Weibull distribution

The increasing wind power generation requires the updating of the computational tools that support decision making in the operation and planning of electric power systems. This work describes a methodology to model the spatial correlations among wind speeds probability distributions in probabilistic power flow. The proposed methodology is based on Nataf transformation and Monte Carlo Simulation. The proposed methodology is illustrated in case studies with the IEEE 24 bus test system, highlighting the importance of adequately considering such correlations.

Due to environmental concerns and increased energy demand, natural esters are among the alternatives to mineral oils in transformers. This study examines the electrical behavior of natural ester-based ZnO nanofluids at different concentrations in the range of 0.05–0.4 g/L. AC breakdown voltages are measured in a horizontally positioned sphere–sphere electrode system according to IEC 60156 specifications. The measurement data are analyzed using Weibull and normal distribution functions. Breakdown voltages with 1%, 10% and 50% probability are also estimated, these probabilities being of great interest for the design of power electrical components. Experimental results show that AC breakdown voltage increases with the concentration of ZnO nanoparticles, except for the concentration of 0.05 and 0.4 g/L of ZnO. Moreover, breakdown voltages at 1% and 10% probability increase by 22.7% and 13.2% when adding 0.1 g/L ZnO to natural ester, respectively.

Compared to Sn-Pb solder joints, our understanding of the fatigue of SnAgCu solder joints is far from complete. The challenges to achieving a complete understanding of SnAgCu solder joint fatigue arise partly from their significantly different creep behavior and vulnerability to micro structure evolution (aging). In this paper, we present results from thermal fatigue tests carried out with the help of a simulated power cycling tester. The test specimens were 1.27 mm pitch Ceramic Ball-Grid Array (CBGA) components with two lead-free solder alloy compositions - Sn3.8Ag0.7Cu and Sn3.0Ag0.5Cu. The components were subjected to hot dwells at 100degC for 10, 30 and 60 minutes to study the effect of dwell time on the fatigue life -a total of 48 components were tested. The resulting failure data was fit to a Weibull distribution. The packages were stored at room temperature prior to testing and the effect of the time of storage on the fatigue life was also studied. Finite element analyses were performed to study the effect of hot dwell time on the fatigue life of the CBGA component.

In today's business transactions, there are various reasons, namely, bulk purchase discounts, re-ordering costs, seasonality of products, inflation induced demand, etc., which force the buyer to order more than the warehouse capacity. Such situations call for additional storage space to store the excess units purchased. This additional storage space is typically a rented warehouse. Inflation plays a very interesting and significant role here: It increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organisation prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space, which is facilitated by a rented warehouse. Ignoring the effects of the time value of money and inflation might yield misleading results. In this study, a two-warehouse inventory model with linear trend in demand under inflationary conditions having different rates of deterioration has been developed. Shortages at the owned warehouse are also allowed subject to partial backlogging. The solution methodology provided in the model helps to decide on the feasibility of renting a warehouse. Finally, findings have been illustrated with the help of numerical examples. Comprehensive sensitivity analysis has also been provided.

Wind data collected over a period of three years at four different locations in Gökçeada were evaluated to estimate the potential of wind energy in the north-western part of Turkey. The data from the selected stations were used to estimate the regional mean wind speed distribution of Gökçeada, which revealed that four distinct regions exist with values from 1.0 to 4.0; 4.1 to 6.0, 6.1 to 8.0 and greater than 8.1 m/s. For each station, an extensive analysis was carried out to find the monthly average wind speed and its distribution. Several types of probabilistic distribution were matched to these distributions including the Weibull distribution. It was observed that one third of the island enjoys annual wind speeds greater than 6.0 m/s. This potential can be converted to electrical energy by means of wind farms, and the energy extracted from this source may supply electricity to the island and a small part of the mainland.

D-alpha-tocopheryl poly(ethylene glycol) 1000 succinate (TPGS 1000) is a widely used form of vitamin E. TPGS 1000 is comprised of a hydrophilic polar (water-soluble) head and a lipophilic (water-insoluble) alkyl tail. TPGS 1000 has been used as a solubilizer, an emulsifier and as a vehicle for lipid-based drug delivery formulations. Most recently, TPGS 1000 has been recognized as an effective oral absorption enhancer. An enhancing effect is consistent with a surfactant-induced inhibition of P-glycoprotein (P-gp), and perhaps other drug transporter proteins; however, the exact inhibition mechanism(s) remain unclear. Therefore, in an attempt to generate additional knowledge, we have synthesized and tested various TPGS analogs containing different PEG chain length (TPGS 200/238/400/600/1000/2000/3400/3500/4000/6000). These results demonstrate a relationship between TPGS PEG chain length and influence on rhodamine 123 (RHO) transport in Caco-2 monolayers, a relationship which may be illustrated using a Weibull distribution.

Compared to Sn-Pb solder joints, our understanding of the fatigue of SnAgCu solder joints is far from complete. The challenges to achieving a complete understanding of SnAgCu solder joint fatigue arise partly from their significantly different creep behavior ...

