scholarly journals Stress-Strength Weibull Analysis with Different Shape Parameter β and Probabilistic Safety Factor

DYNA ◽  
2020 ◽  
Vol 87 (215) ◽  
pp. 28-33 ◽  
Author(s):  
Manuel Baro ◽  
Manuel Roman Piña Monarrez ◽  
Baldomero Villa
Keyword(s):  
Weibull Distribution ◽  
Safety Factor ◽  
Shape Parameter ◽  
Random Variable ◽  
Strength Analysis ◽  
Weibull Analysis ◽  
Shape Parameters ◽  
The Relationship ◽  
Close Solution ◽  
Probabilistic Safety

Since products are subjected to a random variable stress-strength, their reliability must be determined using the stress-strength analysis. Unfortunately, when both, stress and strength, follow a Weibull distribution with different shape parameters, the reliability stress-strength has not a close solution. Therefore, in this paper, the formulation to perform the analysis stress-strength Weibull with different shape parameters is derived. Furthermore, the formulation to determine the safety factor that corresponds to the designed reliability is also given. And because the relationship between the derived safety factor and the designed reliability is unique, then because reliability is random, the derived safety factor is random.

Life Prediction of Hull Based on Weibull Distribution

2011 ◽  
Vol 317-319 ◽  
pp. 2325-2330
Author(s):  
Jin Long Guo ◽  
Yan You Chai ◽  
Yang Han ◽  
Hao Zhang
Keyword(s):  
Weibull Distribution ◽  
Life Span ◽  
Lower Limit ◽  
Life Prediction ◽  
Estimation Method ◽  
Engineering Application ◽  
Shape Parameters ◽  
Life Estimation ◽  
Failure Data ◽  
The Relationship

In order to research the relationship between the life of hull with different structure and the reliability while using, a life estimation method for hull based on test was proposed. By assuming that the hull life span satisfied the Weibull distribution, with zero-failure data, confidence limit γ and reliability R, the confidence lower limit of reliable life were given according to test data of the hull life span. If the lower limit of the shape parameters of the Weibull distribution were known, this method can accumulate all of zero-failure data to increase the analysis presion of reliability greatly. At last, using this method, under the hull reliability R and the confidence γ, the confidence lower limit of reliable life with the hull structures as steel, titanium alloy and aluminum alloy were computed. The results indicate that the method is easy to compute and very convenient for engineering application.

scholarly journals A Novel Gamma Distributed Random Variable (RV) Generation Method for Clutter Simulation with Non-Integral Shape Parameters

Sensors ◽  
2020 ◽  
Vol 20 (4) ◽  
pp. 955
Author(s):  
Shichao Chen ◽  
Feng Luo ◽  
Chong Hu
Keyword(s):  
Computational Complexity ◽  
Beta Distribution ◽  
Shape Parameter ◽  
Random Variable ◽  
Shape Parameters ◽  
Analysis And Design ◽  
Non Linear ◽  
Improved Methods ◽  
Very High ◽  
Research Endeavour

Sea clutter simulation is a well-known research endeavour in radar detector analysis and design, and many approaches to it have been proposed in recent years, among which zero memory non-linear (ZMNL) and spherically invariant random process (SIRP) are the most two widely used methods for compound Gaussian distribution. However, the shape parameter of the compound Gaussian clutter model cannot be a non-integer nor non-semi-integer in the ZMNL method, and the computational complexity of the SIRP method is very high because of the complex non-linear operation. Although some improved methods have been proposed to solve the problem, the fitting degree of these methods is not high because of the introduction of Beta distribution. To overcome these disadvantages, a novel Gamma distributed random variable (RV) generation method for clutter simulation is proposed in this paper. In our method, Gamma RV with non-integral or non-semi-integral shape parameters is generated directly by multiplying an integral-shape-parameter Gamma RV with a Beta RV whose parameters are larger than 0.5, thus avoiding the deviation of simulation of Beta RV. A large number of simulation experimental results show that the proposed method not only can be used in the clutter simulation with a non-integer or non-semi-integer shape parameter value, but also has higher fitting degree than the existing methods.

