The diploma project is focused on investigating the reliability of multi-state technical systems. A summary of the basic conception of renewal theory and stochastic processes is given in this paper. The possibility of solving multi-state systems reliability by using Markov models or simulation is shown. The software Reliab. S. M. S. O. 1.0 was created for solving non-homogeneous series, parallel, series-parallel and parallel-series systems. Outputs of this software are described in chapter 10. This work also contains $\beta$-factor method and theory of common-cause failures. The diploma project was supported by project from MSMT of the Czech Republic no. 1M06047 "Centre for Quality and Reliability of Production" and by grant from Grant Agency of the Czech Republic (Czech Science Foundation) reg. no. 103/08/1658 "Advanced optimum design of composed concrete structures".

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Traditionally, source coding (data compression) and channel coding (error protection) are performed separately and sequentially, resulting in what we call a tandem (separate) coding system. In practical implementations, however, tandem coding might involve a large delay and a high coding/decoding complexity, since one needs to remove the redundancy in the source coding part and then insert certain redundancy in the channel coding part. On the other hand, joint source-channel coding (JSCC), which coordinates source and channel coding or combines them into a single step, may offer substantial improvements over the tandem coding approach. This thesis deals with the fundamental Shannon-theoretic limits for a variety of communication systems via JSCC. More specifically, we investigate the reliability function (which is the largest rate at which the coding probability of error vanishes exponentially with increasing blocklength) for JSCC for the following discrete-time communication systems: (i) discrete memoryless systems; (ii) discrete memoryless systems with perfect channel feedback; (iii) discrete memoryless systems with source side information; (iv) discrete systems with Markovian memory; (v) continuous-valued (particularly Gaussian) memoryless systems; (vi) discrete asymmetric 2-user source-channel systems. For the above systems, we establish upper and lower bounds for the JSCC reliability function and we analytically compute these bounds. The conditions for which the upper and lower bounds coincide are also provided. We show that the conditions are satisfied for a large class of source-channel systems, and hence exactly determine the reliability function. We next provide a systematic comparison between the JSCC reliability function and the tandem coding reliability function (the reliability function resulting from separate source and channel coding). We show that the JSCC reliability function is substantially larger than the tandem coding reliability function for most cases. In particular, the JSCC reliability function is close to twice as large as the tandem coding reliability function for many source-channel pairs. This exponent gain provides a theoretical underpinning and justification for JSCC design as opposed to the widely used tandem coding method, since JSCC will yield a faster exponential rate of decay for the system error probability and thus provides substantial reductions in complexity and coding/decoding delay for real-world communication systems. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-05-13 22:31:56.425