihood Function
• 3.2.4 Fisher Information Matrix
• 3.2.5 Optimal Test Plan
• 3.3 Optimum Failure-Censored Step-Stress PALT Model
• 3.3.1 Case I: Number of Failures Pre-Specified
• 3.3.1.1 Assumptions
• 3.3.1.2 Test Procedure
• 3.3.1.3 Log-Likelihood Function
• 3.3.1.4 Fisher Information Matrix
• 3.3.1.5 Optimal Test Plan
• 3.3.2 Case II: Proportion of Units Failing Before Censoring Pre-Specified
• 3.3.2.1 Assumptions
• 3.3.2.2 Test Procedure
• 3.3.2.3 Log-Likelihood Function
• 3.3.2.4 Fisher Information Matrix
• 3.3.2.5 Optimal Test Plan
• 3.4 Numerical Examples
• 3.4.1 Type-I Censoring
• 3.4.1.1 Optimal Plan
• 3.4.1.2 Simulated Data
• 3.4.1.3 MLEs of the Design Parameters
• 3.4.1.4 Confidence Intervals
• 3.4.1.5 Graphical Goodness of Fit
• 3.4.1.6 Coverage Probabilities
• 3.4.2 Type-II Censoring: Case I Number of Failures Pre-Specified
• 3.4.2.1 Optimal Plan
• 3.4.2.2 Simulated Data
• 3.4.2.3 MLEs of the Design Parameters
• 3.4.2.4 Confidence Intervals
• 3.4.2.5 Graphical Goodness of Fit
• 3.4.2.6 Coverage Probabilities
• 3.4.3 Type-II Censoring: Case II Proportion of Censoring Pre-Specified
• 3.4.3.1 Optimal Plan
• 3.4.3.2 Simulated Data
• 3.4.3.3 MLEs of the Design Parameters
• 3.4.3.4 Confidence Intervals
• 3.5 Sensitivity Analysis
• 3.5.1 Type-I Censoring and Type-II Censoring (Case: I Number of Failures Pre-Specified)
• 3.5.2 Type-II Censoring (Case II: Proportion of Items Failing before Censoring Pre-Specified)
• 3.6 Comparative Study for Type-II Censoring (Case II Proportion of Items Failing Before Censoring Pre-Specified)
• 3.7 Summary
• 4. Optimum Ramp-Stress Fully Accelerated Life Test Plans Under Type-I Censoring
• 4.1 Introduction
• 4.1.1 Notation
• 4.1.2 Burr Type-XII Life Distribution
• 4.2 Optimum Multi-Level Ramp-Stress ALT Plan Without Stress Upper Bound
• 4.2.1 Assumptions
• 4.2.2 Test Procedure
• 4.2.3 Life Distribution under Multi-Level Ramp-Test without Stress Upper Bound
• 4.2.4 Log-Likelihood Function
• 4.2.5 Parameter Estimation
• 4.2.6 Fisher Information Matrix
• 4.2.7 Asymptotic Variance of the MLE of Logarithm of Quantile at Design Stress
• 4.3 Optimum Multi-Objective Ramp-Stress ALT Plan With Stress Upper Bound
• 4.3.1 Assumptions
• 4.3.2 Test Procedure
• 4.3.3 Life Distribution under Ramp-Stress with Stress Upper Bound
• 4.3.4 Log-Likelihood Function
• 4.3.5 Parameter Estimation
• 4.3.6 Fisher Information Matrix
• 4.3.7 Asymptotic Variance of the MLE of Logarithm of Quantile at Design Stress
• 4.4 Formulation of a Multi-Objective Optimization Problem
• 4.4.1 Optimization Problem For Multi-Level Ramp-Stress ALT Plan without Stress Upper Bound
• 4.4.2 Optimization Problem For Ramp-Stress ALT Plan with Stress Upper Bound
• 4.5 Numerical Examples
• 4.5.1 Multi-Level Ramp-Stress ALT Plan without Stress Upper Bound
• 4.5.1.1 Optimal Plan
• 4.5.1.2 Simulated Data
• 4.5.1.3 MLEs of the Design Parameters
• 4.5.1.4 Confidence Intervals
• 4.5.2 Ramp-Stress ALT Plan with Stress Upper Bound
• 4.5.2.1 Optimal Plan
• 4.5.2.2 Simulated Data
• 4.5.2.3 MLEs of the Design Parameters
• 4.5.2.4 Confidence Intervals
• 4.6 Sensitivity Analysis
• 4.7 Comparative Study
• 4.7.1 Multi-Level Ramp-Stress ALT Plan without Stress Upper Bound
• 4.7.2 Ramp-Stress ALT Plan with Stress Upper Bound
• 4.8 Summary
• 5. Optimum Fully Accelerated Life Test Plans with Modified Stress Loading Schemes under Type-I Censoring
• 5.1 Introduction
• 5.1.1 Notation
• 5.1.2 Burr Type-XII Lifetime Distribution
• 5.2 Optimum Multi-Objective Modified Step-Stress ALTPlan
• 5.2.1 Assumptions
• 5.2.2 Test Procedure
• 5.2.3 Life Distribution Under Modified Step-Stress
• 5.2.4 Log-Likelihood Function
• 5.2.5 Fisher Information Matrix
• 5.2.6 Asymptotic Variance of the MLEs of Logarithm of Quantile q at Design Stress
• 5.3 Optimum Multi-Objective Modified Constant-Stress ALT Plan
