Exponentiated Log-logistic Distribution Research Articles

Double Acceptance Sampling Plan for Odd Generalized Exponential Log-logistic Distribution Based on Truncated Life Test

According to the results of industrial research, product failure time is correlated with fatigue weakness, which is typically produced by repeated stress variations. A double acceptance sampling strategy was presented for shortened life tests where the lifespan of test products follows an odd generalized exponential log-logistic distribution (OGELLD), according to the findings of this study. The minimum sample sizes for the first and second samples are calculated using a producer’s risk of 0.05 to ensure that the actual median life is greater than the specified life at the chosen consumer confidence level. Based on various ratios of genuine median life to stipulated life, we analyzed operational features; we observed that reduced producer risk at the defined level was associated with the lowest median ratios to the specified level. Finally, an illustration is offered to help in the grasp of the suggested framework.

Group Acceptance Sampling Plans for Resubmitted Lots Under Odd Generalized Exponential Log-Logistic Distribution

In this manuscript, we developed resubmitted lots with group acceptance sampling plan for the lifetime of the product follows the odd generalized exponential log logistic distribution introduced by Rosaiah et al. (2016c). The values of the design parameters of the proposed plan are obtained which are satisfying the both producer’s as well consumer’s risk by fixing the experiment termination time. An application of the proposed plan to the industry is presented and the Kolmogorov-Smirnov test was conducted. However, this plan provides reasonable fit for lifetime of items of ball bearings data. Finally, the advantage of the proposed plan reduces the sample size as compared with the ordinary group sampling scheme. An example is given to illustrate the methodology.

TIME TRUNCATED ACCEPTANCE SAMPLING PLAN FOR ODDS EXPONENTIAL LOG-LOGISTIC DISTRIBUTION

In this paper, the multiple deferred state repetitive acceptance sampling plan (MDSRASP) is proposed and designed for assuring a 50th percentile lifetime of the products under odds exponential log-logistic (OELL) distribution. The optimum parameters of the proposed plan are determined based on satisfying various blends of producer’s risk and consumer’s risk for definite quality levels in light of 50th percentile. The aim is to minimize the average sample number (ASN), though the constraints are connected with the lot acceptance probability at the acceptable and limiting quality levels. The efficiency of the proposed plan is compared with single sampling plan using ASN. Tables are formed to present the outcomes and comparison of the proposed plan with existing sampling plan is done in terms of ASN.

Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications

Heavy tailed distributions have a big role in studying risk data sets. Statisticians in many cases search and try to find new or relatively new statistical models to fit data sets in different fields. This article introduced a relatively new heavy-tailed statistical model by using alpha power transformation and exponentiated log-logistic distribution which called alpha power exponentiated log-logistic distribution. Its statistical properties were derived mathematically such as moments, moment generating function, quantile function, entropy, inequality curves and order statistics. Five estimation methods were introduced mathematically and the behaviour of the proposed model parameters was checked by randomly generated data sets and these estimation methods. Also, some actuarial measures were deduced mathematically such as value at risk, tail value at risk, tail variance and tail variance premium. Numerical values for these measures were performed and proved that the proposed distribution has a heavier tail than others compared models. Finally, three real data sets from different fields were used to show how these proposed models fitting these data sets than other many wells known and related models.

Repetitive acceptance sampling plan for odds exponential log-logistic distribution based on truncated life test

ABSTRACT In this paper, we construct repetitive acceptance sampling plan (RASP) by attributes for the truncated life test under odds exponential log-logistic distribution (OELLD). The design parameters are determined by satisfying both the producer’s and consumer’s risk for the specified quality levels based on percentiles. The objective is to minimize the average sample number (ASN), where as the constraints are related to lot acceptance probability at the acceptable and limiting quality levels. The authors compare the average sample number (ASN) of the proposed repetative acceptance sampling plan and the ordinary single sampling plan is discussed. Tables are constructed for various values of shape parameter. The results are demonstrated with the help of real- life data.

Bayesian Analysis of Two-Parameter Exponentiated Log-logistic Distribution

In this paper, the parameters of the two-parameter exponentiated log-logistic distribution based on a complete sample are estimated using the Markov chain Monte Carlo (MCMC) method. In order to perform full Bayesian analysis of the two-parameter exponentiated log-logistic distribution, the procedures are developed using the MCMC simulation method in Open BUGS, established software. The researcher has obtained the Bayes estimates of the parameters and their probability intervals are presented. The researcher has also discussed the estimation of the reliability function. For illustration under independent gamma priors, the real data set is considered.

