When measurements are made on units of production in time order, a problem of considerable importance is to test whether the random disturbances from a regression model are autocorrelated in time. Tool-wear processes provide an example that is important in itself and for which regression models can sometimes be useful in modeling and controlling the process. For these processes, because of compensator actions and direct interventions inter alia, the deterministic components of the data are frequently from regression regimes with different coefficients and variances, but the random components have the same autocorrelations. A test based on the normalized uniform (NU) residuals obtained from conditional probability integral transformations (CPIT) is given for testing for laghautocorrelation of residuals from full-rank normal errors regression models. The exact distribution theory of these values permits the evaluation of the significance level for this test. Some limited power comparisons are made with the Durbin-Watson (D-W) statistic for a one-sample simple linear regression model, and for this case the new NU test has power somewhat less than the exact D-W statistic, but much better than the D-W bounds test. Percentage points are given for tests for lags 1-6, and formulas are given that can treat all situations.