One possible approach to life extension of aerospace components is to take those parts or subsystems that have run the limited initial life estimate and been removed from service, and to operate them in simulated service for periods of time beyond the initial life estimate. It is often the case that such testing must be suspended before the part reaches the point of actual failure. A need therefore exists to use such suspended test data to infer a life limit.
The standard deviation of the estimated life can generally be reliably quantified by applying results from laboratory material tests and information on the variability of the unit’s dimensions. The derived life estimate must therefore be consistent with the known standard deviation.
The problem is structured as a variational one, that is, a problem of finding the values of a set of variables — the hypothetical duration of the individual suspended tests if they had been continued to failure — subject to the constraints that the period of continuation must be equal to or greater that zero, and that the standard deviation of the average value of the life of the sample set be equal to the known, predetermined value. The problem is made determinate by applying the conservative requirement that calculated average life of the sample set be the lowest possible value.
Although the problem is nonlinear and not amenable to traditional linear programming solution, a very simple pair of algorithms have been identified which permit exact solution for all ranges of objective standard deviation. Solutions to typical problems are given to illustrate the utility of the procedure.