The combined-unified hybrid sampling approach was introduced as a general model that combines the unified hybrid censoring sampling approach and the combined hybrid censoring approach into a unified approach. In this paper, we apply this censoring sampling approach to improve the estimation of the parameter via a novel five-parameter expansion distribution, which we call the generalized Weibull-modified Weibull model. The new distribution contains five parameters and is therefore very flexible in terms of accommodating different types of data. The new distribution provides graphs of the probability density function, e.g., symmetric or right skewed. The graph of the risk function can have a shape similar to a monomer of the increasing or decreasing model. Using the Monte Carlo method, the maximum likelihood approach is used in the estimation procedure. The Copula model was used to discuss the two marginal univariate distributions. The asymptotic confidence intervals of the parameters were developed. We present some simulation results to validate the theoretical results. Finally, a data set with failure times for 50 electronic components was analyzed to illustrate the applicability and potential of the proposed model.
Engineering , Likelihood Functions , Reproducibility of Results , Computer Simulation , Monte Carlo Method
The entropy of Tsallis is a different measure of uncertainty for the Shannon entropy. The present work aims to study some additional properties of this measure and then initiate its connection with the usual stochastic order. Some other properties of the dynamical version of this measure are also investigated. It is well known that systems having greater lifetimes and small uncertainty are preferred systems and that the reliability of a system usually decreases as its uncertainty increases. Since Tsallis entropy measures uncertainty, the above remark leads us to study the Tsallis entropy of the lifetime of coherent systems and also the lifetime of mixed systems where the components have lifetimes which are independent and further, identically distributed (the iid case). Finally, we give some bounds on the Tsallis entropy of the systems and clarify their applicability.
An alternate measure of uncertainty, termed the fractional generalized cumulative residual entropy, has been introduced in the literature. In this paper, we first investigate some variability properties this measure has and then establish its connection to other dispersion measures. Moreover, we prove under sufficient conditions that this measure preserves the location-independent riskier order. We then elaborate on the fractional survival functional entropy of coherent and mixed systems' lifetime in the case that the component lifetimes are dependent and they have identical distributions. Finally, we give some bounds and illustrate the usefulness of the given bounds.
The fractional generalized cumulative residual entropy (FGCRE) has been introduced recently as a novel uncertainty measure which can be compared with the fractional Shannon entropy. Various properties of the FGCRE have been studied in the literature. In this paper, further results for this measure are obtained. The results include new representations of the FGCRE and a derivation of some bounds for it. We conduct a number of stochastic comparisons using this measure and detect the connections it has with some well-known stochastic orders and other reliability measures. We also show that the FGCRE is the Bayesian risk of a mean residual lifetime (MRL) under a suitable prior distribution function. A normalized version of the FGCRE is considered and its properties and connections with the Lorenz curve ordering are studied. The dynamic version of the measure is considered in the context of the residual lifetime and appropriate aging paths.
Recently, the two-parameter Xgamma distribution (TPXGD) is suggested as a new lifetime distribution for modeling some real data. The TPXGD is investigated in different areas and generalized to other forms by many of the researchers. The acceptance sampling plans are one of the main important statistical tools in production and engineering fields. In this paper, modified acceptance sampling plans for the TPXGD are proposed with the assumption that the lifetime is truncated at a predetermined level. The mean of the TPXGD model is utilized as a quality parameter. The variables of the acceptance sampling plans including the acceptance numbers, the minimum sample sizes, operating characteristic function and the producer's risk are investigated for various values of the model parameters. Numerical examples are offered to illustrate the process of the proposed plans. Also, a real data is fitted to the TPXGD and an application based on the suggested acceptance sampling plans is considered for explanation.
Models, Statistical , Sample Size
