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The probability distribution of major length and aspect ratio (major length/minor length) of wear debris collected from gear oil used in planetary gear drive were analysed and modelled. The paper aims to find an appropriate probability distribution model to forecast the kind of wear particles at different running hour of the machine.

Used gear oil of the planetary gear box of a slab caster was drained out and charged with a fresh oil of grade (EP-460). Six chronological oil samples were collected at different time interval between 480 and 1,992 h of machine running. The oil samples were filtered to separate wear particles, and microscopic study of wear debris was carried out at 100X magnification. Statistical modelling of wear debris distribution was done using Weibull and exponential probability distribution model. A comparison was studied among actual, Weibull and exponential probability distribution of major length and aspect ratio of wear particles.

Distribution of major length of wear particle was found to be closer to the exponential probability density function, whereas Weibull probability density function fitted better to distribution of aspect ratio of wear particle.

The potential of the developed model can be used to analyse the distribution of major length and aspect ratio of wear debris present in planetary gear box of slab caster machine.

The purpose of this paper is to provide a method to predict the situation of a loaded element in the compressive stress curve to prevent failure of crucial elements in load-bearing masonry walls and to propose a material model to simulate a compressive element successfully in Abaqus software to study the structural safety by using non-linear finite element analysis.

A Weibull distribution function was rewritten to relate between failure probability function and axial strain during uniaxial compressive loading. Weibull distribution parameters (shape and scale parameters) were defined by detected acoustic emission (AE) events with a linear regression. It was shown that the shape parameter of Weibull distribution was able to illustrate the effects of the added fibers on increasing or decreasing the specimens’ brittleness. Since both Weibull function and compressive stress are functions of compressive strain, a relation between compressive stress and normalized cumulative AE hits was calculated when the compressive strain was available. By suggested procedures, it was possible to monitor pretested plain or random distributed short fibers reinforced adobe elements (with AE sensor and strain detector) in a masonry building under uniaxial compression loading to predict the situation of element in the compressive stress‒strain curve, hence predicting the time to element collapse by an AE sensor and a strain detector. In the predicted compressive stress‒strain curve, the peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus were predicted successfully. With a proposed material model, it was illustrated that the needed parameters for simulating a specimen in Abaqus software with concrete damage plasticity were peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus.

The AE cumulative hits versus strain plots corresponding to the stress‒strain curves can be divided into four stages: inactivity period, discontinuous growth period, continuous growth period and constant period, which can predict the densifying, linear, non-linear and residual stress part of the stress‒strain relationship. By supposing that the relation between cumulative AE hits and compressive strain complies with a Weibull distribution function, a linear analysis was conducted to calibrate the parameters of Weibull distribution by AE cumulative hits for predicting the failure probability as a function of compressive strain. Parameters of m and θ were able to predict the brittleness of the plain and tire fibers reinforced adobe elements successfully. The calibrated failure probability function showed sufficient representation of the cumulative AE hit curve. A mathematical model for the stress–strain relationship prediction of the specimens after detecting the first AE hit was developed by the relationship between compressive stress versus the Weibull failure probability function, which was validated against the experimental data and gave good predictions for both plain and short fibers reinforced adobe specimens. Then, the authors were able to monitor and predict the situation of an element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression loading by an AE sensor and a strain detector. The proposed model was successfully able to predict the main mechanical properties of different adobe specimens which are necessary for material modeling with concrete damage plasticity in Abaqus. These properties include peak compressive strength and its corresponding axial strain, the compressive strength and its corresponding axial strain at the point with maximum compressive Young’s modulus and the maximum compressive Young’s modulus.

The authors were not able to decide about the effects of the specimens’ shape, as only cubic specimens were chosen; by testing different shape and different size specimens, the authors would be able to generalize the results.

The paper includes implications for monitoring techniques and predicting the time to the collapse of pretested elements (with AE sensor and strain detector) in a masonry structure.

This paper proposes a new method to monitor and predict the situation of a loaded element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression load by an AE sensor and a strain detector.

While Six Sigma metrics have been studied by researchers in detail for normal distribution-based data, in this paper, we have attempted to study the Six Sigma metrics for two-parameter Weibull distribution that is useful in many life test data analyses.

In the theory of Six Sigma, most of the processes are assumed normal and Six Sigma metrics are determined for such a process of interest. In reliability studies non-normal distributions are more appropriate for life tests. In this paper, a theoretical procedure is developed for determining Six Sigma metrics when the underlying process follows two-parameter Weibull distribution. Numerical evaluations are also considered to study the proposed method.

In this paper, by matching the probabilities under different normal process-based sigma quality levels (SQLs), we first determined the Six Sigma specification limits (Lower and Upper Six Sigma Limits- LSSL and USSL) for the two-parameter Weibull distribution by setting different values for the shape parameter and the scaling parameter. Then, the lower SQL (LSQL) and upper SQL (USQL) values are obtained for the Weibull distribution with centered and shifted cases. We presented numerical results for Six Sigma metrics of Weibull distribution with different parameter settings. We also simulated a set of 1,000 values from this Weibull distribution for both centered and shifted cases to evaluate the Six Sigma performance metrics. It is found that the SQLs under two-parameter Weibull distribution are slightly lesser than those when the process is assumed normal.

