A New Useful Exponential Model with Applications to Quality Control and Actuarial Data

Abstract

The compounding approach is used to introduce a new family of distributions called exponentiated Bell G, analogy to exponentiated G Poisson. Several essential properties of the proposed family are obtained. The special model called exponentiated Bell exponential (EBellE) is presented along with properties. Furthermore, the risk theory related measures including value-at-risk and expected-shortfall are also computed for the special model. Group acceptance sampling plan is designed when a lifetime of a product or item follows an EBellE model taking median as a quality parameter. The parameters of the proposed model are estimated by considering maximum likelihood approach along with simulation analysis. The usefulness of the proposed model is illustrated by practical means which yield better fits as compared to several exponential related extended models.

The development of an extended Weibull model with applications to medicine, industry and actuarial sciences

“…These DBellD properties inspired the development of its generalized class, compared mathematically and empirically to the CP-G class and its particular models. Fayomi et al 7 expanded the DBellD and produced its generalized class, the exponentiated Bell-G (EBell-G) family. The cdf for the EBell-G family of distributions is provided by 7 as where and represent the Bell and shape parameter, respectively.…”

“…Fayomi et al 7 expanded the DBellD and produced its generalized class, the exponentiated Bell-G (EBell-G) family. The cdf for the EBell-G family of distributions is provided by 7 as where and represent the Bell and shape parameter, respectively. In the case of complementary and competing risks, Algarni 8 proposed its complementary version.…”

Process Optimization of Spark Plasma Sintered Parameters for Ti-Al-Cr-Nb-Ni-Cu-Co High Entropy Alloy by Response Surface Methodology

“…The potential of SPS among other fabrication routes is enormous. It can compact the powders to nanostructure ultra-fine grains, nearnet shaped profile void of segregation with high densification capable of producing high structural bond that serves as barrier to coarsening of the grains [21,22]. Several research has seen the use of user-defined design of the response surface technique (UDD-RSM); a statistical approach for the optimization of operating parameters in the design and fabrication of different alloy materials with optimum service properties.…”

On the Odd Perks Exponential Model: An Application to Quality Control Data

“…Several researchers developed a GASP predicted on a truncated life test for instances when the product followed various sorts of probability distributions. For example, [3] investigated GASP based on the log-logistic and inverse Rayleigh distributions, and the same for [4] with the Marshall-Olkin extended Lomax distribution, [5] with the Marshall-Olkin extended Weibull distribution, [6] with the generalized exponential distribution, [7] with the inverse Weibull distribution, [8] with the odd generalized exponential log-logistic distribution, [9] with the Marshall-Olkin Kumaraswamy exponential distribution, and [10] with the exponentiated Bell exponential distribution.…”