  An alternative parameter $R_{J_z}$ is introduced as the ratio of one of two
kinds of opposite-sign current to the total current and investigate the
relationship between the quantity and the hemispheric sign rule of helicity
(HSR) that is established by a series of previous statistical studies. The
classification of current in each hemisphere is according to the following
rule: If the product of the current and the corresponding longitudinal field
component contributes a consistent sign with reference to the HSR, it is called
"HSR-compliant" current, or else it is called "HSR-noncompliant" current.
Firstly, the consistence between the butterfly diagram of the $R_{J_z}$ and the
current helicity was obtained in a statistical study. Active regions with
$R_{J_z}$ smaller than 0.5 tend to obey the HSR whereas those with $R_{J_z}$
greater than 0.5 tend to disobey the HSR. The "HSR-compliant" current systems
have 60\% probability of realization compared to 40\% of "HSR-noncompliant"
current systems. Overall, the HSR is violated for active regions in which the
"HSR-noncompliant" current is greater than the "HSR-compliant" current.
Secondly, the $R_{J_z}$ parameter was subsequently used to study the evolution
of current systems in the case analyses of flare-productive active regions NOAA
AR 11158 and 11283. It is found that there were "$R_{J_z}$-quasi-stationary"
phase that is relatively flare quiescent and "$R_{J_z}$-dynamic" phase that is
covered by the occurrence of large flares.
