Abstract
Models with the bathtub-shaped hazard rate function are widely used in lifetime analysis and reliability engineering. In this paper, we adopted the reduced new modified Weibull (RNMW) distribution with a bathtub-shaped hazard rate function. Under consideration that the population units are failing with two independent causes of failure and the failure time is distributed with RNMW distribution, we formulate the model which is known as competing risks model. The model parameters under the type-II censoring scheme are estimated with the maximum likelihood method with the corresponding asymptotic confidence intervals. Also, the Bayes point and credible intervals with the help of MCMC methods are constructed. The real and simulated datasets are analyzed for illustrative purposes. Finally, the estimators are compared with the Monte Carlo simulation study.
Highlights
In the past few years, different modifications of Weibull distribution were constructed with a bathtub-shaped hazard rate function. ese modifications were discussed with different authors, see [1,2,3,4]
new reduced modified Weibull (NRMW): Reduced new modified Weibull PDF: Probability density function CDF: Cumulative distribution function S(.): Survival function HF: Hazard function ti: e observed time to failure tij: ith time to failure under cause j δj: Indicator denoted to the cause MCMC: Markov chain Monte Carlo MH: Metropolis–Hastings algorithm mean squared error (MSE): Mean squared error mean interval length (MIL): Mean interval length CP: Coverage percentage MLE: Maximum likelihood estimate LF: Loss function ACI: Approximate confidence interval CI: Credible intervals
Different types of censoring schemes are available, see [27], and the type-II censoring scheme presents the simple type of censoring, saving the number of failures needed for statistical inference
Summary
In the past few years, different modifications of Weibull distribution were constructed with a bathtub-shaped hazard rate function. ese modifications were discussed with different authors, see [1,2,3,4]. In the past few years, different modifications of Weibull distribution were constructed with a bathtub-shaped hazard rate function. Some modification models of Weibull distribution are discussed with with two or three parameters’ vectors [4,5,6]. E unimodal, decreasing, increasing, or bathtub-shaped hazard rate beta-Weibull distribution was proposed by Lee et al [10]. Almalki and Yuan [12] have presented new modified Weibull distribution with five parameters and distribution function (CDF) given by. Almalki [13] presented a new version of new modified Weibull distribution with a bathtub-shaped failure rate function (FRF) called reduced new modified Weibull distribution by taking β1 β2 (1/2), with CDF given by.
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