Various kinds of order effects are introduced as well as effects of three-way deadlocks to account for the departues from the Bradley-Terry model for paired comparisons. The parameterization is made in terms of a three-way contigency table. A method of testing an appropriate sequence of null hypothesis is given. The maximum likelihood estimators for the cell frequencies under each hypothesis are obtained by a general iterative scaling procedure for contigency tables.

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In the analysis of field life data, the competing risks model has been used for the inference of characteristics of a particular failure mode. In this paper, the reliability function of one failure mode under competing risks model has been estimated by nonparametric method from incomplete data where some of the failure times are observed without observing the cause failure. Assuming that failure rate functions of all failure modes are continuous and smooth, several iterative estimation methods which are application of EM algorithm are proposed, and the properties of these estimators are investigated by Monte Carlo simulation. The result shows that by using the proposed estimation methods the failure time data without observing the cause of failure can contribute in the improvement of efficiencies.

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