This paper deals with the estimation of the stress-strength Reliability Parameter R ¼ Pð Y\XÞ , when X and Y are independent random variables, where X and Y have inverted gamma distribution. The maximum likelihood estimator and the approximate maximum likelihood estimator of R are obtained. The Bayesian estimation of the Reliability Parameter has been also discussed under the assumption of independent gamma prior, squared error loss and Linex error loss functions. Finally, two real data applications are given for showing the flexibility and potentiality of the inverted gamma distribution.

‎In this paper, under adaptive hybrid progressive censoring samples, Bayes estimation of the multi-component Reliability, with the non-identical-component strengths, in unit generalized Gompertz distribution is considered. This problem is solved in three cases. In the first case, strengths and stress variables are assumed to have unknown, uncommon Parameters. In the second case, it is assumed that strengths and stress variables have two common and one uncommon Parameter, so all of these Parameters are unknown. In the third case, it is assumed that strengths and stress variables have two known common Parameters and one unknown uncommon Parameter. In each of these cases, Bayes estimation of the multi-component Reliability, with the non-identical-component strengths, is obtained with different methods. Finally, different estimations are compared using the Monte Carlo simulation, and the results are implemented on one real data set.

In this paper, we delve into Bayesian inference related to multi-component stress-strength Parameters, focusing on non-identical component strengths within a two-Parameter Rayleigh distribution under the progressive first failure censoring scheme. We explore various scenarios: the general case, and instances where the common location Parameter is either unknown or known. For each scenario, point and interval estimates are derived using methods including the MCMC method, Lindley's approximation, exact Bayes estimates, and HPD credible intervals. The efficacy of these methods is evaluated using a Monte Carlo simulation, and their practical applications are demonstrated with a real data set.

In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the Reliability Parameter under the stress-strength model when the stress and strength are independent exponential random variables with di erent scale Parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated using the law of large numbers and Monte Carlo integration. For the two-stage sequential procedure, explicit formulas for the distribution of the total sample size, the expected value and mean squared error of the maximum likelihood estimator of the Reliability Parameter under the stress-strength model are provided. Moreover, it is shown that both proposed sequential procedures are finite, and in exceptional cases, the exact distribution of stopping times is degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally using real data, the procedures are clearly illustrated.

The Parameters of Reliability for the most family marginal distribution is estimated with the assumption of independence between two component stress and strength, but, unfortunately when these two component are correlated, have been less discussed. Recently, a method based on a copula function for estimating the Reliability Parameter is proposed under the assumption of correlation between stress and strength components. In this paper, this method is used to estimate the Reliability Parameter when the distribution of componets is Generalized Exponential (GE). For this purpose FGM, generalized FGM and frank copula function have been used. Then simulation is also used to demonstrate the suitability of the estimates. In the end, Reliability Parameter for data relative contribution of major groups in terms of age breakdown of the population of urban and rural areas in Iran in the year 1390 will be estimated.

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.

Earthquake is one of the most important natural phenomena that causes economic damages and human losses due to the damage and breakage of structures. The unfortunate economic and social consequences caused by earthquakes, determine the importance of evaluating and improving existing buildings against earthquakes. This issue is particularly important for schools and educational buildings. School buildings, due to their demographic structure, are important buildings whose safe design, implementation and control of behavior and performance are of great importance. Experience of past earthquakes shows that damage to schools can lead to high casualties and human catastrophe; therefore, design regulations also provide stricter rules and regulations for the design of educational buildings. Seismic performance control of existing educational buildings is also of special importance and various methods including linear and nonlinear analysis have been recommended by different regulations and instructions. On the other hand, there are many uncertainties in the study of structural performance that prevent a definite achievement of the structural performance response. Some of these uncertainties are inherent, such as the impossibility of predicting the intensity of future earthquakes, and some are due to errors in analysis and calculations, so the probabilistic expression of structural performance is a logical way to study structural performance. There are several methods to check the Reliability of the structure that are different in terms of hypotheses, methods and accuracy, so the effect of uncertainty in each method should be considered appropriately. A review of past research shows that many studies have been conducted on the possible evaluation of the seismic behavior of concrete structures, but there are few studies on the behavior of real examples of such buildings. In this study, two repetitive types of Kermanshah concrete structural schools are non-linearly modeled and analyzed and evaluated using time-history dynamic analysis under the effect of 12 possible earthquake records, appropriate to the type of land and distance from the fault. In order to evaluate the seismic Reliability of these schools, based on the specific levels of intensity, the probability of reaching the response to the corresponding values ​​is determined at different levels of damage. The maximum structural drift is considered as the response, and the performance levels defined in the FEMA356 guideline are considered as the failure criterion. The fragility curves of the studied schools have been compared and verified with the behavior of a sample of these schools in a real earthquake, as well as the fragility curves presented in the technical manual of the Hazus earthquake model. In this study, the non-linear behavior of important structures such as schools, which are designed in a linear way, is evaluated and compared. Also, expressing the probability of vulnerability of such structures for possible earthquakes can provide the performance of important structures in each region. The results show that the probabilistic expression of the structure's performance is a suitable method to express the behavior and performance of the structure. The type of ground of the school building and the distance of the building from the fault has a significant effect on the seismic performance and response of the structure. With the increase of storeys, the probability of reaching the school drift to different functional levels is always higher and by increasing the earthquake intensity this proability increases as well. Also, the structures of the studied schools, despite the irregularity in the plan, have a good performance in order to take into account the effects of earthquake intensity, site ground and site distance from the fault. This information can be widely used in crisis management, urban management decisions and future planning of the region.

The main goal of this study was finding an appropriate pattern for estimating Reliability of cereal harvester specially John Deer 955 combine in Farahan region. In this purpose, five steps including: selecting the statistical community, recording of data related to repairs and their abundance with the time of operation, choosing a suitable distribution function which fallow repairs, estimating the Parameter of distribution function, and using estimated functions for determining of Reliability were considered. In this case, five JD955 combine with 1800, 1000, 900, 800 and 445 worked hours were selected, randomly. Combines were divided to five main parts including: cutting and feeding unit, belts and chains, engine, hydraulic system and rest of combine mechanisms including: threshing system, separating system, cleaning system and transmition system. All of repairs were recorded based of time duration of work and systems. Repairs were divided into major and minor levels. Finally, time duration between impairments and their abundance types were recorded separately for each system. Based on data distribution and their variations, coefficient b>1, and general form of graph inferred from survival function, Weibull distribution function was selected as the best equation to make clear of impairments. The general form of Weibull function was selected with three Parameters, but it changed to F(X)=1-EXP(-X^(b/a)) form because first impairments could occurre in initial time of combine operation. In order to estimating of Weibull function Parameters, maximum likelihood estimated (MLE) method was used. For anticipating the time between repairs, Mont carlo method was used. Results showed that Reliability of studied combines was zero after 130 hours operation and time duration between repairs of combine was calculated by 42.8 hours.

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.