Kalman filter, outliers, missing observations, time series analysis, 93E20, 62F35,

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An effective way of improving the reliability of a system is the allocation of active redundancy. Let 1 X , 2 X be independent lifetimes of the components 1 C and 2 C , respectively, which form a series system. Let denoteX is the lifetime of a redundancy (say S ) independent of 1 X and 2 X . That is C is preferred to 2 C for redundancy. In this paper we use the same criterion of Singh and Misra (1994) and we investigate the allocation of one active redundancy when it differs depending on the component with which it is to be allocated. We find sufficient conditions for the optimization which depend on the components and redundancies probability distributions. We also compare the allocation of two active redundancies (say 1 S and 2 S ) in two different ways, that is, 1 S with 1 C and 2 S with 2 C and viceversa. For this case the hazard rate order plays an important role. We obtain results for the allocation of more than two active redundancies to a kout-of-n systems. Note: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accesible. Keywords

Partial least squares (PLS) regression is a linear regression technique developed to relate many regressors to one or several response variables. Robust methods are introduced to reduce or remove the effect of outlying data points. In this paper, we show that if the sample covariance matrix is properly robustified further robustification of the linear regression steps of the PLS algorithm becomes unnecessary. The robust estimate of the covariance matrix is computed by searching for outliers in univariate projections of the data on a combination of random directions (Stahel-Donoho) and specific directions obtained by maximizing and minimizing the kurtosis coefficient of the projected data, as proposed by Peña and Prieto [1]. It is shown that this procedure is fast to apply and provides better results than other methods proposed in the literature. Its performance is illustrated by Monte Carlo and by an example, where the algorithm is able to show features of the data which were undetected by previous methods.

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