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• A new hybrid condition-/age-based maintenance policy is proposed for deteriorating units whose observed degradation paths are simultaneously affected by temporal variability, unit to unit variability, and measurement error. • The proposed maintenance policy uses in a combined manner a perfect and an imperfect measurement procedure. • The actual (hidden) degradation phenomenon process is described by using a gamma process with random effect. • The measurement error is modeled as a non-Gaussian random variable that depends in stochastic sense on the measured degradation level. • A comparative study with other maintenance policies is developed to demonstrate the utility of the proposed approach in terms of long-run average maintenance cost rate. In this paper, a hybrid condition-/age-based maintenance policy is proposed for deteriorating units whose observed degradation paths are affected by temporal variability, unit to unit variability, and measurement error. The hidden degradation process is described by using a gamma model with random effect. The measurement error is modeled as a non-Gaussian random variable. Units are assumed to fail when their degradation level exceeds a given threshold. The suggested maintenance policy consists in using the information obtained at a predetermined inspection time to decide whether to immediately replace the unit or to postpone its replacement to a successive predetermined time. The inspection involves measuring the degradation level of the unit. It is supposed that an imperfect procedure is firstly adopted, which provides a perturbed measurement of the true degradation level. However, it is also supposed that a more expensive perfect measurement procedure can be optionally used, depending on the result provided by the imperfect one. The proposed maintenance policy is applied to a real-world inspired case of a pipeline. The performances of the policy are measured in terms of the long-run average maintenance cost rate. Obtained results demonstrate the affordability and utility of the proposed approach. [ABSTRACT FROM AUTHOR]