با توجه به بحران هاي زیست محيطي نا شي از گرمایش زمين و همچنين نياز روز افزون جوامع بشري به تأمين انرژي، لزوم  جایگزیني منابع فسییلي با منابع پایدار و پاک روز به روز بيشتر مي شود.  در ميان همه ي انرژي هاي نو، انرژي باد به دليل توسعه یافتگي تکنولوژي آن، صرفه اقتصادي بيشتر، دارا بودن و در دسترس بودن، نسبت به سایر انرژي هاي نو در جهان پیشي گرفته است. ایجاد یک مزرعه برق بادي مستلزم یافتن مناطق مناسب و داراي ظرفيت بالا، با توان توجيه اقتصادي است. در این مطالعه به برر سي پتانسيل توان برق بادي در ا ستان البرز با استفاده از آناليز داده ها ي ثبت شده ي سرعت، جهت و دماي باد در بازه هاي ده دقيقه اي تو سط سازمان انرژي هاي نو ) سانا(  در دو ایستگاه طالقان و اشتهارد پرداخته شد. داده ها با توزیع ویبول آناليز شدند و نتيجه نشان داد که اشتهارد با پتانسيل باد w/m2 25 / 133 در منطقه مرزي کلاس طبقه بندي باد قرار گرفت و طالقان با پتانسيل باد  w/m2 710 / 35 براي این منظور نامناسب بود.

The Weibull and Log-Normal distributions are frequently used in reliability to analyze lifetime (or failure time) data. The ratio of maximized likelihood (RML) has been extensively used in choosing between the two distributions. The Kullback-Leibler information is a measure of uncertainty between two densities. We examine the use of Kullback-Leibler Divergence (KLD) in discriminating either the Weibull or Log-Normal distribution. An advantage of the KLD is that it incorporates entropy of each model. We explain the applicability of the KLD by a real data set and the consistency of the KLD with the RML is established.

The geometrical factors defining an adhesive joint are of great importance as its design greatly conditions the performance of the bonding. One of the most relevant geometrical factors is the thickness of the adhesive as it decisively influences the mechanical properties of the bonding and has a clear economic impact on the manufacturing processes or long runs.The traditional mechanical joints (riveting, welding, etc.) are characterised by a predictable performance, and are very reliable in service conditions. Thus, structural adhesive joints will only be selected in industrial applications demanding mechanical requirements and adverse environmental conditions if the suitable reliability (the same or higher than the mechanical joints) is guaranteed.For this purpose, the objective of this paper is to analyse the influence of the adhesive thickness on the mechanical behaviour of the joint and, by means of a statistical analysis based on Weibull distribution, propose the optimum thickness for the adhesive combining the best mechanical performance and high reliability. This procedure, which is applicable without a great deal of difficulty to other joints and adhesives, provides a general use for a more reliable use of adhesive bondings and, therefore, for a better and wider use in the industrial manufacturing processes.

This article presents a brief analysis of some probability distributions used in modeling and analysing the reliability of systems or items such as equipment. First, the concepts of Life Data Analysis (LDA-Life Data Analysis) are presented and later a detailed explanation will be made of the most important concepts and methods associated with the life distributions used in reliability analysis, such as Exponential, Lognormal, Weibull and Gumbel.

In this paper we introduce, for the first time, the Weibull-Geometric distribution which generalizes the exponential-geometric distribution proposed by Adamidis and Loukas (1998). The hazard function of the last distribution is monotone decreasing but the hazard function of the new distribution can take more general forms. Unlike the Weibull distribution, the proposed distribution is useful for modeling unimodal failure rates. We derive the cumulative distribution and hazard functions, the density of the order statistics and calculate expressions for its moments and for the moments of the order statistics. We give expressions for the R\'enyi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an algorithm EM (Dempster et al., 1977; McLachlan and Krishnan, 1997) is provided for estimating the parameters. We obtain the information matrix and discuss inference. Applications to real data sets are given to show the flexibility and potentiality of the proposed distribution.

La velocidad del viento cambia continuamente, por lo que es necesario describirlo de forma estadística. Es conveniente establecer un modelo de las frecuencias de las velocidades del viento que venga descrito por una función matemática continua en vez de por una tabla de valores discretos.

While major failures command attention, they tend to be sporadic in nature and generally result from a chain of minor failures which combine in a specific or unusual way to result in a major failure. For more common and expensive in the long run are chronic, everyday failures, which don’t cross reporting thresholds or raise warning flags. Such failures may cost companies millions of dollars in maintenance costs, lost profit opportunities, and wasted product over time.
When failure-related costs are tracked and reported accurately, reliability analytics specially reliability growth/ distribution analysis provide an effective and efficient means to identify MTBF, TTF, TTR, failure pattern, failure probability and predict the future failure for an asset on a scientific basis, to avoid such failures, select the appropriate maintenance strategy, and set the appropriate time frequency of preventive maintenance prior expected failure in future.
This paper discusses the forecasting of the next failure for an equipment via reliability analytics where it contains a model, ranging from the model concept and data collection to draw the model outlines and workflow with focusing in reliability growth and reliability distribution where both can predict the future failure. Then next, the established model will be run through a PAM software provided by Meridium for some cases to figure out the great advantage in predicting of next failure of an equipment. In addition of that, the obtained data will be reviewed and analyzed in detail in terms of the failure rate and the failure pattern.

Keywords: [Failure, Predict, Growth rate, Reliability growth, Reliability distribution, Weibull distribution, APM, Asset, MTBF, MTTR, MTTF, taxonomic, PDF, failure pattern]