Inferences for the Type-II Exponentiated Log-Logistic Distribution Based on Order Statistics with Application

In this paper, we first derive the exact explicit expressions for the single and product moments of order statistics from the type-II exponentiated log-logistic distribution, and then use these results to compute the means, variances, skewness and kurtosis of rth order statistics. Besides, best linear unbiased estimators (BLUEs) for the location and scale parameters for the type-II exponentiated log-logistic distribution with known shape parameters are studied. Finally, the results are illustrated with a real data set.

A time-truncated two-stage group acceptance sampling plan for odds exponential log-logistic distribution

In this article, two-stage group acceptance sampling plan is developed assuming that the lifetime of the test units follows odds exponential log-logistic distribution and the life test is terminated at a prefixed time. The acceptance of the lot mainly depends on the number of failures observed from each group either in the first or second stage of sampling. We examine the quality of organizations necessary for each of the two stages of the proposed lifetime distribution as to slash the average sample number under the satisfactory constraints of producer’s and consumer’s risk together. The proposed plan is compared with the single-stage group acceptance sampling plan as a special case in terms of the average sample number and the operating characteristics.

Odd generalized exponential log logistic distribution: A new acceptance sampling plans based on percentiles

<span>In this paper, acceptance sampling plans are developed for the odd generalized exponential log logistic distribution based on percentiles when the life test is truncated at a pre-specified (pre-determined) time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given consumer’s risk. The operating characteristic values of the sampling plans as well as the producer’s risk are presented. One example with real data set is also given as an illustration.</span>

Frequentist Parameter Estimation of Two-Parameter Exponentiated Log-logistic Distribution BB

In this paper, we have considered frequentist parameter estimation of two parameter exponentiated log-logistic distribution based on a complete sample. The parameters are estimated using a likelihood-based classical inferential procedure. This study has tried to compute MLEs along with their asymptotic confidence interval, contour plot and standard errors. The K-S test statistic, Quantile-Quantile (QQ) and Probability-Probability (PP) plots are used to check the validity of the model. All the computations are performed in R software. Areal data set is considered for illustration of the purposed inferential procedures.

Application of the Exponentiated Log-Logistic Weibull Distribution to Censored Data

In a recent paper, a new model called the Exponentiated Log-Logistic Weibull (ELLoGW) distribution with applications to reliability, survival analysis and income data was proposed. In this study, we applied the recently developed ELLoGW model to a wide range of censored data. We found that the ELLoGW distribution is a very competitive model for describing censored observations in life-time reliability problems such as survival analysis. This work shows that in certain cases, the ELLoGW distribution performs better than other parametric model such as the Log-Logistic Weibull, Exponentiated Log-Logistic Exponential, Log-Logistic Exponential distributions and the non-nested Gamma-Dagum (GD).

THE ODD GENERALIZED EXPONENTIAL LOG-LOGISTIC DISTRIBUTION GROUP ACCEPTANCE SAMPLING PLAN

Abstract In this manuscript, a group acceptance sampling plan (GASP) is developed when the lifetime of the items follows odd generalized exponential log-logistic distribution (OGELLD), the multiple number of items as a group can be tested simultaneously in a tester. The design parameters such as the minimum group size and the acceptance number are derived when the consumer’s risk and the test termination time are specified. The operating characteristic (OC) function values are calculated (intended) according to various quality levels and the minimum ratios of the true average life to the specified average life at the specified producer’s risk are derived. The methodology is illustrated through real data.

