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This paper deals with residual lifetimes of sequential  k -out-of- n  systems when component lifetimes are dependent. Given the first  j  component failure times, an unbiased predictor for the ( j  +  i )-th component failure time is derived. Maximum likelihood prediction of future component failure times is also studied. Estimation of the nuisance parameters is investigated under the conditional proportional hazard rates model with the Exponential baseline distribution and the Gumbel-Hougaard copula. Illustrative examples are also given.

Residual lifetime prediction for sequential k -out-of- n systems with dependent component lifetimes