A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data. POLO distribution accommodate both inverted bathtub and decreasing hazard rate. Several statistical and reliability properties are derived. Point estimation via method of moments and maximum likelihood and the interval estimation are also studied. The simulation schemes are calculated to examine the bias and mean square error of the maximum likelihood parameter estimators. Finally, a real data application about the remission time of bladder cancer is used to illustrate the usefulness of the proposed distribution in modelling real data application. The characteristics of the fitting data using the proposed distribution are compared with known extensions of Lomax distribution. The comparison showed that the POLO distribution outfit most well-known extensions of Lomax distribution.

First‐failure progressive censoring schemes have potential usefulness in practice where budget constraints in place or there is a necessary for speedy test. To test the process capability, the lifetime performance index CL is widely recommended for evaluating the performance of the products lifetime. This paper is devoted to construct the maximum likelihood estimator of the lifetime performance index CL and the hypothesis testing technique for implementing CL under first‐failure progressive censoring sample from Kumaraswamy population. Finally, to illustrate the potentiality of the proposed procedure, two real engineering applications and a simulated example are given.

Several optimality criteria have been considered in the literature as information-based criteria. The probability-based criteria have been recently proposed for maximizing the probability of a desired outcome. However, designs that are optimal for the information-based criteria may be inadequate for probability-based criteria. This paper introduces the DE-and EDPM-optimum designs for multi aims of optimality for Generalized Linear Models (GLMs). An equivalence theorem is proved for both compound criteria. Finally, two numerical examples are given to illustrate the potentiality of the proposed compound criteria.

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