  In this paper I have studied the fiber bundle model with a fraction {\alpha}
of infinitely strong fibers. Inclusion of such unbreakable fraction has been
proven to affect the failure process in early studies, especially around a
critical value {\alpha}_c . The present work has a twofold purpose: (i) study
of failure abruptness, mainly the brittle to quasi-brittle transition point
({\delta}_c ) with varying {\alpha} and (ii) variation of {\alpha}_c as we
change the disorder introduced in the model. The brittle to quasi-brittle
transition is confirmed from the failure abruptness. On the other hand, the
{\alpha}_c is obtained from the knowledge of failure abruptness and statistics
of avalanches. It is observed that {\delta}_c scales to lower values,
suggesting more quasi-brittle like continuous failure even at low strength of
disorder, when {\alpha} is increased. Also, the critical fraction {\alpha}_c,
required to make the model deviate from the conventional results, increases
with decreasing {\delta} values. The analytical expression for {\alpha}_c shows
good agreement with the numerical result. Finally, the findings in the paper
are compared with previous results as well as with the real life application of
composite materials.
