Narrow Results

This paper provides an approach for assessing the uncertainty associated with the estimate of the availability of a two-state repairable system. During the design stage it is often necessary to allocate scarce testing resources among various components in an efficient manner. Although there are a variety of importance and uncertainty measures for the reliability of a system, there are limited measures for systems availability. This study attempts to fill the gaps on availability importance measures and provide insights for techniques to reduce the variance of a system-level availability estimate efficiently. The variance importance measure is constructed such that it provides a measure of the improvement in the variance of the system level availability estimate through the reduction of the variance of the various component availability estimates. In addition, a cost model is developed that trades-off cost and uncertainty. The measure is illustrated for five common system structures. Monte Carlo Simulation is used to illustrate the use of the assessment tools on a specific problem. Observations conclude that results are consistent with reliability importance measures.

A stable dynamic system implies safety, reliability, and satisfactory performance. However, the determination of stability is very difficult when the system is nonlinear and when the ever present uncertainties in the components must be considered. Herein a response-based approach that uses both system and time information obtained through singular value decomposition is presented to determine the stability space of nonlinear, uncertain dynamic systems: any approximating linearization of the nonlinearities has been obviated. The approach extends previous work for linear systems that invoked only the variability of the left singular vectors to predict stability. In the new approach, the variability of the right singular vectors is augmented to that of the left singular vectors and it is shown that a simulation time span, as short as two or three periods, is sufficient to predict stability over the entire life-time dynamics rendering the method very efficient. The stability space is a subset of the design space and its robustness is proportional to the tolerances assigned to the random design variables. Errors due to sampling size, time increments, and number of singular vectors used are controllable. The method can be implemented with readily available software. A study of a practical engineering system with different tolerances and different time spans shows the efficacy of the proposed approach.

We study the joint linear complexity of linear recurring multisequences, i.e., of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random linear recurring multisequences are determined. These results extend the corresponding results on the expectation and variance of the joint linear complexity of random periodic multisequences. Then we enumerate the linear recurring multisequences with fixed joint linear complexity and determine the generating polynomial for the distribution of joint linear complexities. The proofs use new methods that enable us to obtain results of great generality.

To select an optimal solution from the Pareto frontier based on decision-maker preference or responses priority may not be the best practice and may lead to unexpected results in practice due to the variability that is inherent to some optimal solutions. The assessment of optimal solutions reproducibility has been ignored so far, though this information is critical for the decision-maker in the optimal solution selection process. This chapter explores the Quality of Prediction metric usefulness to help him/her in selecting a solution for multiresponse problems. Results from two case studies show that quality of prediction value cannot be ignored.