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The purpose of this article is to compare maintenance policies based on Weibull and q-Weibull models.

This paper uses analytical developments, several figures and tables for graphical and numerical comparison. Previously published hydropower equipment data are used as examples.

Models for optimal maintenance interval determination based on q-Weibull distribution were defined. Closed-form expressions were found, and this allows the application of the method with small computational effort.

The use of the q-Weibull model to guide the definition of maintenance strategy allows decision-making to be more consistent with sample data. The flexibility of the q-Weibull model is able to produce failure rate modeling with five different formats: decreasing, constant, increasing, unimodal and U-shaped. In this way, the maintenance strategies resulting from this model should be more assertive.

Expressions for determining the optimal interval of preventive maintenance were deduced from q-Weibull distribution. Expected costs per maintenance cycle of Brazilian hydropower equipment were calculated with q-Weibull and Weibull distributions. These results were compared in terms of absolute values and trends. Although a large number of works on corrective and preventive maintenance have been proposed, no applications of the q-Weibull distribution were found in literature.

Historically, reliability of systems has been tracked based on a common assumption that, at the system level, the failure rate follows the exponential distribution, and is therefore assumed to be constant over the useful life of the system. However, this method, while adequate for many purposes, does not necessarily provide the early warning system that many companies need to stay ahead of expensive quality or reliability fixes. This paper presents a new method that provides the needed early warning, at a reasonable analysis cost, by combining the use of two reliability distributions for the purpose of analyzing fielded systems. In particular, this paper describes a hypothesized relationship between a key parameter contained in the Weibull distribution and within the Army Material Systems Analysis Activity (AMSAA) reliability growth model. Actual data from General Electric Transportation Systems (GETS) were used to explore this relationship. The results suggest that there indeed exists a significant relationship between the two models and both can be used in tandem to track reliability of systems.

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 compare four life data models, namely the exponential and the Weibull models, and their corresponding generalized versions, q-exponential and q-Weibull models, by means of one practical application.

Application of the models to a practical example (a welding station), with estimation of parameters by the use of the least squares method, and the Akaike Information Criterion (AIC).

The data of the example considered in this paper is divided into three regimes, decreasing, constant and increasing failure rate, and the q-Weibull model describes the bathtub curve displayed by the data with a single set of parameters.

The simplicity and flexibility of the q-Weibull model may be very useful for practitioners of reliability analysis, and its benefits surpasses the inconvenience of the additional parameter, as AIC shows.

The q-Weibull model is compared in detail with other three models, through the analysis of one example that clearly exhibits a bathtub curve, and it is shown that it can describe the whole time range with a single set of parameters.

The purpose of this paper is to understand the consequence of the use of mixed Weibull distribution in the cell formation problem. In reliability theory, a mixed distribution is used for more than one hazard cause, and the Weibull distribution can be used for ascendant, monotonous and descendant failure rate. Here, the authors mixed these two theme and use it in a common problem in group technology.

In this paper, the authors made a non-polynomial-hard mathematical model based on past research and solved it with an exact algorithm. The algorithm is coded and solved in GAMS to illustrate the model, and the authors use simulation. A common numerical example is solved with the model, and the results are compared.

Reliability analysis model based on the mixed Weibull distribution approach will give options to a user to select the suitable failure rate and modes for a specific situation. If the user uses the exponential or Weibull distribution instead of the mixed Weibull distribution, the calculated cost and reliability are wrong; therefore, it leads to user making wrong decisions.

The model the authors use is the one used in past research, but in the past, researchers did not use the mixed distribution for explaining failure time. Therefore, the model can be considered as a new and more complete model.

Describes a probabilistic methodology for fracture assessments of flawed structures constructed of ferritic steels using the research code WSTRESS. The probabilistic formulation for cleavage fracture implements a multiaxial form of the weakest link model which couples the macroscopic fracture behavior with a micromechanics model based on the statistics of microcracks. The Weibull stress, σ_w, emerges as a suitable near‐tip parameter to provide a connection between the microregime of failure and remote loading (J). WSTRESS builds on an iterative procedure to incorporate a 3‐D finite element description of the crack‐tip stress field and measured values of fracture toughness to calibrate the Weibull modulus, m, and the scale parameter, σ_u. Specific features of the code include statistical inference of Weibull parameters based on uncensored and censored models (with maximum likelihood method), construction of confidence intervals, several definitions for the near‐tip fracture process zone and other general facilities such as spatial integration of the stress field (to incorporate the random orientation of microcracks) and stochastic simulation of fracture data using the Monte Carlo method. The code also includes a convenient free‐form command language and a seamless interface with finite element results files stored in Patran binary or ASCII format.

