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A competing risk model is developed for an individual who is subject to two risks of death or failure. One risk is the failure of a single organ which has a constant hazard rate. The other risk is the failure of a two organ system in which one of the two organs must survive in order that the system not fail. Each organ in this two organ system has a constant hazard rate, and the hazard rate increases when only one organ is working. The two risks are assumed to operate independently. Maximum likelihood estimating equations are developed along with the formulas for the large sample variance-covariance matrix of the requisite parameters.