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.

Strength measurement of rock requires testing that must be carried out on test specimens with particular sizes in order to fulfill testing standards or suggested methods. Often, the coring process breaks up the weaker core pieces, and they are too small to be used in either index tests or conventional strength tests such as point load index (Is) and Brazilian tensile strength (BTS). One of the index tests to indirectly determine the rock strength is the block punch index (BPI) test, which requires flat disc specimens without special treatment. This study aimed to evaluate the applicability of the BPI test for predicting the uniaxial compressive strength (UCS), BTS and IS of the sandstones by empirical equations. Also, we have compared the performance of the BPI and IS for predicting the UCS and BTS. It was experimentally shown that BPI is a reliable method for predicting the UCS, BTS and Is of the sandstones under study. Moreover, the results indicate that BPI could be utilized with same importance as Is for predicting the UCS, while predicting the BTS by Is appears to be more reliable than BPI.

How to profoundly change the beliefs of the polytheists during the age of revelation from the denial of the Prophet (pbuh) to the certainty of his Message and the acceptance of his full guardianship is a question worthy of attention. The order of verses about prophecy based on the order of revelation is the reason to lead a transformative process and a special Quranic method in institutionalizing the belief of prophecy in the lives of Arabs. In the first stage, the Holy Quran in the first Makkī (Arabic: المکّیّ, suras revealed in Mecca) chapters has prepared the community from the motivational side to accept the truth of the Prophet’s (pbuh) prophecy and briefly stating the key issues surrounding it. The Holy Book of Quran at the time of the emergence of oppositions and doubts (the second stage) destroyed the arguments of the polytheists and explained the prophecy and proved its authenticity from a cognitive perspective in the second stage by presenting clear arguments. and the Holy Book of Quran in the third stage after Madanī (Arabic: المدنیّ, suras revealed in Medina) period has undertaken measures in order to fulfill the goals of the Massage by explaining the true position of the Prophet (pbuh) to deepen and operationalize the Prophetic belief through explaining practical duties for the Prophet (pbuh) and behavior based on the acceptance of Walaya (Arabic: ولایة, meaning “guardianship” or “governance”).

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.

Water reservoir systems have important role to control the surface water and provide various demands, such as irrigation, domestic, industrial and hydroelectric power generation. Therefore, it is necessary to study the behavior of these systems to provide demand satisfactorily. Assessment the reservoir system behavior during the drought periods is very important. Water release, always is less then the demand during the drought period. This study, assess the performance of within-year and over-year reservoir systems under different values of vulnerability index. Sustainability index was used to obtain the optimal performance of reservoir systems. Reservoir system was simulated using modified SPA method. Assessment of reservoir performance under different values of vulnerability index in sites showed that the sustainability for within-year system is generally maximum at 25% vulnerability and for over-year system is maximum at 35%-40% vulnerability.

The Taguchi method is a useful technique to improve the performance of products or processes at a lower cost and in lesser time. This procedure can be categorized as the static and dynamic quality characteristics. The optimization of multiple responses has received increasing attention over the last few years in many manufacturing organizations.Several approaches dealing with multiple static quality characteristic problems have been reported in the literature. However, little attention has been made on optimizing the multiple dynamic quality characteristics.In this paper, we investigate multivariate signal response systems (Dynamic Taguchi) and propose a method based on multivariate process capability. Simulated data shows that the proposed method can increase robustness of dynamic Taguchi method. Furthermore, the proposed method is capable to find the optimal value of controllable factors in a continuous space.

The very complex movements in the stock prices are usually taken as random or stochastic, but they may be produced by a deterministic data generating process. Chaos refers to the nonlinear dynamic deterministic process that generates a series, which appears like random, but has a long memory. In the Economics and Finance literature, stock prices are known to be random due to their complexities, and therefore being unpredictable. In this paper, we test for chaos in the stock prices using the data from the daily and weekly stock prices listed in the Tehran Exchange Market (TEPIX) in 1377-1382 (1998-2003). We apply three tests for chaos, namely; BDS, Lyaponov Exponent, and Neural Networks; to the residuals of linear (ARIMA) and nonlinear (GARCH) models. The BDS and the Neural Networks tests results show that there exists nonlinearity in the ARIMA residuals, but not in the GARCH residuals. However, the Lyaponove exponent test result is positive for all different dimensions indicating that the TEPIX is chaotic.