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The basic model starts with three stochastic processes satisfying y(t) = x(t) + z(t). Observations are made on the y-process from which inferences are made about the production process, x(t). The z-process constitutes noise. For each unit of time that x(t) = x the income is i(x). The producer, at a cost in both time and money, can repair the y-process, i.e., bring its value back to zero. Continuous surveillance at no cost and intermittent surveillance with a fixed cost for each observation are considered, When the x- and z-processes are independent Poisson processes, it is shown that the strategies which maximize the average income per unit of time depend only on the last observed value of the y-process. Production is continued until the y-process exceeds a specified integer which depends on the economic parameters. When i(x) is nonincreasing and costly inspections are being made, the time between inspections decreases as a function of the last observed value of the y-process. The model is a generalization of the model used in Ref. [3]1 .

This paper concerns reliability theoretic problems involving systems of n components subject to stochastic hazard rates with independent increments. General methods are given for finding the probabilities of service at specified times and the joint characteristic function of the system failure time and the component hazard rates at the time of failure. These methods involve evaluation of integrals of the form where u′ is an n-component row vector, W(t) is an n by n matrix, and X(t) is an n-component stochastic process with independent increments and X(0) = 0. Some illustrative applications to one component systems and multicomponents systems in series and in parallel are presented.

Resuls are given for the case of a production process which behaves as a Wiener process. Some of the results applicable to the Wiener case as well as the Poisson case are stated; others are extended to the present case. (Author)