KopyKitab. Quality, Reliability and Maintainability. Statistical Methods for. K. Muralidharan A. Syamsundar. Maintainability

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1 Statistical Methods for Quality, Reliability and Maintainability LSL Design width USL Bathtub failure rate curve Maintainability Time K. Muralidharan A. Syamsundar

2 Statistical Methods for Quality, Reliability and Maintainability

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4 Statistical Methods for Quality, Reliability and Maintainability K. MURALIDHARAN Professor and Head, Department of Statistics The Maharaja Sayajirao University of Baroda Vadodara A. SYAMSUNDAR Deputy General Manager (Research and Development) Visakhapatnam Steel Plant Visakhapatnam New Delhi

5 STATISTICAL METHODS FOR QUALITY, RELIABILITY AND MAINTAINABILITY K. Muralidharan and A. Syamsundar 2012 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus, New Delhi and Printed by Raj Press, New Delhi

6 To Our Parents

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8 Preface xv Acknowledgements xvii PART I QUALITY vii Contents 1. Basics of Quality Introduction Deming s Quality Philosophy Crosby s Quality Philosophy Juran s Quality Philosophy Taguchi Quality Philosophy Necessity of Quality Voice of Customer Quality Function Deployment Quality Metrics and Measurements Quality Metrics Quality Measurements Data Types Nominal Scale Ordinal Scale Interval Scale Ratio Scale Measurement System Analysis (MSA) Gage R&R Acceptance Criteria for MSA 22

9 viii Contents Interpretation of MSA Results Assessing Bias of Nominal/Ordinal Data Achieving Quality Quality Assurance Quality Policy Quality System Quality Planning Quality Audits Quality Budgets Quality Circles Quality Control Managing Quality Total Quality Management KAIZEN Approach S Approach ISO Exercises 36 References Quality and Process Quality Versus Process Process Understanding Process Management Information about the Process Process Orientation Process Model: SIPOC Process Analysis Process Data Collection Objectives of Data Collection Visualisation of Data Process Accuracy Measures Process Variations Types of Variation Significance of Measuring Variation Process Precision Measures Measures of Symmetry and Shape Quality and Process Control Process Control Using Variable Data Process Control Using Attributes Data 79 Exercises 85 References 88

10 Contents ix 3. Process Capability and Quality Introduction Measuring Uncertainty Random Experiment and Probability Probability Distributions Mathematical Expectation and Variance Uncertainty Models Binomial Distribution Poisson Distribution Normal Distribution Process Capability Indices Process Potential Index (C p Index) Process Performance Index (C pk Index) 107 Exercises 110 References Process Improvement and Quality Process Improvement Improving a Process Data Six Sigma Lean Six Sigma Capability Maturity Model Integration 124 Exercises 127 References Process Data Management Data Management Data Warehousing Data Warehouse Architecture Data Warehouse Implementation Data Mining 131 Exercises 133 References 133 PART II RELIABILITY 6. Basics of Reliability Introduction Quality and Reliability Reliability Engineering 138

11 x Contents Software Reliability Reasons for Collecting Reliability Data Reliability Requirements Reliability Modeling Reliability Test Requirements Life Testing and Reliability Need for Life Test Accelerated Life Testing 145 Exercises 146 References Reliability Tools Reliability Data Repairable System and Non-repairable System Data Likelihood Principle Censoring Concepts Type-1 Censoring (Time Censoring) Type-2 Censoring (Failure Censoring) Random Censoring Hybrid Censoring Progressive (Multiply) Censoring Bathtub Curves Mean Time to Failure Mean Time Between Failures 155 Exercises 156 References Reliability Models and Inferences Statistical Inference Discrete Failure Time Models and Inferences Continuous Failure Time Models and Inferences Exponential Distribution Weibull Distribution Gamma Distribution Lognormal Distribution Logistic Distribution Beta Distribution Smallest Extreme Value Distribution Largest Extreme Value Distribution Mixture Distributions 187 Exercises 189 References 191

