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We address the problem of minimax detecting and isolating abrupt changes in random signals. The criterion of optimality consists in minimizing the maximum mean detection/isolation delay for a given maximum probability of false isolation and mean time before a false alarm. It seems that such a criterion has many practical applications, especially for safety-critical applications, in monitoring dangerous industrial processes and also when the decision should be made in a hostile environment. The redundant strapdown inertial reference unit integrity monitoring problem is discussed. An asymptotic lower bound for the mean detection/isolation delay is given.