Archived automatic vehicle location (AVL) data are widely used in bus transportation, but typically contain anomalies, such as missing data points and unseen bus overtakings. These anomalies may alter the measurement of time reliability (i.e., headways and schedule time deviations) of buses at stops with respect to passenger experiences. However, in many studies, anomalies are ignored, neglected, or partially addressed. This paper investigates the effect of AVL anomalies on headways and schedule deviations, which are keys for regularity and punctuality evaluations and are well-practicized among bus operators worldwide. The analysis is carried out on six scenarios, each representing a combination of AVL data anomalies. The outcomes show that addressing anomalies result in more severe regularity measures, which point out criticalities suffered by passengers, whereas it can be skipped for the measurement of punctuality. In addition, an increase of 5% of missing data results in the increase of 5% in the coefficient of variation of the headway, but it does not lead to meaningful variations in punctuality measures. These results are useful for both practitioners interested in passenger-oriented measurement of time reliability and researchers working on the disclosure of the determinants of unreliability