This paper aims to exploit an orthogonal space-time block code (OSTBC) and maximal ratio combining (MRC) techniques to evaluate error rate performance of multiple-input multiple-output system for different modulation schemes operating over single- and double-Weibull fading channels.

The authors provided a novel analytical expression for cumulative distribution function (CDF) of double-Weibull distribution in the form of Meijer-G function. They also evaluated probability density function (PDF) and CDF for single- and double-Weibull random variables. CDF-based closed-form expressions of symbol error rate (SER) are computed for the proposed systems’ design.

Based on simulation and analytical results, the authors have shown that double-Weibull fading which shows the cascaded nature of channel gives significantly poor SER performance compared to that of single-Weibull fading. Moreover, MRC offers an improved error rate performance compared to that of OSTBC. As the fading parameter increases for any modulation technique, the required signal-to-noise ratio (SNR) gap between single- and double-Weibull fading decreases. Finally, it is observed that the analytical results are a good approximation to simulation results.

For practical implication, the authors use a number of antennas at the base station, but solely to maximize performance, one can use receive diversity, i.e. MRC.

Using higher-order modulation (i.e. 16-QAM), 4 and 1 dB less SNR is required at high and less fading, respectively, in single-Weibull fading as compared to double-Weibull fading. Hence, at higher-order modulation, double-Weibull channel model performs better as compared to lower-order modulation.

Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.

The research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.

The proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.

The models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.

These models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.

A unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

Cox's model with Weibull distribution and Cox's with exponential distribution are the most important models in reliability analysis. This paper seeks to show that, with a large sample size based on expectation maximization (EM) algorithm, both models give similar results.

The parameters of the models have been estimated by method of maximum likelihood based on EM algorithm. The objective of this analysis is to fit the modification of Cox's model with Weibull distribution and Cox's with exponential distribution, examine its performance and compare their results with Crowder et al.

A simulation study indicates that the parametric Cox's model with Weibull distribution gives similar results to Cox's with exponential distribution, especially for a large sample size. Also, the modification of the two models showed better results compared with Crowder et al., especially for the second causes of failure.

A modification of the two competing risk models has mostly been applied in failure time data and simulation data. The results of the simulation study indicate that the Weibull and exponential are suitable for Cox's model as they are easy to use and it can achieve even higher accuracy compared with other distribution models.

Downtime is a process parameter that substantially impacts on the operating hours and results in production losses, thus motivating maintenance engineers to control process plants. Notwithstanding, the impacting nature of process equipment failure on the operating hours in bottling plants remains inadequately examined. In this paper, the cause-and-effect analysis was used to establish the root cause of the downtime problem and Pareto analysis employed to justify the greatest opportunities for improvement in reducing downtime and increasing reliability levels. Weibull analysis is then conducted on the industrial setting. Novel aspect ratios are proposed.

Using the Weibull failure function of machines as a principal facilitator to produce failure predictions, the downtime behaviour of a process plant was modelled and tested with practical data from a bottling process plant. This research was conducted in a Nigerian process bottling plant where historical data were examined.

The analysis of the results shows the following principal outcome: First, the machines with the highest and least downtime values are 2 and 5, respectively, with correspondingly mean values of 22.83 and 4.39 h monthly. Second, the total downtime 92.05 and 142.14 h for the observed and target downtime, with a coefficient of determination of 0.5848 was recorded. Third, as month 1 was taken as the base period (target), all the machines, except M5 had accepted performance, indicating proper preventive maintenance plan execution for the bottling process plant. Availability shows a direct relationship between the failure and uptime of the machines and the downtime impacts on production. Two machines had random failure pattern and five machines exhibited a wear-out failure pattern and probably due to old age and wear of components in the machines.

The major contribution of the paper is the Weibull modelling in a unique application to a bottling plant to avoid current practices that use reliability software that is not easily accessible.