This paper considers the reliability analysis of systems whose operation time is managed with regard to criticality of faults. Several analysis approaches are proposed for the numerical probability analysis of one such operational scenario: FOTM (flight operation time management). The equations derived for the Markov chain based method are novel and their implementation in the tool SPNP (Stochastic Petri Net Program) could help in assessing the risk reduction due to FOTM. The analysis methods are quite general and can be applied to other similar situations where system-failure risk is decreased by operation-time management.

A family of algorithms is presented for transposition of a matrix which is stored sequentially on a file. The basic method is a variant of the balanced tape merge algorithm. The new balanced merge transposition method is compared to published methods.

Algorithms for in-place matrix transposition make use of the cyclic structure of the transposition mapping.A clear introduction to the process was given in 1958 by Windley [6].In 1968 Boothroyd presented ACM Algorithm 302 [1].Then in 1970 Laflin and Brefner presented ACM Algorithm 380 which they showed to be significantly faster than Algorithm 302 [4].In this paper a number of theoretical results describing the transposition process are derived.Algorithms 302 and 380 are described and applications of some of the theoretical results to accelerate both algorithms are described.Finally, experimental comparison of the performance of Algorithm 380 and the improved version is p~esentcd. Theoretical DevelopmentFortran conventions are assumed.The m ×n matrix A is stored by column in a vector ~ of adjacent storage locations.It is convenient to number components of from 0 to mn-1.Using this convention, matrix element A(I, J) is stored in yk, where k = m(J -1) W I -1.The transposition process moves the contents of y~ to y~ where p = n(I --1) ~-J --1.Thus the transposition process can be regarded as a permutation mapping acting on the indices of ~.The symbol ~r is used to denote this mapping, and the set of indices which ~ permutes is denoted by S. With this notation, S = [0, 1, ..., mn-1] and the formal equation r(k) = p indicates that the contents of storage location yk is moved to location y~ in the transposition process.The theoretical material is organized in three sections: additional notation, development of general properties of ~r, and description of the fixed point properties of ~',