The quality of some processes is defined by a simple Linear function between a response and an explanatory variable, which is named a simple Linear profile. Various capability indices have been introduced in the literature for these processes. Some of them are functional, that use all domain of the explanatory variable instead of its levels values. Therefore, these methods may fail to account capability of the process and overstate it. This paper applies fuzzy logic to deal with the explanatory variable domain and introduces two capability indices. Then, investigates and compares the performance of the proposed indices and some existing ones, using a simulation study. Results show that one of the new proposed indices has the best performance based on the mean square error and mean absolute error criteria.

A pro le is a relation between one response variable and one or more explanatory variables that represent the quality of a product or the performance of a process. Process Capability Indices (PCI) is measured to evaluate processes in producing conforming products. All existing methods that measure process capability indices in a simple Linear pro le consider response variables at some levels of explanatory variable and ignore all ranges of x-values. In this paper, a functional approach is proposed to measure the process capability index of simple Linear pro les in all ranges of explanatory variable. This new approach follows the traditional de nition of process capability indices and leads to their accurate values for a simple Linear pro le. The functional approach uses a reference pro le, functional speci cation limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability at each level of the explanatory variable in a simple Linear pro le, as well as the unique value of a process capability index for a simple Linear pro le. A comparison study using a non-conforming proportion method shows the better performance of functional process capability indices in measuring the process capability in a simple Linear pro le.

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.

In an increasing number of practical situations, the quality of a process or product can be effectively characterized and summarized by a profile. A profile is usually a functional relationship between a response variable and one or more explanatory variables which can be modeled frequently using Linear or nonLinear regression models. In this paper, we study the effect of non-normality on profile monitoring in Phase II when within or between autocorrelation is present. Different levels of autocorrelation and skewed and heavy-tailed symmetric nonnormal distributions are used in our study to evaluate the performance of three existing monitoring schemes numerically. Simulation results indicate that the non-normality and autocorrelation can have a significant effect on the in-control performances of the considered schemes. Results also indicate that the out-of-control performances of the schemes are not very sensitive to low and moderate levels of autocorrelation in moderate and large shifts.

Background: Linear frontal bone fractures are common injuries in road traffic accidents. Pneumocephalus and CSF (cerebrospinal fluid) leak are both factors influencing their outcome. Persistent pneumocephalus and CSF leak are main indications for surgical treatment. Objectives: Surgical indications are rarely discussed in Linear frontal bone fractures. We report results on patients with Linear frontal bone fractures, clinical data, management, surgical indications and outcome. Methods: From 2011 to 2015, 121 patients were admitted to our institution with a diagnosis of frontal bone fractures (compound depressed fractures excluded). Fractures were classified into three types, Type A: fracture involving anterior wall of the frontal sinus; Type B: fracture involving posterior wall of the frontal sinus and Type C: fracture of frontobasal region without involving the frontal sinus. All patients were followed for more than 6 months. Results: A total of 112 patients were conservatively treated with standard pneumocephalus protocol. Nine patients underwent surgical intervention. The indications for surgery were the presence of persistent pneumocephalus in CT scan and persistent CSF leak. The presence of pneumocephalus or CSF leak in Type B patients sinus cranialisation with repair of the defect were the variables mainly influencing the outcome (P < 0. 001). Conclusions: Frontal bone fracture needs careful attention to prevent its complications such as a CSF leak and meningitis. Patients need clinical and radiological evaluation. Patients with persistent CSF leak or pneumocephalus should always be treated surgically and others should be managed conservatively.

Non-cooperative intelligent control agents (ICAs) with dedicated cost functions, can lead the system to poor performance and in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the feedback Nash equilibrium point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR control system based on the FNEP for a Linear time-invariant system. For this purpose, two control strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) problem (i.e. a supervisory problem), and the second one is a decentralized control problem (i.e. an infinite horizon Linear-quadratic differential game). Then, while examining the optimal solution of each of the above strategies on the performance of the other, the necessary and sufficient conditions for the equivalence of the two problems are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR controller is presented. It is shown that the theorems could be extended from a two-agent control system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

Background and aim: According to the importance of avoiding injuries to the neurovascular bundles in certain surgical procedures (e.g. placement of implants), an accurate location of the mandibular is neccessary. The aim of the present study was to evaluate and compare between the accuracy of the panoramic spiral tomography in location of the mandibular canal.Methods and materials: In this study, by means of the odonto Rama 2000 (Traphy, French), panoramic radiographies were taken and by means of Cranex tome multifunctional unit (orion corporation Sordex, finland), tomographic slices were taken at 3 different location in each posterior mandible segments (distal to the mental foramen). Then the dry mandibles were sectiond at these 3 sites with specialized desiged drill. The fallowing 2 measurments were performed both on the panoramic radiographies (A, B), tomograms (A’, B’) and the bone sections (A’’, B”) at the 3 sites.Findings: The research was on 6 dry mandibles (36 sites). We found an average mean difference of 3.9 mm with a standard deviation of 1.57 in panoramic radiography and an average mean differences of 0.21mm with a standard deviation of 0.21 in spiral tomography. The report of data showed that 16.4% of cases are in+_0.5mm and 41.4% of cases are in+_1mm (overstimate and underestimate) in panoramic radiography and 94.6% of cases are in+_0.5mm and 97.3% of cases are in+_1mm in spiral tomography. ICC in panoramic radiography was 0.6932 and in spiral tomography was 0.9982 (P<0.001) Conclusion and recommendation: Spiral tomography using the Cranex tome multifunctional x-ray unit provides accurate information and sufficient detailes or preoperative planning of implant in the posterior mandible and this method is recommended for surgures, periodontists and prosthodontists.

Statement of Problem: Evaluation of diagnostic records as a supplement to direct examination has an important role in treatment planning of orthodontic patients with aesthetic needs. Photogrammetry as a quantitative tool has recently attracted the attention of researchers again.Purpose: The purpose of this study was to design computer software to analyze orthodontic patients’ facial profile photographic images and to estimate reliability and validity of its measurement.Materials and Method: profile photographic images of 20 volunteered students were taken in the natural head position with standard technique. Manual Linear and angular measurements were used as a gold standard and compared with the results obtained from Aesthetic analyzer Software (designed for that purpose). Dahlberg’s method error and Intraclass Correlation Coefficient (ICC) was used to estimate validity, reliability and inter-examiner errors.Results: Almost all the measurements showed a high correlation between the manual and computerized method (ICC>0.75). The maximum method errors computed from Dahlberg’s formula were 1.345 mm in Linear and 3.294 degrees in angular measurements. At the highest levels, inter-examiner errors were 1.684 mm and 3.741 degrees in Linear and angular measurements, respectively.Conclusion: Although a low budget has been allocated for the design of Aesthetic Analyzer software, its features are comparable with commercially available products. The software’s capabilities can be increased. The results of the current study indicated that the software is accurate and repeatable in photographic analysis of orthodontic patients.