Process Capability Indices (PCI) show that the Process conforms to the specification limits,when the product quality depends on more than one characteristic, Multivariate Process Capability Indices (MCPI) are used. By modifying the Process capability indices, the Process incapability indices are created,these indices then provide information about the accuracy and precision of the Process separately. In the real world, in most cases, the parameters cannot be specified precisely,therefore, the use of fuzzy sets can solve this problem in statistical quality control. The purpose of this paper is to present, for the first time, a Multivariate Process incapability index by considering the measurement error in a fuzzy environment. The presented index is shown for practical examples solved by considering Triangular Fuzzy Numbers,then the capability of the model is compared to the time when fuzzy logic is not used. The obtained results emphasize that ignoring the measurement error also leads to the incorrect calculation of Process capability, causing a lot of damage to manufacturing industries, especially high-tech ones.

One advantage of Process incapability index over the classical Process capability index is that it provides uncontaminated separation between Process accuracy and Process precision. However, the value of the index is difficult to determine accurately when Process parameters cannot be determined precisely. In such a case, fuzzy set theory can be applied to obtain more flexible and sensitive information. In this paper, a fuzzy Process incapability index is proposed when the specification limits are assumed to be type-2 fuzzy. When the Process mean and variance are unknown and when the observations are measured imprecisely, three fuzzy estimators are considered. A simulation study is conducted based on the Thin-Film-Transistor Liquid-Crystal Display (TFT-LCD) fuzzy Process. By applying the total integral value method to the membership function of a fuzzy index, it becomes easier to make a comparison of the quality of different Processes.

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.

Abstract:  In some practical applications, the quality of a product or Process is defined by a profile, which is a relationship between a response variable and one or more explanatory variables. Simple linear profiles (SLPs) are one of the various types of profiles in which the product or Process quality is related to a simple linear function between a response and an explanatory variable. In this article, a functional capability index for a simple linear profile with asymmetric tolerance is introduced. The performance of the proposed index and existing ones (  and ) are studied using numerical examples and simulation studies in terms of mean absolute error (MAE), mean square error (MSE) and absolute percentage error (APE) metrics. The results show that the new index performs better than the two existing indices. Furthermore, confidence intervals for the proposed index are constructed using three bootstrap methods, and their performance is evaluated using simulation studies. A real-world case study is presented to demonstrate the application of the proposed index.

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.