In this paper, several diagnostics measures are proposed based on case-deletion model for log-Birnbaum–Saunders regression models (LBSRM), which might be a necessary supplement of the recent work presented by Galea et al. 2004. Influence diagnostics in log-Birnbaum–Saunders regression models. J. Appl. Statist. 31, 1049–1064 who studied the influence diagnostics for LBSRM mainly based on the local influence analysis. It is shown that the case-deletion model is equivalent to the mean-shift outlier model in LBSRM and an outlier test is presented based on mean-shift outlier model. Furthermore, we investigate a test of homogeneity for shape parameter in LBSRM, which is a problem mentioned by both Rieck and Nedelman 1991. A log-linear model for the Birnbaum–Saunders distribution. Technometrics 33, 51–60 and Galea et al. 2004. Influence diagnostics in log-Birnbaum–Saunders regression models. J. Appl. Statist. 31, 1049–1064. We obtain the likelihood ratio and score statistics for such test. Finally, a numerical example is given to illustrate our methodology and the properties of likelihood ratio and score statistics are investigated through Monte Carlo simulations.