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This note provides some extensions on optimal policies on price, warranty length and production rate proposed by Wu et al. (2009) . [1] (Wu, C.C.; Chou, C.Y.; Huang C. Optimal price, warranty length and production rate for free replacement policy in the static demand market. Omega 2009; 37: 29-39.) More specifically, the assumptions of the original paper is extended in this note from the production rate being positive and the second derivative of the demand function with respect to price and warranty-length being negative to no restrictions on both  

Weibull distributions play an important role in reliability studies and have many applications in engineering. It normally appears in the statistical scripts as having two parameters, making it easy to estimate its parameters. However, once you go beyond the two parameter distribution, things become complicated. For example, estimating the parameters of a three-parameter Weibull distribution has historically been a complicated and sometimes contentious line of research since classical estimation procedures such as Maximum Likelihood Estimation (MLE) have become almost too complicated to implement. In this paper, we will discuss an approach that takes advantage of Artificial Neural Networks... 

Wind generation is one of the most successful sources of renewable energy for the production of electrical energy. The technical characteristics of wind generation make existing conventional generation models not directly applicable. This paper presents an analytical method for the reliability assessment of the flat-rated wind turbine generation systems. An example of flat rating is that of the MOD-2, a second-generation class of wind turbines. The power-velocity characteristic of the flat-rated wind turbines is employed in this paper to model the operating behavior of the installed wind turbine generators. For wind-power potential estimation, the Weibull distribution model is used. The... 

CFAR detector is an essential component in any radar system. This component ensures that the system may not be overloaded by false targets. In the past it was common to model the interfering signal (clutter) in a radar system with a Rayleigh distribution. But as a progress in the radar systems, nowadays the Rayleigh model is insufficient, therefore some other models such as Weibull and lognormal are proposed and CFAR detectors for these models are developed through the papers. But majority of these proposed CFAR detectors are derived for single pulse operation. When more than one pulse exists, it is proposed to use binary integrator to improve the performance. It is mentioned through... 

SUMMARY: In this paper, we study the effects of anomalies on the distribution of TCP flow interarrival time process. We show empirically that despite the variety of data networks in size, number of users, applications, and load, the interarrival times of normal flows comply with the Weibull distribution, whereas specific irregularities (anomalies) causes deviations from the distribution. We first estimate the scale and shape parameters and then check the discrepancy of the data from a Weibull distribution with the estimated parameters. We also utilize the Weibull counting model to recheck the conformance of small flow interarrival times with the distribution. We perform our experiments on a... 

Order statistic (OS) CFAR processor is a powerful detector, but similar to many other CFAR detectors, suffers from clutter edge as well as interfering targets. To overcome these problems, two derivations of this detector have been developed. These are order statistic greatest of (OSGO) and order statistic smallest of (OSSO) CFAR processors. The cost, paid for this improvement, is a considerable decrease in detection probability for homogenous Weibull clutter. Furthermore, a substantial performance degradation of OSGO in interfering target (high target masking effect) and an excessive false alarm of OSSO in clutter edge, also, occur. This behavior is a result of non-soft rules used in these... 

In Distributed detection systems, restricting the output of the local decision to one bit certainly implies a substantial information loss. In this paper, we consider the fuzzy detection, which uses a function called membership function for mapping the observation space of each local detector to a value between 0 and 1, indicating the degree of assurance about presence or absence of a signal. In this case, we examine the problem of distributed Maximum Likelihood (ML) and Order Statistic (OS) constant false alarm rate (CFAR) detections using fuzzy fusion rules such as "Algebraic Product"(AP), "Algebraic Sum"(AS), "Union"(Un) and " Intersection"(IS) in the fusion centre. For the Weibull... 

