Contemporary manufacturers face tremendous commercial pressures to assemble works of high reliability, defined as 'the probability of the product performing its role under the stated conditions and over a specified period of time'. A start-up demonstration testing approach (in terms of runs, frequency, scans), is frequently used as a proxy for this critical concept of reliability. Often it is the foundation on which the decision to accept or reject a unit is made. Reliability Analysis and Plans for Successive Testing: Start-up Demonstration Tests and Applications discusses all past and recent developments on start-up demonstration tests in the context of current numerical and illustrative examples to clarify available methods for distribution theorists and applied mathematicians dealing with control problems. Since the criteria used in start-up demonstration tests are closely related to general pattern waiting problems, defined on sequences of discrete random variables and the authors provide a discussion about the relation between the theory of start-up demonstrating testing with some well-known discrete distributions. Throughout, while describing all the developments, the authors will also comment on the panorama of open problems with issues of further interest.