Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

Determination of optimal post-warranty variable maintenance period for repairable second-hand product based on mean residual life

Due to the increased transactions of second-hand products in the market, the optimization of maintenance strategy for the second-hand product has become very important issue to attract a great attention from many researchers of late. This paper proposes a new post-warranty strategy with a variable self-maintenance period for the second-hand product, assuming that the product is replaced by another one on the first failure following a fixed length of post-warranty self-maintenance period. During the non-renewing warranty period, the product is subject to preventive maintenance periodically at a prorated cost while only minimal repair is implemented at each failure by the dealer. The main goal of this study is to determine an optimal length of post-warranty self-maintenance period which minimizes the expected cost rate per unit time during the product’s life cycle from the user’s perspective. This approach considers not only the periodic preventive maintenance during the warranty period, but also the remaining life distribution of the product after the warranty expires, which is the significant difference of this work from many existing maintenance policies. For this purpose, we formulate the expected length of life cycle and evaluate the expected total cost incurred during the life cycle of the second-had product which is purchased at the age of [Formula: see text] The existence of the optimal self-maintenance period is proved analytically under mild conditions and the proposed maintenance model is compared with an existing model with regard to the expected cost rate. Finally, assuming that the life distribution of the product follows a Weibull distribution, the effect of relevant parameters on the optimal self-maintenance period is analyzed numerically.

Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

Mean Residual Lifetime Frailty Models: A Weighted Perspective

The mean residual life frailty model and a subsequent weighted multiplicative mean residual life model that requires weighted multiplicative mean residual lives are considered. The expression and the shape of a mean residual life for some semiparametric models and also for a multiplicative degradation model are given in separate examples. The frailty model represents the lifetime of the population in which the random parameter combines the effects of the subpopulations. We show that for some regular dependencies of the population lifetime on the random parameter, some aging properties of the subpopulations’ lifetimes are preserved for the population lifetime. We indicate that the weighted multiplicative mean residual life model generates positive dependencies of this type. The copula function associated with the model is also derived. Necessary and sufficient conditions for certain aging properties of population lifetimes in the model are determined. Preservation of stochastic orders of two random parameters for the resulting population lifetimes in the model is acquired.

A New Skewed Discrete Model: Properties, Inference, and Applications

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.

Application to Engineering and Medical Data Using Three-Parameter Exponential Model

This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.

Mathematical Modeling of Survivability Function for Thermoelectric Module

Developing an optimized reliability model for thermoelectric module at the stress where the probability of module to functions without abruptive failure is a challenging aspect. One of the major reasons is the mismatch of thermal expansion coefficient, which has severe effects on segmented moduli compared to unsegmented moduli. The likelihood of a thermoelectric module to survive at certain level of thermo-mechanical stresses varies by varying number of component (layers) in thermoelectric leg. On another hand, selection of an adequate distribution model to predict reliability and sustainability of the thermoelectric module requires development of new optimized stress-strength-based model. In this paper the predictive reliability model for high temperature segmented module is derived from parametric Lognormal mean residual life and nonparametric Lognormal-kernel survival function to measure probability of module to survive at certain thermo-mechanical stress. A comprehensive comparative discussion has been done to illustrate the maximum likelihood based on Bayesian nonparametric lognormal-Kernel inference method regarding to Monte Carlo simulation, Weibull’s distribution, and Lognormal mean residual life for various shapes for the survival function. It has been demonstrated that nonparametric lognormal-kernel survival function has high ratio of probability to predict the survival of module at higher discrete thermo-mechanical stress data.

A New Scale-Invariant Lindley Extension Distribution and Its Applications

A new scale-invariant extension of the Lindley distribution and its power generalization has been introduced. The moments and the moment-generating functions of the proposed models have closed forms. The failure rate, the mean residual life, and the α -quantile residual life functions have been explored. The failure rate function of these models accommodates increasing, bathtub-shaped, and increasing then bathtub-shaped forms. The parameters of the models have been estimated by the maximum likelihood method for the complete and right-censored data. In a simulation study, the efficiency and consistency of the maximum likelihood estimator have been investigated. Then, the proposed models were fitted to four data sets to show their flexibility and applicability.