Summary: A method for robust estimation and multiple outlier detection in time series generated by autoregressive integrated moving average processes in industrial environments is developed. The procedure is based on reweighted maximum likelihood estimation using P. J. Huber’s [Ann. Stat. 1, 799-821 (1973; Zbl 0289.62033)] or redescending weights and, therefore, generalizes the well-established robust \(M\)-estimation procedures used in the regression framework. When the scalar process is nonstationary, the computations required can be performed equally well using either the original undifferenced series or auxiliary differenced series. Whereas the latter alternative may be preferred for scalar series, the former might be extended to cope with vector partially nonstationary time series without differencing the series, thus avoiding noninvertibility and parameter identifiability problems caused by overdifferencing. The overall strategy is applied in two real industrial data sets.