求常数 $p$ 的取值范围，使得对于所有实数 $x$，$y = px^2 - 4x + p - 3$ 始终为正。

1. State the conditions for a quadratic expression to be always positive

For $y = px^2 - 4x + p - 3$ to be always positive for all real $x$, we must have:

1. The coefficient of $x^2$ is positive: $p > 0$
2. The discriminant is negative: $b^2 - 4ac < 0$

2. Form and simplify the discriminant inequality

$(-4)^2 - 4(p)(p - 3) < 0$
$16 - 4p^2 + 12p < 0$
Divide by $-4$ and flip the inequality sign:
$p^2 - 3p - 4 > 0$

3. Solve the quadratic inequality

$(p - 4)(p + 1) > 0$
Therefore, $p < -1$ or $p > 4$.

4. Combine conditions to find the final range of $p$

Since we also require $p > 0$, we take the intersection of $p > 0$ and ($p < -1$ or $p > 4$).
This gives $p > 4$.