Spacecraft Reliability and Multi-State Failures

Joseph Homer Saleh and Jean-François Castet, Georgia Institute of Technology, USA

• 1 On time, reliability, and spacecraft 11.1 On time and reliability 11.1.1 Reliability: from the word to the engineering discipline 11.1.2 Brief (pre)history of reliability engineering: the enablers and the catalyst 21.2 On spacecraft and reliability: early studies 41.2.1 Overview of early spacecraft reliability and on-orbit failure studies 61.2.2 Beyond the failure rate emphasis in spacecraft reliability studies 71.3 Book organization 72 Nonparametric reliability analysis of spacecraft failure data 92.1 Introduction 92.2 Database and data description 102.3 Nonparametric analysis of spacecraft failure data 112.3.1 Complete versus censored data set 112.3.2 Empirical reliability function from a complete data set 132.3.3 Kaplan–Meier estimator 142.3.4 Kaplan–Meier plot of satellite reliability 162.4 Confidence interval analysis 172.5 Discussion and limitation 202.A Appendix 213 Parametric analysis and Weibull modeling of spacecraft reliability 233.1 Weibull distribution: an overview 243.2 Probability plots or graphical estimation 253.2.1 Procedure 253.2.2 Weibull plot and Weibull fit of spacecraft reliability 253.2.3 Advantages and limitations of the graphical estimation method 263.3 Maximum likelihood estimation (MLE) 273.3.1 MLE derivation of a Weibull distribution 283.3.2 MLE Weibull fit for spacecraft reliability 303.4 Comparative analysis of the spacecraft reliability parametric fits 313.4.1 MLE versus graphical estimation Weibull fits 313.4.2 MLE Weibull versus MLE lognormal fits 333.5 Finite mixture distributions 333.5.1 Methods for estimating parameters of mixture distributions 343.5.2 The 2-Weibull mixture distribution of spacecraft reliability 363.6 Comparative analysis of the single versus the mixture distribution Weibull fits 384 Data specialization: statistical analysis of spacecraft reliability by orbit and mass categories 434.1 Introduction 434.2 Data description and mass categorization 454.3 Nonparametric analysis of satellite reliability by mass category 464.4 Parametric analysis of satellite reliability by mass category 484.4.1 MLE of single Weibull fit 494.4.2 Mixture distributions 514.4.3 Failure rates 544.5 Orbit characterization 564.6 Nonparametric analysis of spacecraft reliability by mass and orbit category 574.7 Parametric analysis of satellite reliability by mass and orbit category 604.8 Hypotheses for causal explanations 614.8.1 Testing 634.8.2 Procurement and parts selection 634.8.3 Factors intrinsically related to the design of the spacecraft 644.8.4 Factors related to the space environment 654.A Appendix: Tabular data and confidence interval analysis 674.A.1 Tabular data for the nonparametric reliability results in Figure 4.1 and Figure 4.8 674.A.2 Confidence interval analysis 685 Spacecraft subsystem reliability 715.1 Spacecraft subsystem identification 715.2 Nonparametric reliability analysis of spacecraft subsystems 725.3 Weibull modeling of spacecraft subsystem reliability 755.4 Comparative analysis of subsystem failures 786 Time to anomaly and failure of spacecraft subsystems: exploratory data analysis 836.1 Introduction 836.2 Anomaly and failure events 846.3 Distribution of anomalies and failure events by subsystem 866.4 Time to anomaly and failure of spacecraft subsystems 907 Multi-state failure analysis of spacecraft subsystems 977.1 Introduction 977.2 Setting the stage: multi-state failure analysis and the state transition diagram 997.3 Nonparametric analyses of spacecraft subsystems’ multi-state failures 1017.3.1 Censored data and the Kaplan–Meier estimator 1017.3.2 Confidence interval analysis 1037.3.3 Nonparametric estimations of the conditional probabilities of transitioning between states 1037.4 Parametric analyses of spacecraft subsystems’ multi-state failures 1087.4.1 MLE Weibull fit of the nonparametric estimates ˆPi j 1087.4.2 Testing the parametric models of the multi-state failure analysis 1097.5 Comparative reliability and multi-state failure analysis of spacecraft subsystems 1137.5.1 Gyro subsystem 1137.5.2 Thruster subsystem 1157.5.3 TTC subsystem 1177.A Appendix 1188 Toward survivability analysis of spacecraft and space-based networks 1238.1 Introduction 1238.2 Overview of survivability and resiliency 1248.2.1 On survivability 1258.2.2 On resiliency 1268.2.3 Comparing survivability and resiliency 1278.3 Survivability framework 1288.4 Introduction to stochastic Petri nets (SPNs) 1298.5 SPNs for spacecraft modeling and survivability analysis 1318.5.1 Testing the SPN models 1388.5.2 Monte Carlo simulation runs for the SPN models 1408.5.3 Results 1418.5.4 Limitations 144A.8 Appendix: SPN model of the space-based network (SBN) in Figure 8.6 and its schematic explanation 146Epilogue 149Appendix A Geosynchronous communication satellites: system reliability and subsystem anomalies and failures 151A.1 Part I: System reliability analysis 151A.1.1 Nonparametric analysis of satellite failure data 152A.1.2 Confidence interval analysis 153A.1.3 Parametric fits of geosynchronous communication satellite reliability 155A.2 Part II: Subsystem anomalies and failures 160A.2.1 Subsystem health scorecard 161A.2.2 Comparative analysis of subsystem health scorecard 164Appendix B Electrical power subsystem: comparative analysis of failure events in LEO and GEO 179B.1 Introduction 179B.2 Database, sample analyzed, and classes of failure events 180B.3 Brief literature review 181B.3.1 Space environment in LEO and GEO 181B.3.2 Operational constraints on the EPS in LEO and GEO 182B.4 Reliability and multi-state failure analyses of the EPS 182B.5 Comparative analysis of the EPS failure behaviour in LEO and GEO 185B.6 Conclusion 193References 195Index 201