A family of shrinkage estimators for Weibull shape parameter in censored sampling

The present paper deals with the estimation of the shape parameter α of Generalized Exponential GE (α, λ) distribution when the scale parameter λ is known, by using preliminary test single stage shrinkage (SSS) estimator when a prior knowledge available about the shape parameter as initial value due past experiences as well as optimal region R for accepting this prior knowledge.The Expressions for the Bias [B (.)], Mean Squared Error [MSE] and Relative Efficiency [R.Eff (.)] for the proposed estimator is derived.Numerical results about conduct of the considered estimator are discussed include study the mentioned expressions. The numerical results exhibit and put it in tables.Comparisons between the proposed estimator withe classical estimator as well as with some earlier studies were made to show the effect and usefulness of the considered estimator.

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Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

Advances in Methodology and Statistics ◽

10.51936/uivd4115 ◽

2017 ◽

Vol 14 (1) ◽

Author(s):

Leila Barmoodeh ◽

Mehran Naghizadeh Qomi

Keyword(s):

Unbiased Estimator ◽

Shape Parameter ◽

Shrinkage Estimators ◽

Numerical Example ◽

Scale Parameters ◽

Error Loss ◽

Pareto Model

Considering a Pareto model with unknown shape and scale parameters \(\alpha\) and \(\beta\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \(\alpha\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \(\alpha\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \(\alpha\) with the help of a point guess value \(\alpha_0\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.

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Statistical inference about the shape parameter of the Burr type XII distribution under the failure-censored sampling plan

Applied Mathematics and Computation ◽

10.1016/j.amc.2004.02.019 ◽

2005 ◽

Vol 163 (1) ◽

pp. 443-482 ◽

Cited By ~ 27

Author(s):

Jong-Wuu Wu ◽

Huei-Yi Yu

Keyword(s):

Statistical Inference ◽

Shape Parameter ◽

Sampling Plan ◽

Censored Sampling ◽

Burr Type Xii

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Employ Shrinkage Estimation Technique for the Reliability System in Stress-Strength Models: special case of Exponentiated Family Distribution

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/33.4.2508 ◽

2020 ◽

Vol 33 (4) ◽

pp. 50

Author(s):

Eman A.A. ◽

Abbas N .S.

Keyword(s):

Shape Parameter ◽

Mean Squared Error ◽

Scale Parameter ◽

Estimation Methods ◽

Shrinkage Estimation ◽

Shrinkage Estimators ◽

Strength Model ◽

Squared Error ◽

Strength Models ◽

Special Case

A reliability system of the multi-component stress-strength model R(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown shape parameter α and known scale parameter λ equal to two and parameter θ equal to three. Different estimation methods of R(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.

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Effect of Kaiser Window Shape Parameter for the Enhancement of Rotor Faults Diagnosis

International Review of Automatic Control (IREACO) ◽

10.15866/ireaco.v10i6.13077 ◽

2017 ◽

Vol 10 (6) ◽

pp. 461

Author(s):

Mohammed-El-Amine Khodja ◽

Ahmed Hamida Boudinar ◽

Azeddine Bendiabdellah

Keyword(s):

Shape Parameter ◽

Rotor Faults ◽

Faults Diagnosis ◽

Kaiser Window

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Burn-In Acceleration Considerations in 130nm and 90nm Products

ISTFA 2005: Conference Proceedings from the 31st International Symposium for Testing and Failure Analysis ◽

10.31399/asm.cp.istfa2005p0389 ◽

2005 ◽

Author(s):

Nobuyuki Wakai ◽

Yuji Kobira ◽

Takashi Setoya ◽

Tamotsu Oishi ◽

Shinichi Yamasaki

Keyword(s):

Failure Analysis ◽

Shape Parameter ◽

Defect Density ◽

Failure Mechanisms ◽

Effective Procedure ◽

Time Period ◽

Related Defect ◽

The Relationship

Abstract An effective procedure to determine the Burn-In acceleration factors for 130nm and 90 nm processes are discussed in this paper. The relationship among yield, defect density, and reliability, is well known and well documented for defect mechanisms. In particular, it is important to determine the suitable acceleration factors for temperature and voltage to estimate the exact Burn- In conditions needed to screen these defects. The approach in this paper is found to be useful for recent Cu-processes which are difficult to control from a defectivity standpoint. Performing an evaluation with test vehicles of 130nm and 90nm technology, the following acceleration factors were obtained, Ea>0.9ev and β (Beta)>-5.85. In addition, it was determined that a lower defect density gave a lower Weibull shape parameter. As a result of failure analysis, it is found that the main failures in these technologies were caused by particles, and their Weibull shape parameter “m” was changed depending of the related defect density. These factors can be applied for an immature time period where the process and products have failure mechanisms dominated by defects. Thus, an effective Burn-In is possible with classification from the standpoint of defect density, even from a period of technology immaturity.

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