Inference of a competing risks model with partially observed failure causes under improved adaptive type-II progressive censoring

Abstract

In this paper, a competing risks model is analyzed based on improved adaptive type-II progressive censored sample (IAT-II PCS). Two independent competing causes of failures are considered. It is assumed that lifetimes of the competing causes of failure follow exponential distributions with different means. Maximum likelihood estimators (MLEs) for the unknown model parameters are obtained. Using asymptotic normality property of MLE, the asymptotic confidence intervals are constructed. Existence and uniqueness properties of the MLEs are studied. Further, bootstrap confidence intervals are computed. The Bayes estimators are obtained under symmetric and asymmetric loss functions with non-informative and informative priors. For informative priors, independent gamma distributions are considered. Highest posterior density (HPD) credible intervals are obtained. A Monte Carlo simulation study is carried out to compare performance of the established estimates. Furthermore, three different optimality criteria are proposed to obtain the optimal censoring plan. Finally, a real-life data set is considered for illustrative purposes.

Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

“…Remark 3 From (6), several works can be obtained as special cases, such as: (i) progressively Type-II censored competing risks by Pareek et al (2009) when T 1 → ∞; (ii) adaptive progressively Type-II censored competing risks Weibull models with common shape parameter by Ren and Gui (2021a) when T 2 → ∞; (iii) improved adaptive Type-II progressively censored competing risks exponential data by Dutta and Kayal (2021) when α = 1.…”

Estimation Based on Adaptive Progressively Censored under Competing Risks Model with Engineering Applications

“…For q � − 2, it reduces to the Pr loss function (Norstrom [26]) which is an asymmetric loss function. Based on (15), (16), and (22), the Bayes estimators of λ 1 and λ 2 using the GE loss function are, respectively, given by…”

“…Competing risks model under APCS-TII data is studied by Ashour and Nassar [14] and Hemmati and Khorram [6]. Recently, Dutta and Kayal [15] studied competing risk model based on improved APCS-TII sample under independent exponential distributions.…”

Inference for a general family of inverted exponentiated distributions under unified hybrid censoring with partially observed competing risks data

“…In reliability analysis, to get around the issue of model identifiability, many researchers assume that the causes of failure are independent. See, for example Panwar et al (2015), Ashour and Nassar (2017), Koley and Kundu (2017), Wang (2018), Wang and Li (2019), Mahto et al (2021), Dutta and Kayal (2022b), Dutta and Kayal (2022a) and Dutta et al (2023). However, in general, it is not easy to verify the assumption that the causes of failure are independent to each other.…”