The theoretical approach proposed for determining Six Sigma metrics for Weibull distribution is new to the Six Sigma Quality practitioners who commonly deal with normal process or normal approximation to non-normal processes. The procedure developed here is, in fact, used to first determine LSSL and USSL followed by which LSQL and USQL are obtained. This in turn has helped to compute the Six Sigma metrics such as defects per million opportunities (DPMOs) and the parts that are extremely good per million opportunities (EGPMOs) under two-parameter Weibull distribution for lower-the-better (LTB) and higher-the-better (HTB) quality characteristics. We believe that this approach is quite new to the practitioners, and it is not only useful to the practitioners but will also serve to motivate the researchers to do more work in this field of research.

The purpose of this paper is to analyze mathematical aspects of the q‐Weibull model and explore the influence of the parameter q.

The paper uses analytical developments with graph illustrations and an application to a practical example.

The q‐Weibull distribution function is able to reproduce the bathtub shape curve for the failure rate function with a single set of parameters. Moments of the distribution are also presented.

The generalized q‐Weibull distribution unifies various possible descriptions for the failure rate function: monotonically decreasing, monotonically increasing, unimodal and U‐shaped (bathtub) curves. It recovers the usual Weibull distribution as a particular case. It represents a unification of models usually found in reliability analysis. Q‐Weibull model has its inspiration in nonextensive statistics, used to describe complex systems with long‐range interactions and/or long‐term memory. This theoretical background may help the understanding of the underlying mechanisms for failure events in engineering problems.

Q‐Weibull model has already been introduced in the literature, but it was not realized that it is able to reproduce a bathtub curve using a unique set of parameters. The paper brings a mapping of the parameters, showing the range of the parameters that should be used for each type of curve.

The purpose of this paper is to investigate wind power potential of site using wind speed, wind direction and other meteorological data including temperature and air density collected over a period of one year.

The site-specific air density, wind shear, wind power density, annual energy yield and capacity factors have been calculated at 30 and 10 m above the ground level (AGL). The Weibull parameters have been calculated using empirical, maximum likelihood, modified maximum likelihood, energy pattern and graphical methods to determine the other dependent parameters. The accuracies of these methods are determined using correlation coefficient (R²) and root mean square error (RMSE) values.

The site-specific wind shear coefficient was found to be 0.18. The annual mean wind speeds were found to be 5.174 and 4.670 m/s at 30 and 10 m heights, respectively, with corresponding standard deviations of 2.085 and 2.059. The mean wind power densities were found to be 59.50 and 46.75 W/m² at 30 and 10 m heights, respectively. According to the economic assessment, the wind turbine A is capable of producing wind energy at the lowest value of US$ 0.034/kWh.

This assessment provides the sustainable solution of energy which minimizes the dependence on continuous supply of oil and gas to run the conventional power plants that is a major cause of increasing load shedding in the significant industrial and thickly populated city of Pakistan. Also, this will minimize the quarrel between the local power producer and oil and gas supplier during the peak season.

This wind resource assessment has some important social implications including decreasing the environmental issues, enhancing the uninterrupted supply of electricity and decreasing cost of energy per kWh for the masses of Karachi.

The results are showing that the location can be used for installing the wind energy power plant at the lower cost per kWh compared to other energy sources. The wind energy is termed as sustainable solution at the lowest cost.

The purpose of this paper is contribution to estimate the potential of wind energy in Douala in Cameroon, by modeling and predicting the regime of wind. The paper deals with the analysis and comparison of seven numerical methods for the assessment of effectiveness in determining the parameters for the Weibull distribution, using wind speed data collected at Douala International Airport in Cameroon, in the period from September 2011 to May 2013, obtained by meteorological equipment belonging to the Laboratory of Energy Research of the Institute of Geological and Mining Research.

By using ANOVA, root mean square error and chi-square tests to compare the proposed methods, this study aims to determine which methods are effective in determining the parameters of the Weibull distribution for the available data, in an attempt to establish acceptable criteria for better usage of wind power in Douala, which is the economic capital and ought to have prominence in the use of renewable sources for electricity generation in Cameroon.

The study helps to determine that moment, empirical and energy pattern factor methods used to determine the shape parameter k and the scale parameter c of the Weibull distribution present a better curve fit with the histogram of the wind speed. This fact is clearly validated by means of the statistical tests. But, all the seven methods gave excellent performance. Then, k reaching levels ranging from 3.5 to 5.5 and c range from 1.7 to 2.4.

