Abstract
When a new software is produced it is usually tested for failure several times in succession (whenever a failure is detected the software is rectified and tested again for failure). Suppose X1, X2, …, Xk denote the times between failures. Usually these variables will be dependent because of inter-dependence between the different components of the software. For the customer the main characteristic of interest is the value t for which the probability Pr{min(X1, X2, …, Xk) ≥ t} would be high. In this paper we consider a number of dependence models for X1, X2, …, Xk based on multivariate exponential, multivariate Lomax and multivariate Weibull distributions. For each model we show how t could be determined for a specified degree of reliability. We also assess the sensitivity of t with respect to k failures and with respect to the dependence and the marginal parameters of each model.
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