Fault tree analysis is one of the key approaches used to analyze the reliability of critical systems. Fault trees are usually analyzed using mathematical approaches or Monte Carlo simulation (MCS). This paper presents a Fuzzy-Monte Carlo simulation (FMCS) approach in which the uncertain data is generated by the MCS approach. The FMCS approach is applied to the Weibull probability distribution which is widely been used in the analysis of reliability, availability, maintainability and safety (RAMS). Using the fuzzy arithmetic, times to failure (TTF) of the components are generated. These results are processed by a kind of fault tree (e.g. time-to-failure tree) to produce the TTF of the whole... 

The goal of this research is to formulate an inventory control problem of a single item with variable demand dependent on displayed stock level and selling price of the commodity. The item deteriorates based on a three-parameter Weibull distribution and advance payment is needed to purchase the item with the all-unit discount policy. Shortages are allowed partially and backlogged with the rate dependent on the length of customers' waiting time. The corresponding problem is formulated as a profit maximisation model. For solving this problem, four different variants of particle swarm optimisation (PSO) are utilised. Then, the application of the model is illustrated with the help of a numerical... 

In this paper, we analyze the Internet traffic from a different point of view based on Benford's law, an empirical law that describes the distribution of leading digits in a collection of numbers met in naturally occurring phenomena. We claim that Benford's law holds for the inter-arrival times of TCP flows in case of normal traffic. Consequently, any type of anomalies affecting TCP flows, including intentional intrusions or unintended faults and network failures in general, can be detected by investigating the first-digit distributions of the inter-arrival times of TCP SYN packets. In this paper we apply our findings to the detection of intentional attacks, and leave other types of... 

Traffic modeling, traffic decomposition, and traffic engineering are some of the applications of traffic characterization that are mainly based on statistical characteristics of the network traffic. Many empirical analyses on Internet traffic traces show that the flow inter-arrival time distribution generally follows the Weibull distribution. As the scale of the network becomes larger, the Weibull distribution degrades to the Poisson distribution and when the flow arrival rate is high, it asymptotically converges to the Normal distribution. The aggregated traffic on high bandwidth links is the result of statistical multiplexing of many traffic sources, and the flow arrival rate on these... 

In this paper, we study the effects of anomalies on the distribution of TCP flow interarrival time process. We show empirically that despite the variety of data networks in size, number of users, applications, and load, the interarrival times of normal flows comply with the Weibull distribution, whereas specific irregularities (anomalies) causes deviations from the distribution. We first estimate the scale and shape parameters and then check the discrepancy of the data from a Weibull distribution with the estimated parameters. We also utilize the Weibull counting model to recheck the conformance of small flow interarrival times with the distribution. We perform our experiments on a diverse... 

Weibull distribution plays an important role in failure distribution modeling in reliability studies. It is a hard work to estimate the parameters of Weibull distribution. This distribution has three parameters, but for simplicity, a parameter is omitted and as a result, the estimation of the others will be easily done. When the three-parameter distribution is of interest, the estimation procedure will be quite boring. Maximum likelihood estimation is a good method, which is usually used to elaborate on the parameter estimation. The likelihood function formed for the parameter estimation of a three-parameter Weibull distribution is very hard to maximize. Many researchers have studied this... 

This work concerns simultaneous determination of relative permeability, capillary pressure, pore size distribution (PSD), and residual oil saturation data by optimization of well testing data, and introduces a new capillary pressure relationship, based on the Weibull distribution function, for direct determination of the PSD function from capillary pressure parameters. Three consecutive injection, fall off, and production well tests are performed on a predefined synthetic reservoir through simulation, and an optimization algorithm is used to find the parameters of relative permeability and capillary pressure curves as well as the value of residual oil saturation. The PSD function is also... 

The Weibull distribution plays an important role in failure distribution modeling of reliability research. While there are three parameters in the general form of this distribution, for simplicity, one of its parameters is usually omitted and as a result, the others are estimated easily. However, due to its more flexibility, when the general form of the Weibull distribution is of interest, the estimation procedure is not an easy task anymore. For example, in the maximum likelihood estimation method, the likelihood function that is formed for a three-parameter Weibull distribution is very hard to maximize. In this paper, a new hybrid methodology based on a variable neighborhood search and a...