Study on the P-S-N Curve of Sucker Rod Based on Three-Parameter Weibull Distribution

During the oil production process, sucker rods are subjected to cyclic alternating load. After a certain number of cycles, a sucker rod can experience fatigue failure. The number of cycles is called fatigue life (N), and the accurate relationship between maximum stress (S) and fatigue life (N) under a certain reliability (P), namely the P-S-N curve, is an important basis for the reliability analysis and fatigue life prediction of sucker rods. The Basquin model, based on log-normal distribution, is widely used for fitting the P-S-N curves of sucker rods. Due to the limitation of this model, it is difficult to extrapolate the conclusion obtained from a finite fatigue region to the high-cycle or ultra-high-cycle fatigue region, which makes it impossible to estimate the fatigue limit of the sucker rod. Compared to the log-normal distribution, Weibull distribution causes the sucker rod to have a minimum safety life, namely the safety life at 100% survival rate, which complies with the fatigue characteristics of the sucker rod and is more in line with the actual situation. In this study, the fatigue data for ultra-high-strength HL and HY grade sucker rods were obtained through experimental fatigue tests. A new fatigue life model was established and the P-S-N curves of two types of ultra-high strength sucker rods were obtained. For HL- and HY-type ultra-high strength sucker rods, the average error between the fitting result and fatigue test value is 1.25% and 4.39%, respectively. Compared to the S-N curve fitting result obtained from the Basquin model commonly used for sucker rods, the new model based on three-parameter Weibull distribution provides better fitting precision and can estimate fatigue limit more accurately, so this model is more suitable for estimating fatigue life and can better guide the design of ultra-high strength sucker rod strings.

Bayesian method for estimating Weibull parameters for wind resource assessment in the Equatorial region: a comparison between two-parameter and three-parameter Weibull distributions

The two-parameter Weibull distribution has garnered much attention in the assessment of windenergy potential. The estimation of the shape and scale parameters of the distribution has broughtforth a successful tool for the wind energy industry. However, it may be inappropriate to use thetwo-parameter Weibull distribution to assess energy at every location, especially at sites wherelow wind speeds are frequent, such as the Equatorial region. In this work, a robust technique inwind resource assessment using a Bayesian approach for estimating Weibull parameters is firstproposed. Secondly, the wind resource assessment techniques using a two-parameter Weibulldistribution and a three-parameter Weibull distribution which is a generalized form of twoparameterWeibull distribution are compared. Simulation studies confirm that the Bayesianapproach seems a more robust technique for accurate estimation of Weibull parameters. Theresearch is conducted using data from seven sites in Equatorial region from 1o N of Equator to 19oSouth of Equator. Results reveal that a three-parameter Weibull distribution with non-zero shiftparameter is a better fit for wind data having a higher percentage of low wind speeds (0-1 m/s) andlow skewness. However, wind data with a smaller percentage of low wind speeds and highskewness showed better results with a two-parameter distribution that is a special case of threeparameterWeibull distribution with zero shift parameter. The results also demonstrate that theproposed Bayesian approach and application of a three-parameter Weibull distribution areextremely useful in accurate estimate of wind power and annual energy production.

Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis

Online marketing refers to the practices of promoting a company’s brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company’s product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.

Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>