Power Inverted Topp–Leone Distribution in Acceptance Sampling Plans

We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone(PITL)distribution.Major properties of the PITL distribution are stated;including;quantile measures,moments,moment generating function,probability weighted moments,Bonferroni and Lorenz curve,stochastic ordering,incomplete moments,residual life function,and entropy measure.Acceptance sampling plans are developed for the PITL distribution,when the life test is truncated at a pre-specified time.The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors.The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk.Numerical results for given consumer’s risk,parameters of the PITL distribution and the truncation time are obtained.The estimation of the model parameters is argued using maximum likelihood,least squares,weighted least squares,maximum product of spacing and Bayesian methods.A simulation study is confirmed to evaluate and compare the behavior of different estimates.Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions.The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.

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.

PEPX-type lattice design and optimization for the High Energy Photon Source

A new generation of storage ring-based light sources, called diffraction-limited storage rings（DLSR）, with emittance approaching the diffraction limit for multi-ke V photons by using multi-bend achromat lattice, has attracted worldwide and extensive studies of several laboratories, and been seriously considered as a means of upgrading existing facilities in the imminent future. Among various DLSR proposals, the PEPX design demonstrated that it is feasible to achieve sufficient ring acceptance for off-axis injection in a DLSR, by designing the lattice based on the ‘thirdorder achromat’ concept and with a special high-beta injection section. For the High Energy Photon Source（HEPS）planned to be built in Beijing, a PEPX-type lattice has been designed and continuously improved. In this paper, we report the evolution of the PEPX-type design for HEPS, and discuss the main issues relevant to the linear optics design and nonlinear optimization.