Group acceptance sampling plan for resubmitted lots based on life tests for odds exponential log logistic distribution

PurposeThe purpose of this paper is to develop a group acceptance sampling plan (GASP) for a resubmitted lot when the lifetime of a product follows odds exponential log logistic distribution introduced by Rao and Rao (2014). The parameters of the proposed plan such as minimum group size and acceptance number are determined for a pre-specified consumer’s risk, number of testers and the test termination time. The authors compare the proposed plan with the ordinary GASP, and the results are illustrated with live data example.Design/methodology/approachThe parameters of the proposed plan such as minimum group size and acceptance number are determined for a pre-specified consumer’s risk, number of testers and the test termination time.FindingsThe authors determined the group size and acceptance number.Research limitations/implicationsNo specific limitations.Practical implicationsThis methodology can be applicable in industry to study quality control.Social implicationsThis methodology can be applicable in health study.Originality/valueThe parameters of the proposed plan such as minimum group size and acceptance number are determined for a pre-specified consumer’s risk, number of testers and the test termination time.

Conditional double sampling plan based on exponentiated log-logistic model assuring median life

In this paper, we propose a conditional double sampling plan based on the truncated life test for exponentiated log-logistic distribution. The conditional double sampling plan is one of the conditional sampling plans. Tables are also constructed for the selection of optimal parameters of proposed sampling plan for specified two points on the operating characteristic curve namely the acceptable reliability level and the limiting tolerance reliability level along with the producer and consumer’s risks.

Odds Exponential Log Logistic Distribution: Properties and Estimation

We propose a distribution called Odds Exponential Log Logistic Distribution (OELLD), which is an odds family of distribution. Its hazard rate is an increasing and decreasing function based on the value of the parameter. Explicit expressions for the ordinary moments, L-moments, quantile, generating functions, Bonferroni Curve, Lorenz Curve, Gini's index and order statistics are derived. The parameters of the proposed distribution are estimated by using maximum likelihood method and also illustrated by a lifetime data set.

Group acceptance sampling plans for lifetimes following an odds exponential log logistic distribution

A group acceptance sampling plan is developed for odds exponential log logistic distribution (OELLD) based on truncated lifetime with a known shape parameter. At a specified level of consumer risk and at the predefined test termination time, we derived the minimum number of groups required for a given group size and the acceptance number using the two-point approach by satisfying the producer’s and the consumer’s risks at the specified quality levels, while the termination time and the number of testers are specified. The values of operating characteristic (OC) function according to various quality levels are derived and the minimum ratios of true average life to the specified life for given producer’s risk are obtained. The results are illustrated with real lifetime data set. This work is licensed under a Creative Commons Attribution 4.0 International License .

A New Acceptance Sampling Plans Based on Percentiles for Odds Exponential Log Logistic Distribution

In this paper, acceptance sampling plans are developed for the odds exponential log logistic distribution (OELLD) introduced by Rosaiah et al. [1] based on lifetime percentiles when the life test is truncated at a predetermined time. The minimum sample size necessary to ensure the specified lifetime percentile is obtained under a given customer’s risk. The operating characteristic values of the sampling plans as well as the producer’s risk are presented. One example with real data set is also given as an illustration.

The exponentiated-log-logistic geometric distribution: Dual activation

ABSTRACTThe log-logistic distribution is commonly used to model lifetime data. We propose a wider distribution, named the exponentiated log-logistic geometric distribution, based on a double activation approach. We obtain the quantile function, ordinary moments, and generating function. The method of maximum likelihood is used to estimate the model parameters. We propose a new extended regression model based on the logarithm of the exponentiated log-logistic geometric distribution. This regression model can be very useful in the analysis of real data and could provide better fits than other special regression models. The potentiality of the new models is illustrated by means of two applications to real lifetime data sets.

EXACT MOMENT OF GENERALIZED ORDER STATISTICS FROM TYPE II EXPONENTIATED LOG-LOGISTIC DISTRIBUTION

In this paper some new simple expressions for single and product moments of generalized order statistics from type II exponentiated log-logistic distribution have been obtained. The results for order statistics and record values are deduced from the relations derived and some ratio and inverse moments of generalized order statistics are also carried out. Further, a characterization result of this distribution by using the conditional expectation of generalized order statistics is discussed.

Reliability Test Plans for Exponentiated Log-Logistic Distribution

A generalization of the log-logistic distribution called exponentiated log-logistic distribution (in lines of exponentiated Weibull distribution suggested by Mudholkar and Srivastava [Technometrics 37: 436-445, 1995]) is considered. In this paper the operating characteristic for a sampling plan is determined for the case that a lot of products is submitted for inspection with lifetimes specified by an exponentiated log-logistic distribution (ELLD). The results are illustrated by a numerical example.