• 5.3.1 Assumptions
• 5.3.2 Test Procedure
• 5.3.3 Life Distribution under Modified Constant-Stress
• 5.3.4 Log-Likelihood Function
• 5.3.5 Fisher Information Matrix
• 5.3.6 Asymptotic Variance of the MLEs of the Logarithm of Quantile q at Design Stress
• 5.4 Formulation of a Multi-Objective Optimization Problem
• 5.4.1 Modified Step-Stress ALT Plan
• 5.4.2 Modified Constant-Stress ALT Plan
• 5.5 Numerical Examples
• 5.5.1 Modified Step-Stress ALT Plan
• 5.5.1.1 Optimal Plan
• 5.5.1.2 Simulated Data
• 5.5.1.3 MLEs of the Design Parameters
• 5.5.1.4 Confidence Intervals
• 5.5.2 Modified Constant-Stress ALT Plan
• 5.5.2.1 Optimal Plan
• 5.5.2.2 Simulated Data
• 5.5.2.3 MLEs of the Design Parameters
• 5.5.2.4 Confidence Intervals
• 5.6 Sensitivity Analysis
• 5.7 Comparative Study
• 5.7.1 Modified Step-Stress ALT Plan
• 5.7.2 Modified Constant-Stress ALT Plan
• 5.8 Summary
• 6. Optimum Time-Censored Step-Stress Fully ALT with Competing Risks For Failure
• 6.1 Introduction
• 6.1.1 Notation
• 6.2 Assumptions
• 6.3 Test Procedure
• 6.4 Life Distribution Under Step-Stress With Competing Failure Modes
• 6.5 Log-Likelihood
• 6.6 Fisher Information Matrix
• 6.7 Optimal Plan
• 6.8 Testing of Hypotheses
• 6.9 A Numerical Example
• 6.10 Sensitivity Analysis
• 6.11 Summary
• 7. Product Control and Accelerated Life Testing
• 7.1 Introduction
• 7.2 Product Control Metrics
• 7.3 Types of LSPS (RASPs)
• 7.4 LSPs (RASPs) by Attributes
• 7.4.1 Single Sampling RASP
• 7.4.2 Double Sampling Plan
• 7.4.3 Other LSPs By Attributes
• 7.5 LSPs by Variables
• 7.5.1 Variable Sampling Plans for a Process Parameter
• 7.5.1.1 Single Sampling Plan for a Process Parameter
• 7.5.2 Single Sampling by Variables for Proportion Nonconforming
• 7.5.2.1 X-method, k-method and M-method
• 7.5.3 Variable Repetitive Group Sampling Plan (VRGSP) for Proportion Nonconforming
• 7.5.4 Other VRASPs for Proportion Nonconforming
• 7.6 LSPs Based on a Cost Model
• 7.6.1 Types of Warranty Policies
• 7.6.2 Warranty Cost Under a Free Replacement Policy
• 7.6.3 Warranty Cost Under a Pro-Rata Replacement Policy
• 7.6.4 Warranty Cost Under a Combination Free and Pro-Rata Replacement Policy
• 7.6.5 Expected Total Cost for the Sampling Plan
• 7.6.6 Optimal LSP
• 7.7 Optimum Accelerated Life Tests Sampling Plans (ALTSPs)
• 7.8 Sensitivity Analysis
• 7.9 Design of ALTSP and PALTSP Models: A Review
• 7.9.1 Constant-Stress ALTSP Models
• 7.9.2 Time-Varying Stress ALTSP Models
• 7.9.3 RASP With Acceleration Factor
• 7.9.4 Constant-Stress PALTSP Models
• 7.9.5 Time-Varying Stress PALTSP Models
• 8. Optimum Time-Censored Ramp-Stress ALTSPs
• 8.1 Introduction
• 8.1.1 Notation
• 8.2 Assumptions
• 8.3 Log-Logistic Life Distribution Under Ramp-Stress Test
• 8.3.1 Log-Lifetime Distribution
• 8.4 Life Test Procedure
• 8.5 Lot Acceptance Sampling Procedure
• 8.6 Optimum Time-Censored Ramp-Stress ALTSP Under Variable SSP for Proportion Nonconforming
• 8.6.1 Log-Likelihood
• 8.6.2 Fisher Information Matrix
• 8.6.3 Asymptotic Variance of the Test Statistic
• 8.6.4 Operating Characteristic (OC) Function
• 8.6.5 Optimal Plans
• 8.7 Optimum Time-Censored Ramp-Stress ALTSP Under Variable SSP for the Process Parameter Based on Median Lifetime
• 8.7.1 Log-Likelihood
• 8.7.2 Asymptotic Variance of the Test Statistic
• 8.7.3 OC Function
• 8.7.4 Optimal Plan
• 8.8 Cost Structure
• 8.8.1 Cost Structure under Variable SSP for Proportion Nonconforming
• 8.8.2 Cost Structure under Variable SSP for the Process Parameter based on Median Lifetime
• 8.9 Design of Optimal Sampling Plans
• 8.9.1 Design of Optimization Problem for Time-Censored Ramp-Stress ALTSP under Variable SSP for Proportion Nonconforming
• 8.9.2 Design of Optimization Problem for Time-Censored Ramp-Stress ALTSP under Variable SSP for the Process Parameter based on Median Lifetime
