Optimal test plan of discrete alpha power inverse Weibull distribution under censored data

Abstract

When measuring the lifespan of a product or gadget becomes difficult or cumbersome, the discretization phenomena typically occur an unbroken scale. In this study, we have created a discrete alpha power inverse Weibull distribution, which is a discrete of the continuous alpha power inverse Weibull distribution. The probability mass and hazard rate functions of the proposed model have asymmetric shapes. Also, the statistical properties of our current model are calculated. These include quantile, median, moments, skewness, kurtosis, index of dispersion, entropy and order statistics. The numerical values of some statistical properties of discrete alpha power inverse Weibull are calculated, such as minimum, first quantile, median, mean, third quantile, maximum, standard deviation, skewness, kurtosis, index of dispersion. We have calculated the model parameters using the maximum likelihood method under type II censoring. The parameters' asymptotic confidence intervals are built. It is noted that Bootstrap algorithms of estimators are shorter than asymptotic confidence intervals. Four potential optimum test methods are also examined utilizing various optimal criteria. Sometimes, the optimal censoring scheme is the maximum value of the criterion while the optimal test plan of the others is corresponding to the lowest value of the criteria. Numerous simulations are run to evaluate the effectiveness of the methodology that is suggested in this article. Last but not least, the two real data sets are given to illustrate the flexibility of the suggested model in actual real life.