Box-Jenkins methodology is one of the most famous modeling approaches to describe the underlying stochastic structure and forecasting future values of various phenomena. In this methodology, the models are of type ARIMA, that is, autoregressive integrated moving average. Some advantages of those include robustness, easiness to use, and wide applicability in various disciplines ranging from engineering to economics. Inflation has been a highly discussed issue in economics. This research focuses on modeling and forecasting the yearly inflation rate of Iran from 1960 to 2019 using ARIMA. According to various measures, different ARIMA models are investigated to confirm their effectiveness. It is here showed that non-seasonal ARIMA (1,0,0) is the most appropriate model for this application.

It has been proved that the quality control charts with variable sampling schemes are more effective than the classical ones in improving statistical measures. The Average Number of False Alarms (ANF), Average Number of Samples (ANS), Average Number of Inspected Items (ANI), and Adjusted Average Time to Signal (AATS) have been the most important statistical measures always being attending in the evaluation of control charts. Thus, this study was conducted aiming at illustrating a comprehensive analytical review on the U control chart via the statistical measures. To this end, different levels of the possible factors were determined, and the results of calculating the statistical measures and the obtained parameters on the sampling schemes of the U control chart were presented. The results indicated that the variable U control charts were capable of improving the effectiveness of statistical measures, especially for detecting shifts and number of false alarms.

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Many scientific researches have shown an obvious fact that the quality control charts with variable sampling schemes are more effective than the classical ones in improving statistical measures. The average number of false alarms (ANF), the average number of samples (ANS), the average number of inspected items (ANI), and the adjusted average time to signal (AATS) are the most important statistical measures that have always been attending in the evaluation of control charts. In this paper, a comprehensive analytical review on the U control chart by the statistical measures have been explained. For this purpose, different levels of the possible factors are determined and presented the results of calculating the statistical measures with the obtained parameters on the sampling schemes of the U control chart. It is shown that the variable U control charts are able to improve the effectiveness statistical, especially for detecting shifts and number of false alarms.