عنوان البحث(Papers / Research Title)
Numerical Comparison Function for Weibull Dis,
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
كوثر فوزي حمزة الحسن
Citation Information
كوثر,فوزي,حمزة,الحسن ,Numerical Comparison Function for Weibull Dis, , Time 5/8/2011 1:05:31 PM : كلية التربية للعلوم الصرفة
وصف الابستركت (Abstract)
Numerical Comparison Function for Weibull Distribution Probability Values with Possibility
الوصف الكامل (Full Abstract)
Abstract
The relationship between possibility and probability is cleared through the rang of functions values for each one of them, which is equivalent to be in the closed interval [0, 1], and it has some variation in values. The goal of this research is to find the type of relation and to decrease the variations in values through finding a combination between several probability distributions and membership function in fuzzy logic to be either continuous or discrete .In this paper the weibull distribution has been exploited with a continuous membership function, Gaussian membership and applied failure rate function with that distribution.
Introduction:
Someone asks, why we don’t use the statistic instead of fuzzy logic? More detailed difference between the concepts led us use one instead of the other. That is, the difference between the degree of membership in the set (of some member), and a probability of being in that set.
The point of difference is, the probability involves a crisp set theory (probability of it belongs to class or not), and don’t allow for an element to be a partial member in a class (or a set, as in fuzzy logic1).
Probability is an indicator of frequency or likelihood that an element is in a class, while fuzzy set theory deals with the similarity of an element to a class [3] that is between elements in a class.
Anyone who doesn’t know and haven t study fuzzy logic and fuzzy sets think ,that fuzziness is just a clever disguise for probability, which is never true for more information see [1].
Although fuzzy logic is known latterly ,it has been communicated with many other sciences for its benefits in practical applications(applicable branches).Since 1991, fuzzy logic is used in technology as an industrial tool in reference[5]to be fuzzy control, but the theoretical side stay requisite .
Probability theory and fuzzy set theory have been communicated since they were depend on same range to be in closed interval ,also membership function(MF) that characterize the fuzzy set depend on some parameters(time_ verify parameters)and its values chosen from parameter space(real number).While probability distribution also depend on parameters describe the distribution and determine its values and shape ,which chosen from parameter space, many ways used to locate these parameter values.Also the values of MF constraints are as, [6], [9], while probability has a main condition as .
To shed light on such a relationship, a probability distribution used to compare the values that computed by Weibull distribution function with that values computed by Gaussian MF (both were continuous functions)on tables for values of dependent variable(s) applied for both functions and values for parameters that be in each function . 2.Weibull Probability Density Function [8]The density functions as;
…. (1)
where a,b>0 and x>0 is called the weibull density, a distribution that has been successfully used in reliability theory .From the Weibull distribution, the general equation for failure rate is given by:
1 A fuzzy logic is basically a multi_valued logic that allows intermediate values to be defined between conventional evaluations like; true/false ,black/white ,yes/no ,high/ low (see any reference on fuzzy logic).
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