In this paper, a Multivariate-Multistage Quality Control (MVMSQC) procedure is investigated, hi this procedure discriminate analysis, linear regression and control chart theory are combined to control the means of correlated characteristics of a process, which involves several serial stages. Furthermore, the quality of the output at each stage depends on the output of the previous stage as well as the process of the current stage. The theoretical aspects and the applications of this procedure are enhanced and clarified and its performance is evaluated through a series of simulated data. Both in-control (type one error) and out-of-control (type two error) Average Run Length (ARL) studies are made and the performance of the MVMSQC methodology is discussed.

This investigation deals with transient analysis of cold standby system with n units. Chapman-Kolmogorov equations are developed for repair facility with two repairmen and solved by using matrix technique. Availability and reliability factors have been obtained with probability of the system. A particular case has also been discussed.

In this research article, we estimate the multicomponent stress– strength reliability of a system when strength and stress variates are drawn from an exponentiated Weibull distribution with different shape parameters and, and common scale parameter, respectively. The reliability is estimated using the best single observation percentile method and maximum liklihood method of estimation when samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets we illustrate the procedure. Keywords: Stress– Strength, reliability, Maximum likelihood estimation, Best single observation percentile estimation, Mean square error, Confidence intervals, Gompertz distribution.

Introduction In this paper, the reliability of the multicomponent stress-strength model is studied. The system components may experience the same or different stress levels. In some cases, several stresses are imposed on a system simultaneously, and if the system’, s strength is greater than the stresses, the system remains intact. This article considers a multicomponent system with n2 components when n1 stresses are imposed on each component simultaneously, and all stresses and strengths are independent. The main subject of this model is the study of Rr, k = P(Xr: n1 < Yk: n2), where Xr: n1 is the rth ordered stress variable and Yk: n2 is the kth ordered strength variable. The stress and strength variables distributions are considered the inverse Exponential with unknown scale parameters. Based on the inverse Exponential distribution, Rr, k is obtained. The k-out-of-n2: F system and its exceptional cases, series and parallel systems are studied. In a k-out-of-n2: F system, the system is failed if at least k components fail. Therefore, the reliability of the system is Rn1, k = P( at least n2 􀀀,k + 1 of the Yis exceed Xn1: n1). The special cases of this system are series and parallel systems, whose the stress-strength reliabilities are Rn1, 1 and Rn1, n2, respectively. Rn1, k is the probability that the maximum of stresses is less than the kth strength, Rn1, 1 is the probability that the maximum of stresses is less than the minimum of strengths and Rn1, n2 is the probability that the maximum of stresses is less than the maximum of strengths. Material and Methods One of the most important topics in stress-strength models is the estimation of the reliability parameter. We take a random sample from each distribution of stress and strength variables. The scale parameters are estimated by the maximum likelihood method, and according to the invariance property of this estimator, Rr, k is estimated. Also, the maximum likelihood estimators of Rn1, k, Rn1, 1 and Rn1, n2 are provided. Using the Delta method, the asymptotic distribution of the estimation of Rr, k and the asymptotic confidence interval for Rr, k have been obtained. Results and Discussion Simulation study for the n1 = 5stress and n2 = 7strength model is performed. The stress-strength reliability of the 3-out-of-7: F system and that of the series and parallel systems are estimated. Simulation results show that if the sample size increases, the absolute value of the bias of the maximum likelihood estimator and the mean square error always decreases. Also, two real data sets are considered. The Exponential and inverse Exponential distributions were fitted to both data sets. In the n1 = 5 stress and n2 = 7 strength model, it is observed that when r = 5 and k = 3,7, the inverse Exponential distribution is better than the Exponential distribution and for r = 5 and k = 1, the Exponential distribution is better than the inverse Exponential distribution. Conclusion In this article, we considered the n1stress-n2strength model if the distributions of stress and strength variables are inverse Exponential with different parameters. Using the maximum likelihood method, Rr, k is estimated, and its asymptotic confidence interval is derived. The simulation results show that for Rn1, k, the absolute values of its biases are small. If the sample size increases, the trend of the biases’,absolute values decreases and the mean square error is constantly decreasing. The paper’, s results can be used for the stress-strength model when several stresses are applied to the system components simultaneously, and each component has its strength. Further research in this model can be done with other probability distributions.

