1 Introduction.- 2 Basic probability theory.- 3 Application of the binomial distribution.- 4 Network modelling and evaluation of simple systems.- 5 Network modelling and evaluation of complex systems.- 6 Probability distributions in reliability evaluation.- 7 System reliability evaluation using probability distributions.- 8 Discrete Markov chains.- 9 Continuous Markov processes.- 10 Frequency and duration techniques.- 11 Approximate system reliability evaluation.- 12 Systems with non-exponential distributions.- 13 Monte Carlo simulation.- 14 Epilogue.- Appendices.- Appendix 1—Rules of Boolean algebra.- Appendix 2—Probability distributions.- A2.1 The normal distribution function.- A2.2 Ordinate heights of the normal distribution.- A2.4 Kolmogorov-Smirnov critical values.- Appendix 3—Elementary matrix algebra.- A3.1 Concepts of matrices.- A3.2 Square matrix.- A3.3 Column matrix (or vector).- A3.4 Row matrix (or vector).- A3.5 Transposed matrix.- A3.6 Diagonal matrix.- A3.7 Identity (or unit) matrix.- A3.8 Symmetric matrix.- A3.9 Determinant of a matrix.- A3.10 Co-factors.- A3.11 Evaluation of determinants.- A3.12 Addition of matrices.- A3.13 Subtraction of matrices.- A3.14 Multiplication of matrices.- A3.15 Multiplication by a constant.- A3.16 Inverse of a matrix.- A3.17 Solution of simultaneous equations.- A3.18 Cramer’s rule for solving simultaneous equations.- Appendix 4—Differential equations and Laplace transforms.- A4.1 Differential equations.- A4.2 Laplace transforms.- A4.3 Solving differential equations using Laplace transforms.- Appendix 5—Confidence levels and limits.- A5.1 Introduction.- A5.2 Unavailability at selected confidence levels.- A5.3 Failure rate at selected confidence levels.- A5.4 Conclusions.- Problems.- References.- Solutions.