Several sampling distribution properties of the estimator for Cpk are presented under the assumption that the data are normal, independent and identically distributed. In this paper using these assumptions, the expectation, variance and skewness are calculated by statistical methods, since the sampling distribution is weakly skewed, it is concluded that a symmetric interval estimator for Cpk might be reasonable. Also a symmetric interval estimator has been developed.

The present study proposes several methods for improving the parameter estimation of interval-censored exponential lifetime data. These methods can be regarded as the versions of substitution method which are based on the most probable time of occurring failures or the meantime of failures in each inspection interval. Based on simulation studies, the methods proposed in this present study can improve the existing estimators which are based on the midpoint of inspection intervals “, or”,the exponential probability plot.

In this paper, point prediction and prediction intervals (PIs) of artificial neural network (ANN) based downscaling for mean monthly precipitation and temperature of two stations (Tabriz and Ardabil in North West of Iran) were evaluated using general circulation models (GCMs). PIs were constructed by novel Upper Lower Bound Estimation (LUBE) method in which an ANN with two outputs was constructed for estimating the prediction bounds. Also, Bootstrap method as a classic technique for assessing uncertainty of ANN was used to further examine the proposed LUBE method. In this way, the accuracy of PIs was quantified by coverage and width criteria. Three GCMs, Can-ESM2, BNU-ESM, INM-CM4 and ensemble-GCM (ensemble of mentioned models) were used in four grid points around each of station for evaluating ANNbased downscaling of precipitation and temperature parameters. Comparison between the results of two methods indicated that LUBE method could lead to more reliable results than the Bootstrap method. PIs width and coverage probability were 10% to 40% lower and 2% to 10% higher than the Bootstrap method for different GCMs, respectively. Ensemble-GCM led to more accurate results so that computed PIs width and coverage probability were 10% to 60% lower and 2% to 20% higher than those for the single GCMs.

In this paper, we study the estimation problems for the Burr type III distribution based on a complete sample. The maximum likelihood method is used to derive the point estimators of the parameter. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Two numerical examples with real data set and simulated data, are presented to illustrate the methods proposed here.

In point estimation of the value of a parameter, especially when the estimator under consideration has a probability density function, then the limit that the expected value of the estimator actually equaled the value of the parameter being estimated will tend towards zero for the estimator to be asymptotically unbiased. Hence, some interval about a point estimate needs to be included to accommodate for the region of an unbiased estimate. But in several occurrences when the random variable is not normally distributed as is common in practice; then the interval estimated for the location and scale parameters may be too wide to give the desired assurance. In this study, we have obtained some results on the confidence procedure for the location and scale parameters for symmetric and asymmetric exponential power distribution which is robust in the case of skewness or cases alike: tail heavier; and or thinner than the normal distribution using pivotal quantities approach, and on the basis of a random sample of fixed size n. Some simulation studies and applications are also examined.

Evaluation of production products is a process of necessity to check product quality. One of the criteria for evaluating the quality of the manufactured product is the quality characteristic of the process performance index, which has recently considered a number of researchers in statistical articles. Estimation of process performance index can be done according to the type of statistical distribution of product quality by different methods, including the maximum likelihood method, the least error squared method, the maximum product of distances and quantization. In this article, the estimation of the process performance index is presented using the gamma distribution using method of estimation, moment, maximum likelihood and interval shrinkage estimator. To provide the interval contraction estimator, after proving the unbiasedness of the torque estimators asymptotically, it is shown that the performance index estimator is also unbiased. Next, the efficiency of the estimators is compared using the square error criterion.

First roof weighting interval in mechanized longwall mining is related directly to the applied loads on support system and thus, has important role on stability, safety, and continuity of operation. This paper presents an innovative approach based on cavability of immediate roof to estimate first roof weighting interval. Nine inherent parameters of roof strata and its surrounding environment which affect caving process were taken into account to develop a classification system, incorporating fuzzy hybrid multi criteria decision-making technique. Roof Strata Cavability index (RSCi) was defined as summation of ratings for all parameters. Subsequently, the relationship between RSCi and extracted volume until the first caving moment (i. e. the extraction height× panel width × first roof weighting interval) was determined using linear and non-linear regression models. Models were proposed and validated using the actual field data collected from different longwall panels around the world. Results indicated that the quadratic polynomial model gave a better performance in the estimation of first roof weighting interval, compared to the other models. It was concluded that the proposed approach is an accurate and flexible tool to estimate first roof weighting interval in longwall mining.

In this article, two methods are proposed tp give the interval estimation for parameters exponential distribution under double type II censoring. Kambo (1978), Balakrishnan (1990) and Raqab (1995) use maximum likelihood estimator to construct interval estimation. All of this method need an assumption that sample is exponentially distributed. we will use shorter interval than the traditional method.