Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.

Semiparametric quantile-difference estimation for length-biased and right-censored data

Prevalent cohort studies frequently involve length-biased and right-censored data, a fact that has drawn considerable attention in survival analysis. In this article, we consider survival data arising from lengthbiased sampling, and propose a new semiparametric-model-based approach to estimate quantile differences of failure time. We establish the asymptotic properties of our new estimators theoretically under mild technical conditions, and propose a resampling method for estimating their asymptotic variance. We then conduct simulations to evaluate the empirical performance and efficiency of the proposed estimators, and demonstrate their application by a real data analysis.

Analyzing Right-Censored Length-Biased Data with Additive Hazards Model

Length-biased data are often encountered in observational studies, when the survival times are left-truncated and right-censored and the truncation times follow a uniform distribution. In this article, we propose to analyze such data with the additive hazards model, which specifies that the hazard function is the sum of an arbitrary baseline hazard function and a regression function of covariates. We develop estimating equation approaches to estimate the regression parameters. The resultant estimators are shown to be consistent and asymptotically normal. Some simulation studies and a real data example are used to evaluate the finite sample properties of the proposed estimators.

Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored Data

Length-biased data are encountered in many fields,including economics,engineering and epidemiological cohort studies.There are two main challenges in the analysis of such data:the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data.In this paper,a proportional mean residual life varyingcoefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model.Asymptotic properties are investigated for the proposed estimators.The finite sample performance of the proposed methodology is demonstrated by simulation studies.Finally,the method is applied to a real data set concerning the Academy Awards.

Nonparametrie Quantile Inference for Cause-specific Residual Life Function Under Length-biased Sampling

This paper considers a competing risks model for right-censored and length-biased survival data from prevalent sampling.We propose a nonparametric quantile inference procedure for cause-specific residual life distribution with competing risks data.We also derive the asymptotic properties of the proposed estimators of this quantile function.Simulation studies and the unemployment data demonstrate the practical utility of the methodology.

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.