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Warranty forecasting of repairable systems is very important for manufacturers of mass produced systems. It is desired to predict the Expected Number of Failures (ENF) after a censoring time using collected failure data before the censoring time. Moreover, systems may be produced with a defective component resulting in extensive warranty costs even after the defective component is detected and replaced with a new design. In this paper, we present a forecasting method to predict the ENF of a repairable system using observed data which is used to calibrate a Generalized Renewal Processes (GRP) model. Manufacturing of products may exhibit different production patterns with different failure statistics through time. For example, vehicles produced in different months may have different failure intensities because of supply chain differences or different skills of production workers, for example.

We propose a new metamodeling method to characterize the output (response) random process of a dynamic system with random parameters, excited by input random processes. The metamodel can be then used to efficiently estimate the time-dependent reliability of a dynamic system using analytical or simulation-based methods. The metamodel is constructed by decomposing the input random processes using principal components or wavelets and then using a few simulations to estimate the distributions of the decomposition coefficients. A similar decomposition is also performed on the output random process. A kriging model is then established between the input and output decomposition coefficients and subsequently used to quantify the output random process corresponding to a realization of the input random parameters and random processes. What distinguishes our approach from others in metamodeling is that the system input is not deterministic but random.

Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling.

Design optimization often relies on computational models, which are subjected to a validation process to ensure their accuracy. Because validation of computer models in the entire design space can be costly, a recent approach was proposed where design optimization and model validation were concurrently performed using a sequential approach with both fixed and variable-size local domains. The variable-size approach used parametric distributions such as Gaussian to quantify the variability in test data and model predictions, and a maximum likelihood estimation to calibrate the prediction model. Also, a parametric bootstrap method was used to size each local domain. In this article, we generalize the variable-size approach, by not assuming any distribution such as Gaussian. A nonparametric bootstrap methodology is instead used to size the local domains. We expect its generality to be useful in applications where distributional assumptions are difficult to verify, or not met at all.

This paper presents a methodology to evaluate and optimize discrete event systems, such as an assembly line or a call center. First, the methodology estimates the performance of a system for a single probability distribution of the inputs. Probabilistic Reanalysis (PRRA) uses this information to evaluate the effect of changes in the system configuration on its performance. PRRA is integrated with a program to optimize the system. The proposed methodology is dramatically more efficient than one requiring a new Monte Carlo simulation each time we change the system. We demonstrate the approach on a drilling center and an electronic parts factory.