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Two recently introduced model based bias corrected estimators for proportionof true null hypotheses ($\pi_0$) under multiple hypotheses testing scenariohave been restructured for exponentially distributed random observationsavailable for each of the common hypotheses. Based on stochastic ordering, anew motivation behind formulation of some related estimators for $\pi_0$ isgiven. The reduction of bias for the model based estimators are theoreticallyjustified and algorithms for computing the estimators are also presented. Theestimators are also used to formulate a popular adaptive multiple testingprocedure. Extensive numerical study supports superiority of the bias correctedestimators. We also point out the adverse effect of using the model based biascorrection method without proper assessment of the underlying distribution. Acase-study is done with a synthetic dataset in connection with reliability andwarranty studies to demonstrate the applicability of the procedure, under anon-Gaussian set up. The results obtained are in line with the intuition andexperience of the subject expert. An intriguing discussion has been attemptedto conclude the article that also indicates the future scope of study.

Bias corrected estimators for proportion of true null hypotheses under  exponential model: Application of adaptive FDR-controlling in segmented  failure data