The number of defects, as a count time series data, is an important measure of product quality which is widely used in industry. We discuss M-estimation of INARCH-models as appropriate models for analysis and modeling such data, especially, in the presence of outliers. These models are proposed by Elsaied and Fried (2014) for conditional Poisson distributions. They compare between the performance of the conditional maximum likelihood estimator (CML) and Tukey M-estimators with and without bias correction. Liboschik et al. (2017) construct the tscount package in the R programming language, which provide likelihood-based estimation methods for analysis and modeling of count time series based on generalized linear models. In our paper, we compare between the results of the best functions, which are built in the R programming language, for the Tukey M-estimators in the case of the Poisson INARCH(1) model given in Elsaied and Fried (2014) and the tsglm function in the tscount package. We investigate the performance of these estimators under assuming different outliers scenarios by simulations. The usefulness of the chosen functions is applied on a real defects data example.