• 8.10 Numerical Examples
• 8.10.1 Numerical Example on Time-Censored Ramp-Stress ALTSP under Variable SSP for Proportion Nonconforming
• 8.10.2 Numerical Example on Time-Censored Ramp-Stress under Variable SSP for the Process Parameter based on Median Lifetime
• 8.11 Sensitivity Analyses
• 8.12 Summary
• 9. Optimum Time-Censored Step-Stress PALTSP with Warranty Using Tampered Failure Rate Model
• 9.1 Introduction
• 9.1.1 Notation
• 9.2 The Model
• 9.2.1 Assumptions
• 9.2.2 Burr Type-XII Life Distribution
• 9.2.3 Log-Lifetime Distribution
• 9.2.4 Test Procedure
• 9.2.5 Lot Acceptance Sampling Procedure
• 9.2.6 Life Distribution under TFR Model
• 9.3 Parameter Estimation
• 9.4 Fisher Information Matrix
• 9.5 Asymptotic Variance of Test Statistic
• 9.6 Operating Characteristic (OC) Function
• 9.7 Cost Consideration
• 9.7.1 Expected Warranty Cost Per Item
• 9.7.2 Expected Total Cost Per Lot
• 9.8 Formulation of an Optimization Problem
• 9.8.1 Algorithm
• 9.9 Numerical Example
• 9.10 Sensitivity Analysis
• 9.11 Summary
• 10. Optimum Time-Censored Step-Stress PALTSP with Competing Causes of Failure Using Tampered Failure Rate Model
• 10.1 Introduction
• 10.1.1 Notation
• 10.2 Model
• 10.2.1 Assumptions
• 10.2.2 Test Procedure
• 10.2.3 Model Formulation
• 10.3 Lot Acceptance Procedure
• 10.3.1 SSP
• 10.3.2 VRGSP
• 10.4 Log-Likelihood
• 10.5 Fisher Information Matrix
• 10.6 Operating Characteristic (OC) Function
• 10.7 Formulation of an Optimization Problem
• 10.7.1 Bilevel Programming: VRGSP
• 10.7.2 Bilevel Programming: SSP
• 10.8 Illustrative Example
• 10.9 Sensitivity Analyses
• 10.10 Summary
• Appendix A
• A.0 Truncated Distributions and Order Statistics
• A.01 Truncated Distributions
• A.02 Order Statistics
• A.1 Exponential Distribution as a Limiting Case of the Burr Type-XII Distribution
• A.2 Weibull Distribution as a Limiting Case of the Burr Type-XII Distribution
• A.3 Calculations of the Elements of the Fisher Information Matrixin 3.2.4
• A.4 Calculations of Elements of the Fisher Information Matrix Given in 3.3.1.4
• A.5 Calculations of the Elements of the Fisher Information Matrix Given in Section 3.3.2.4
• A.6 Justification for the Use of Linear Cumulative Exposure Model in the Burr Type-XII Distribution in Section 4.2.3
• A.7 Justification for the Use of Linear Cumulative Exposure Model in the Burr Type-XII Distribution in Section 4.3.3
• A.8 Calculations of the Elements of the Fisher Information Matrix Given in Section 4.2.6
• A.9 Calculations of the Elements of the Fisher Information Matrix in Section 4.3.6
• A.10 Justification for the Use of Linear Cumulative Exposure Model in the Burr Type-XII Distribution in Section 5.2.3
• A.11 Calculations of the Elements of the Fisher Information Matrix in Section 5.2.5
• A.12 Justification for the Use of Linear Cumulative Exposure Model in the Burr Type-XII Distribution in Section 5.3.3
• A.13 Calculation of the Elements of the Fisher Information Matrix Given in Section 5.3.5
• Appendix B
• B.1 Calculations of the Elements of the Fisher Information Matrix Given in Section 8.6.2
• B.2 Calculations of the Asymptotic Variance of the Test Statistic Given in Section 8.6.3 for Time-Censored Case
• B.3 Calculations of the Elements of the Fisher Information Matrix Given in Section 9.4
• B.4 Calculation of the Asymptotic Variance of the Test Statistic Given in Section 9.5
• B.5 Calculations of the Second Partial Derivatives and Elements of the Fisher Information Matrix Given in Section 10.5
• B.6 Calculation of the Asymptotic Variance of the Estimated Value of Mean Lifetime, µ, Given in Sections 10.3.1 and 10.3.2
• Appendix C
• C.1 Bilevel Programming
• Appendix D
• D.1 Tampered Failure Rate (TFR) Model under Constant-Stress Setup
• References
• Index

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