Background: In spite of many advantages in Lenke classification of adolescent idiopathic scoliosis, the latest study of Richards et al showed that the King classification is better than had been reported recently and the Lenke classification system of adolescent idiopathic scoliosis is less reliable than previously reported.Methods: In this study, we performed a multi-surgeon comparison of these two classification systems. After teaching and discussing all available data of these classification systems with four spine surgeons, a pilot classification was performed. Then, they independently evaluated preoperative radiographs (standing posteroanterior, lateral, and two supine side-bending views) of 99 patients with adolescent idiopathic scoliosis. The results were determined by calculating the average percentage of intraobserver and interobserver agreement. reliability was quantified using kappa statistics.Findings: The King classification demonstrated good intraobserver and interobserver reliability, with an intraobserver agreement of 85.8% (kappa coefficient, 0.80). Interobserver percentage of agreement averaged 80.8% (kappa coefficient, 0.74). The complete Lenke classification, combining curve type, lumbar modifier, and sagittal thoracic modifier, demonstrated good reliability for both intraobserver and interobserver measurements. The intraobserver percentage of agreement averaged 85.8% (kappa coefficient, 0.82). The interobserver percentage of agreement averaged 80.8% (kappa coefficient, 0.77).Conclusion: In this study, with each investigator performing the radiographic measurements, the King and Lenke classifications were almost similar (the Lenke classification had slightly better results). Such better results might be due to more training of this complex classification system. So, because of greater coverage of idiopathic scoliosis curve and usefulness of Lenke classification system, we prefer using this classification system in our center.

The stress-strength model is a commonly utilized topic in reliability studies. In many reliability analyses involving stress-strength models, it is typically assumed that the stress and strength variables are unrelated. Nevertheless, this assumption is often impractical in real-world scenarios. This research assumes that the strength and stress variables follow the Pareto distribution, and a Gumbel copula is employed to represent their relationship. Additionally, the data is gathered through the Type-I progressively hybrid censoring scheme. The method of maximum likelihood estimation is used for point estimation, while asymptotic and Bootstrap percentile confidence intervals are employed for interval estimation of the unknown parameters and system reliability. Simulation is employed to assess the effectiveness of the suggested estimators. Subsequently, an actual dataset is examined to showcase the practicality of the stress-strength model. Simulation is employed to assess the effectiveness of the suggested estimators. Subsequently, a real dataset is examined to demonstrate the practicality of the stress-strength model.

This study focuses on estimating the reliability of a multicomponent stress-strength model using two Bayesian approaches‎: ‎E-Bayesian and hierarchical Bayesian‎. ‎This model follows Inverse Rayleigh distributions with distinct parameters‎. ‎Additionally‎, ‎the efficiency of the proposed methods is compared by employing Monte Carlo simulation and analyzing a data set.

In this study, the E-Bayesian and hierarchical Bayesian for stress-strength, when X and Y are two independent Rayleigh distributions with different parameters were estimated based on the LINEX loss function. These methods were compared with each other and with the Bayesian estimator using Monte Carlo simulation and two real data sets.

The Big Five Inventory (BFI) is one of the most widely used personality questionnaires, but very few studies have been conducted on its psychometric properties in Iranian population. This study was carried out with the aim of studying the psychometric properties of the BFI questionnaire. For this purpose, 390 university students in Tehran (210 girls and 180 boys) with an age range of 18 to 56 years (M = 27.52; SD = 8.79) were selected using the convenience sampling method and completed BFI and NEO-FFI questionnaires. Cronbach's alpha, multitrait-multimethod matrix, and confirmatory factor analysis were used to estimate the psychometric properties of the questionnaire. The result of the confirmatory factor analysis showed that 15 of the 44 items did not have a strong factor loading (higher than 0.40) on the corresponding factors and were therefore removed from the questionnaire. The fit indices showed that the Persian version of 29 questions (BFI-29) with 5 factors has a good fit with the data. The reliability analysis also showed that the range of Cronbach's alpha coefficients of the factors is from 0.70 to 0.79. The lowest Cronbach's alpha coefficient was related to agreeableness factor and the highest was related to conscientiousness. The findings from the multitrait-multimethod matrix showed that the BFI-29 questionnaire has good convergent and divergent validity with the NEO-FFI questionnaire. In general, based on the results of the present study, it can be said that the BFI-29 questionnaire has desirable psychometric properties and whenever a short tool for personality measurement is needed, this questionnaire can be used.