Nonparametric estimation with recurrent competing risks data.

Nonparametric estimators of component and system life distributions are developed and presented for situations where recurrent competing risks data from series systems are available. The use of recurrences of components' failures leads to improved efficiencies in statistical inference, thereby leading to resource-efficient experimental or study designs or improved inferences about the distributions governing the event times. Finite and asymptotic properties of the estimators are obtained through simulation studies and analytically. The detrimental impact of parametric model misspecification is also vividly demonstrated, lending credence to the virtue of adopting nonparametric or semiparametric models, especially in biomedical settings. The estimators are illustrated by applying them to a data set pertaining to car repairs for vehicles that were under warranty.

Parametric Estimation in a Recurrent Competing Risks Model.

A resource-efficient approach to making inferences about the distributional properties of the failure times in a competing risks setting is presented. Efficiency is gained by observing recurrences of the competing risks over a random monitoring period. The resulting model is called the recurrent competing risks model (RCRM) and is coupled with two repair strategies whenever the system fails. Maximum likelihood estimators of the parameters of the marginal distribution functions associated with each of the competing risks and also of the system lifetime distribution function are presented. Estimators are derived under perfect and partial repair strategies. Consistency and asymptotic properties of the estimators are obtained. The estimation methods are applied to a data set of failures for cars under warranty. Simulation studies are used to ascertain the small sample properties and the efficiency gains of the resulting estimators.

Asymmetric synthesis of 2-alkyl-substituted tetrahydroquinolines by an enantioselective aza-Michael reaction.

An optically active tetrahydroquinoline intermediate (5) was prepared in 8 steps from monoprotected ethylene glycol, using a Pd-catalysed aza-Michael reaction to induce chirality. This can be transformed into three Galipea alkaloids (angustureine, galipeine and cuspareine). The proximity of a benzyloxy group is found to exert profound effects in several steps of the synthesis.