In many real systems in which a STATE variable should be controlled for being in appropriate range, the length of control (REVIEW) intervals is taken to be constant. In such systems, when the cost of REVIEWs and out-of-range values of the STATE variable are considerable, this method may not be optimal. In this paper we let the length of REVIEW intervals to be variable during each operating cycle and construct the related mathematical cost model. Then two scheduled REVIEW METHODS, called U2 and U3, are introduced and the relative annual system costs are analyzed. The model is developed for the case of negative exponential variate as the time between successive consumption points. It is shown that the new METHODS results a significant reduction in the expected annual cost of the system.

A known theorem in probability is adopted and through a probabilistic approach, it is generalized to develop a method for generating RANDOM deviates from the distribution of any continuous RANDOM variable. This method which may be considered as an approximate version of the Inverse Transform algorithm takes two RANDOM numbers to generate a RANDOM deviate. While maintaining all the other advantages of the Inverse Transform method such as the possibility of generating ordered as well as correlated deviates and being applicable to all density functions regardless of their parameter values.

The main pre-request of the forest management and planning program is the availability of quantitative and qualitative data from forest structure. Therefore, the forest INVENTORY plays a vital role in the estimation of the current status and future planning. In this study, spatial pattern of trees in Gorazbon section of Kheyroud forest in northern Iran was simulated to compare the RANDOM systematic sampling and complete RANDOM systematic sampling method based on the full calipering method. By using the Arc GIS software, the spatial pattern of forest trees was simulated. Buffer function was used to calculate the RANDOM systematic sampling and complete RANDOM systematic sampling method based on the full calipering method. In order to compare RANDOM systematic sampling with full calipering single-sample, a t-test was used. The results showed that there was no significant difference between RANDOM systematic sampling and full calipering method to estimate the average diameter of Alnus, Fagus orientalis, and Tilia begonifolia. However, there was a significant difference between two METHODS in the estimation of average diameter of Carpinus orientalis and Quercus persica. The results of T-test revealed that there is no significant difference between Alnus and Tilia begonifolia but significant difference was observed between the trees of the Fagus orientalis, Carpinus orientalis, and Quercus persica. In addition, paired t-test was used to compare the RANDOM systematic sampling and complete RANDOM systematic sampling method. Results showed that there is no significant difference between RANDOM systematic sampling and complete RANDOM systematic sampling method.

This paper extends the sign test to the case where data are observations of fuzzy RANDOM variables, and the hypotheses are imprecise rather than crisp. In this approach,  rst a new notion of fuzzy RANDOM variables is introduced. Then, the -level sets of the imprecise observations are transacted to extend the usual method of sign test. To do this, the concepts of fuzzy median and fuzzy sample median are de ned. We also develop a well-known large sample property of the classical sample median. In addition, the test statistic is extended for investigating fuzzy hypothesis. After that, applying an index called credibility degree, the degree that the observed fuzzy test statistics belongs to the critical region is evaluated. The result provides a fuzzy test function which leads to some degrees to accept or to reject the fuzzy null hypothesis. A numerical example is provided to clarify the discussions made in this paper.

In a celebrated work by Shao [13] several inequalities for negatively associated RANDOM variables were proved. In this paper we obtain some maximal inequalities for associated RANDOM variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].

In the absolutely continuous case, order statistics, record values and several other models of ordered RANDOM variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither records nor weak records are submodels of discrete generalized order statistics. Next, we show that progressively Type-II right censored order statistics from an arbitrary distribution can be embedded in the model of generalized order statistics and then use this fact to establish some distributional properties of progressively Type-II right censored order statistics. Finally, we present some characterizations of the geometric distribution based on progressively Type-II right censored order statistics.

In this paper, the properties of fuzzy RANDOM variables with new meter and some extended results of monotone convergence theorem and dominated convergence theorem for fuzzy RANDOM variables are discussed. The main result is given by usingDp, q -distance defined on the set of fuzzy numbers.