scholarly journals A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
H. V. Kulkarni ◽  
S. K. Powar
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Shape Parameter ◽  
Normal Approximation ◽  
Random Variable ◽  
Industrial Applications ◽  
Small Sample ◽  
Prediction Limit ◽  
Coverage Probabilities ◽  
Small Sample Sizes

We propose a simple close-to-normal approximation to a Weibull random variable (r.v.) and consider the problem of estimation of upper prediction limit (UPL) that includes at leastlout ofmfuture observations from a Weibull distribution at each ofrlocations, based on the proposed approximation and the well-known Box-Cox normal approximation. A comparative study based on Monte Carlo simulations revealed that the normal approximation-based UPLs for Weibull distribution outperform those based on the existing generalized variable (GV) approach. The normal approximation-based UPLs have markedly larger coverage probabilities than GV approach, particularly for small unknown shape parameter where the distribution is highly skewed, and for small sample sizes which are commonly encountered in industrial applications. Results are illustrated with a real dataset for practitioners.

Mechanical and Electrical Products Reliability Estimation under Weibull Distribution Based on Accelerated Life Test

2013 ◽  
Vol 302 ◽  
pp. 332-337
Author(s):  
Bo Wan ◽  
Gui Cui Fu ◽  
Li Wang
Keyword(s):  
Weibull Distribution ◽  
Normal Stress ◽  
Shape Parameter ◽  
Interval Estimation ◽  
Reliability Estimation ◽  
Accelerated Life Test ◽  
Point Estimate ◽  
Life Test ◽  
Accelerated Life ◽  
The Relationship

In practice, most mechanical and electrical products life obeys Weibull distribution.This paper based on the relationship between Weibull distribution and exponential distribution, improved the point estimate of characteristic life during the normal stress and enhanced the precision of analysis. The point estimate of the shape parameter under normal stress level was presented, when the assumption that the shape parameter under different stress levels keeps invariable was got rid of. Meanwhile, a means was put forward to give interval estimation of the Weibull distribution parameter and the lower confidence limit of the reliability. Finally, an example of the mechanical and electrical product’s constant-stress accelerated life test was given and proved that the proposed approach is accuracy. It should be valuable for implement of engineering.

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

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.

scholarly journals Investigation of Feller-Buncher Performance Using Weibull Distribution

Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 284
Author(s):  
Ebru Bilici
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
B Value ◽  
Productivity Analysis ◽  
Volume Data ◽  
Estimation Model ◽  
Distribution Method ◽  
Timber Volume ◽  
C Value ◽  
The Right

With the advancement of technology in forestry, the utilization of advanced machines in forest operations has been increasing in the last decades. Due to their high operating costs, it is crucial to select the right machinery, which is mostly done by using productivity analysis. In this study, a productivity estimation model was developed in order to determine the timber volume cut per unit time for a feller-buncher. The Weibull distribution method was used to develop the productivity model. In the study, the model of the theoretical (estimated) volume distributions obtained with the Weibull probability density function was generated. It was found that the c value was 1.96 and the b value was 0.58 (i.e., b is the scale parameter, and c is the shape parameter). The model indicated that the frequency of the volume data had moved away from 0 as the shape parameter of the Weibull distribution increased. Thus, it was revealed that the shape parameter gives preliminary information about the distribution of the volume frequency. The consistency of the measured timber volume with the estimated timber volume strongly indicated that this approach can be effectively used by decision makers as a key tool to predict the productivity of a feller-buncher used in harvesting operations.

scholarly journals Local Convexity-PreservingC2Rational Cubic Spline for Convex Data

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Jamaludin Md. Ali
Keyword(s):  
Shape Parameter ◽  
Cubic Spline ◽  
Convex Curve ◽  
Shape Feature ◽  
Local Convexity ◽  
Shape Parameters ◽  
Numerical Examples ◽  
2D Data ◽  
Industrial Demand ◽  
Made In

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data usingC2rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing.

New Stochastic Orders Based on Double Truncation

1997 ◽  
Vol 11 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Jorge Navarro ◽  
Felix Belzunce ◽  
Jose M. Ruiz
Keyword(s):  
Likelihood Ratio ◽  
Random Variable ◽  
Stochastic Orders ◽  
Likelihood Ratio Order ◽  
Reliability Measures ◽  
Life Distributions ◽  
The Relationship ◽  
Double Truncation

The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

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