Phase-II monitoring of exponentially distributed process based on Type-II censored data for a possible shift in location–scale

This paper studies a discriminant problem of location-scale family in case of prediction from type II censored samples. Three model selection approaches and two types of predictors are, respectively, proposed to predict the future order statistics from censored data when the best underlying distribution is not clear with several candidates. Two members in the location-scale family, the normal distribution and smallest extreme value distribution, are used as candidates to illustrate the best model competition for the underlying distribution via using the proposed prediction methods. The performance of correct and incorrect selections under correct specification and misspecification is evaluated via using Monte Carlo simulations. Simulation results show that model misspecification has impact on the prediction precision and the proposed three model selection approaches perform well when more than one candidate distributions are competing for the best underlying distribution. Finally, the proposed approaches are applied to three data sets.

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Estimation of P(X

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-05-2016-0070 ◽

2017 ◽

Vol 34 (7) ◽

pp. 1111-1122 ◽

Cited By ~ 2

Author(s):

Soumya Roy ◽

Biswabrata Pradhan ◽

E.V. Gijo

Keyword(s):

Maximum Likelihood ◽

Censored Data ◽

Quality Characteristic ◽

Logistic Distribution ◽

Type Ii ◽

Finite Sample ◽

Data Set ◽

Content Type ◽

Type Ii Censored Data ◽

Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

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Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data

International Journal of Advanced Statistics and Probability ◽

10.14419/ijasp.v6i1.10450 ◽

2018 ◽

Vol 6 (1) ◽

pp. 37

Author(s):

Aisha Fayomi ◽

Hamdah Al-Shammari

Keyword(s):

Censored Data ◽

Geometric Distribution ◽

Asymptotic Variance ◽

Parameters Estimation ◽

Type Ii ◽

Progressive Type ◽

The Em Algorithm ◽

Asymptotic Confidence Intervals ◽

Distribution Parameters ◽

Type Ii Censored Data

This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

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