  Two recently introduced model based bias corrected estimators for proportion
of true null hypotheses ($\pi_0$) under multiple hypotheses testing scenario
have been restructured for exponentially distributed random observations
available for each of the common hypotheses. Based on stochastic ordering, a
new motivation behind formulation of some related estimators for $\pi_0$ is
given. The reduction of bias for the model based estimators are theoretically
justified and algorithms for computing the estimators are also presented. The
estimators are also used to formulate a popular adaptive multiple testing
procedure. Extensive numerical study supports superiority of the bias corrected
estimators. We also point out the adverse effect of using the model based bias
correction method without proper assessment of the underlying distribution. A
case-study is done with a synthetic dataset in connection with reliability and
warranty studies to demonstrate the applicability of the procedure, under a
non-Gaussian set up. The results obtained are in line with the intuition and
experience of the subject expert. An intriguing discussion has been attempted
to conclude the article that also indicates the future scope of study.