Then as far as we are concerned, for a significant contribution, it could be more effective to have a model for prediction of wind characteristics using wind data collected per hour, one at least three years. A comparison of results obtained from lots of other methods (seven in this case) is necessary before an efficient discussion. Standard deviations and errors between measured and predicted data must also be presented.

This paper aims to prevent gasket sealing failure in engineering, accurately predict gasket life, extend system life and improve sealing reliability. The accelerated life test method of flexible graphite composite–reinforced gaskets is established, the life distribution law of flexible graphite composite–reinforced gaskets is revealed, and the life prediction method of flexible graphite composite–reinforced gaskets with different allowable leakage rates is proposed, which can provide a reference for the life prediction of other types of gaskets.

In this study, flexible graphite composite–reinforced gaskets were tested for long-term high-temperature sealing performance on a multi-sample gasket accelerated life test rig. The data were also analyzed using the least squares method and the K-S hypothesis calibration method. A gasket time-dependent leakage model and an accelerated life model were also developed. Constant stress-accelerated life tests were conducted on flexible graphite composite–reinforced gaskets. On this basis, a gasket life prediction method at different allowable leakage rates was proposed.

The life distribution law of flexible graphite composite–reinforced gaskets is revealed. The results show that the life of the gasket obeys the Weibull distribution. The time-correlated leakage model and accelerated life model of the gasket were established. And the accelerated life test method of the flexible graphite composite–reinforced gasket was established. The life distribution parameters, accelerated life model parameters and life estimates of gaskets were obtained through tests. On this basis, a gasket life prediction method under different leakage rates was proposed, which can be used as a reference for other types of gaskets.

The research in this paper can better provide guidance for the use and replacement of gaskets in the project, which is also very meaningful for predicting the leakage condition of gaskets in the bolted flange connection system and taking corresponding control measures to reduce energy waste and pollution and ensure the safe operation of industrial equipment.

A multi-specimen gasket-accelerated life test device has been developed, and the design parameters of the device have reached the international advanced level. The life distribution law of the flexible graphite composite–reinforced gasket was revealed. The accelerated life test method for the flexible graphite composite–reinforced gasket was established. The life prediction method of the flexible graphite composite–reinforced gasket under different allowable leakage rates was proposed.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2023-0254/

The purpose of this paper is to exploit a new and robust method to forecast the long-term extreme dynamic responses for wave energy converters (WECs).

A new adaptive binned kernel density estimation (KDE) methodology is first proposed in this paper.

By examining the calculation results the authors has found that in the tail region the proposed new adaptive binned KDE distribution curve becomes very smooth and fits quite well with the histogram of the measured ocean wave dataset at the National Data Buoy Center (NDBC) station 46,059. Carefully studying the calculation results also reveals that the 50-year extreme power-take-off heaving force value forecasted based on the environmental contour derived using the new method is 3572600N, which is much larger than the value 2709100N forecasted via the Rosenblatt-inverse second-order reliability method (ISORM) contour method.

The proposed method overcomes the disadvantages of all the existing nonparametric and parametric methods for predicting the tail region probability density values of the sea state parameters.

It is concluded that the proposed new adaptive binned KDE method is robust and can forecast well the 50-year extreme dynamic responses for WECs.

This paper develops a model that allows consideration of not only the total maintenance costs but also the overall probability of a system breakdown when determining the time intervals between preventive maintenance activities. Using the model, which assumes that component failures follow a Weibull distribution, managers can determine the required preventive maintenance interval to achieve a desired probability of system failure, and they can calculate the total expected costs of both breakdowns and maintenance actions. The model’s application is illustrated using the impact of four different maintenance policies. The model assures top management that the unavailable system time due to equipment breakdown will be within a specified limit.

Roller compacted concrete (RCC) pavement is used in areas subjected to heavy impact loads; therefore, higher impact resistance is a desirable property of consideration. This study aims to investigate the effect of partial replacement of fine aggregate with crumb rubber (CR) and the addition of nanosilica (NS) by weight of cementitious materials on the impact resistance of roller compacted rubbercrete (RCR).

Four replacement levels of CR (0, 10, 20 and 30 per cent) and four addition levels of NS (0, 1, 2 and 3 per cent) were considered. The impact resistance test was carried out using the drop weight test recommended by ACI 544.

The results showed that the impact resistance of RCR increases with an increase in both CR and NS addition, though for CR above 20 per cent, sudden drop in impact resistance was observed. However, NS reduces the ductility of RCR by decreasing the post-cracking impact resistance. Response surface methodology was used to develop models for predicting the impact resistance of RCR, and the developed models showed a high degree of correlation. As a result of wide variations in the impact drop test data, two-parameter Weibull distribution function was used for the data analysis, and it was found that the probabilistic distributions of the first crack and ultimate failure impact resistance follow the two-parameter Weibull distribution function.

In this work, the effect of partial replacement of fine aggregate with CR and the addition of NS by weight of cementitious materials on the impact resistance of RCC pavement has been investigated. CR has been used to increase the impact resistance of RCC Pavement.