12 Contents xi 9. Reliability Assessment Reliability Plotting PP Plots and QQ Plots Probability Plots Total Time on Test (TTT) Plots Reliability Testing Testing of Hypothesis Reliability Growth Testing Test for Exponentiality Reliability Prediction Confidence Interval Estimation Kaplan Meir Estimation 211 Exercises 214 References Reliability Improvement Introduction Reliability Design Failure Mode and Effects Analysis FMEA Implementation Uses of FMEA Advantages of FMEA Fault Tree Analysis Application of FTA Steps to FTA Environmental Stress Screening 226 Exercises 229 References Repairable System Reliability Repairable System Data Software Reliability Repairable System Reliability Characteristics Repairable System Models Homogeneous Poisson Process Non-homogeneous Poisson Process Renewal Process Power Law Process Modulated Power Law Process Proportional Intensity Models Test for Trend 244 Exercises 246 References 247

13 xii Contents Part III MAINTAINABILITY 12. Basics of Maintainability Introduction Systems, Maintenance, Downtime and Maintainability Systems Maintenance Downtime Maintainability Brief Review of History of Maintainability Maintainability Study Sources Present Study Maintainability Measures and Prediction Maintainability Assessment Maintainability Design and Testing 262 Exercises 263 References Maintainability Measures and Prediction Introduction Maintenance Work, Task, Activity and Schedule Characteristics of Maintenance Activities Maintainability Measures Maintainability Function Maintainability Density Repair Rate Mean Time to Repair Variance of Time to Repair Median Time to Repair Maximum Time to Repair Most Likely Time to Repair or Mode Maintainability Models Exponential Distribution Gamma Distribution Weibull Distribution Normal Distribution Lognormal Distribution Maintenance Task Schedules and Maintainability Activity Block Diagrams Sequential Maintenance Task Simultaneous Maintenance Task Combined Maintenance Task 279

14 Contents xiii 13.7 Expression for Obtaining the Maintainability Measures of a Maintenance Task Maintainability Measures for Sequential Maintenance Task Maintainability Measures for Simultaneous Maintenance Task Maintainability Measures for Combined Maintenance Task Maintainability Measures Considering Covariates Proportional Repair Model Non-proportional Repair Model 285 Exercises 286 References Maintainability Assessment Introduction Empirical Determination of Maintainability Measures of a Maintenance Activity and Identifying Candidate Distributions from Field Data Empirical Determination of Maintainability Measures Identifying Candidate Distributions from Empirical Values of Maintainability Measures Graphical Determination of Maintainability Measures of a Maintenance Activity from Field Data Exponential Distribution Gamma Distribution Weibull Distribution Normal Distribution Lognormal Distribution Analytical Determination of Maintainability Measures of a Maintenance Activity from Field Data Exponential Distribution Gamma Distribution Weibull Distribution Normal Distribution Lognormal Distribution Determination of Maintainability Measures of a Maintenance Task Sequential Maintenance Task Simultaneous Maintenance Task Maintainability Measures for Combined Maintenance Task Goodness of Fit Tests for Maintainability Distributions of a Maintenance Activity from Field Data Kolmogorov Smirnov Statistic Cramer von Mises Statistic Watson Statistic 309

15 xiv Contents Anderson Darling Statistic Greenwood Statistic Conclusion 312 Exercises 312 References Maintainability Design and Testing Introduction Maintainability Design Maintainability Design Process Maintainability Design Features Maintainability Tools Cause and Effect Diagram Fault Tree Analysis Failure Modes and Effects Analysis Maintainability Allocation Failure Rate Complexity Method Variation of the Failure Rate Complexity Method Statistically-based Allocation Method Equal Distribution Method Maintainability Design Predictions Maintainability Testing General Principles and Methods Data Collection Data Transformation Tests for Assessing the Maintainability Characteristics Conclusion 329 Exercises 329 References 330 Appendixes Cumulative Standard Normal Distribution Chi-Squared Values for a Specified Right Tail Area Values of t for a Specified Right Tail Area Values of F for a Specified Right Tail Area F 0.01 n1,n Values of F for a Specified Right Tail Area F n1,n Values of F for a Specified Right Tail Area F 0.05 n1,n Values of F for a Specified Right Tail Area F 0.10 n1,n Values of F for a Specified Right Tail Area F 0.25 n1, n Index

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