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.

Designing Bayesian Two-Sided Group Chain Sampling Plan for Gamma Prior Distribution

Acceptance sampling is used to decide either the whole lot will be accepted or rejected,based on inspection of randomly sampled items from the same lot.As an alternative to traditional sampling plans,it is possible to use Baye-sian approaches using previous knowledge on process variation.This study pre-sents a Bayesian two-sided group chain sampling plan(BTSGChSP)by using various combinations of design parameters.In BTSGChSP,inspection is based on preceding as well as succeeding lots.Poisson function is used to derive the probability of lot acceptance based on defective and non-defective products.Gamma distribution is considered as a suitable prior for Poisson distribution.Four quality regions are found,namely:(i)quality decision region(QDR),(ii)probabil-istic quality region(PQR),(iii)limiting quality region(LQR)and(iv)indifference quality region(IQR).Producer’s risk and consumer’s risk are considered to esti-mate the quality regions,where acceptable quality level(AQL)is associated with producer’s risk and limiting quality level(LQL)is associated with consumer’s risk.Moreover,AQL and LQL are used in the selection of design parameters for BTSGChSP.The values based on all possible combinations of design parameters for BTSGChSP are presented and inflection points’values are found.Thefinding exposes that BTSGChSP is a better substitute for the existing plan for industrial practitioners.

Bayesian Group Chain Sampling Plan for Poisson Distribution with Gamma Prior

Acceptance sampling is a statistical quality control technique that consists of procedures for sentencing one or more incoming lots of finished products.Acceptance or rejection is based on the inspection of sampled products drawn randomly from the lot.The theory of previous acceptance sampling was built upon the assumption that the process from which the lots are produced is stable and the process fraction nonconforming is a constant.Process variability is inevitable due to random fluctuations,which may inadvertently lead to quality variation.As an alternative to traditional sampling plans,Bayesian approach can be used by considering prior information of the process.Using different combinations of design parameters,this study introduces a Bayesian group chain sampling plan(BGChSP).For the first time in group chain sampling plan,the probability of lot acceptance is derived by using Poisson distribution to estimate an average number of defectives.Gamma distribution is used as a prior distribution with Poisson distribution.Taking into account both consumer’s and producer’s risks,this research considers two quality regions namely,probabilistic quality region(PQR)and indifference quality region(IQR).By minimizing consumer’s and producer’s risks,BGChSP can be used to minimize the average number of defective products in industry.

Acceptance sampling plan of accelerated life testing for lognormal distribution under time-censoring

Abstract Lognormal distribution is commonly used in engineering. It is also a life distribution of important research values. For long-life products follow this distribution, it is necessary to apply accelerated testing techniques to product demonstration. This paper describes the development of accelerated life testing sampling plans （ALSPs） for lognormal distribution under time-censoring conditions. ALSPs take both producer and consumer risks into account, and they can be designed to work whether acceleration factor （AF） is known or unknown. When AF is known, lift testing is assumed to be conducted under accelerated conditions with time-censoring. The producer and con- sumer risks are satisfied, and the size of test sample and the size of acceptance number arc opti- mized. Then sensitivity analyses are conducted. When AF is unknown, two or more predetermined levels of accelerated stress are used. The sample sizes and sample proportion allo- cated to each stress level are optimized. The acceptance constant that satisfies producer and consumer risk is obtdned by minimizing the generalized asymptotic variance of the test statistics. Finally, the properties of the two ALSPs （one for known-AF conditions and one for unknown AF conditions） are investigated to show that the proposed method is corrcct and usablc through numerical examples.