Smallest Extreme Value Research Articles

TRENDING PERSPECTIVE IN EVALUATION OF INSPECTION CHARACTERISTICS OF PHARMACEUTICAL COMPOUND: COMPARATIVE STUDY OF CONTROL CHARTS

Background and objectives: The quality and efficacy of the pharmaceutical medicinal product are of paramount importance to the patients. Reproducibility and consistency of the properties of the dosage form start with the constituting ingredients either active or inactive. The present work provides an approach for the trending of one of the crucial inspection characteristics of a well-known excipient that is commonly used as a disintegrant of a water-insoluble synthetic cross-linked Polyvinyl Pyrrolidone (PVP). Establishing manufacturing criteria and quality limits should be assessed from the beginning level of the project using exploratory process-behavior plots. Materials and Methods: This study involved an assay of the initial 16 batches of the manufactured 1-ethenyl pyrrolidine-2-one expressed as a dried substance using a standard analysis method according to British Pharmacopoeia (BP). Exploratory Shewhart charts were plotted after preliminary distribution identification using Statistical Process Control (SPC) software. Based on the goodness of fit test results, the most appropriate assumed distribution was implemented in drawing the Individual/Moving Range (I/MR) control charts. Results: The goodness of fit study and probability plot showed that the most close-fitting to the data dispersion pattern was Johnson transformation to the normal spreading, smallest extreme value and Weibull distribution, respectively. While there were no alarms that could be detected from the process mean and the variability charts, further improvement is required from the supplier side to meet the benchmark minimum limit threshold, in addition, the process mean was not centered but shifted towards the Upper Control Limit (UCL). Conclusion: Implementation of SPC techniques is crucial in the modern competitive healthcare industry. Trending charts play a pivotal role in this perspective. They provide a quantitative estimation for the current situation and the actions needed for the future improvement of the monitored characteristic. Peer Review History: Received: 11 August 2023; Revised: 23 September; Accepted: 29 October, Available online: 15 November 2023 Academic Editor: Dr. Amany Mohamed Alboghdadly, Ibn Sina National College for Medical Studies in Jeddah, Saudi Arabia, amanyalboghdadly@gmail.com Received file: Reviewer's Comments: Average Peer review marks at initial stage: 6.5/10 Average Peer review marks at publication stage: 7.0/10 Reviewers: Dr. Taiwo O Elufioye, University of Ibadan, Nigeria, toonitaiwo@yahoo.com Dr. Bilge Ahsen KARA, Ankara Gazi Mustafa Kemal Hospital, Turkey, ahsndkyc@gmail.com

Circadian and ultradian oscillations in bilateral rhythms of the crayfish chelipeds.

Circadian systems are composed of multiple oscillatory elements that contain both circadian and ultradian oscillations. The relationships between these components maintain a stable temporal function in organisms. They provide a suitable phase to recurrent environmental changes and ensure a suitable temporal sequence of their own functions. Therefore, it is necessary to identify these interactions. Because a circadian rhythm of activity can be recorded in each crayfish cheliped, this paired organ system was used to address the possibility that two quasi-autonomous oscillators exhibiting both circadian and ultradian oscillations underlie these rhythms. The presence of both oscillations was found, both under entrainment and under freerunning. The following features of interactions between these circadian and ultradian oscillations were also observed: (a) circadian modal periods could be a feature of circadian oscillations under entrainment and freerunning; (b) the average period of the rhythm is a function of the proportions between the circadian and ultradian oscillations; (c) the release of both populations of oscillations of Zeitgeber effect results in the maintenance or an increase in their number and frequency under freerunning conditions. These circadian rhythms of activity can be described as mixed probability distributions containing circadian oscillations, individual ultradian oscillations, and ultradian oscillations of Gaussian components. Relationships among these elements can be structured in one of the following six probability distributions: Inverse Gaussian, gamma, Birnbaum-Saunders, Weibull, smallest extreme value, or Laplace. It should be noted that at one end of this order, the inverse Gaussian distribution most often fits the freerunning rhythm segments and at the other end, the Laplace distribution fits only the segments under entrainment. The possible relationships between the circadian and ultradian oscillations of crayfish motor activity rhythms and between the probability distributions of their periodograms are discussed. Also listed are some oscillators that could interact with cheliped rhythms.

Nonparametric control chart using auxiliary information for smallest extreme value distribution

Traditionally, in using an auxiliary variable for quality control applications, the response and auxiliary variables are often assumed to follow a bivariate normal distribution. Given that the response variable and an auxiliary variable are linearly related, a novel process monitoring method is proposed to scrutinize the shifts of the model parameter when the response and auxiliary variables follow the smallest extreme value distributions. Utilizing the estimates of the model parameters as input variables, auxiliary information based (AIB) multivariate sign exponential weighted moving average (AIB-MSEWMA) control chart is proposed. Because the AIB-MSEWMA control chart doesn’t require the multivariate normality distribution assumption for the estimators of model parameters, the AIB-MSEWMA control chart is more reliable than the competitors of the AIB-Hotelling T 2 and AIB multivariate EWMA control charts in terms of the false alarm rate. Finally, the operation of the AIB-MSEWMA control chart is illustrated through a regenerated data set of the car brake system.

EWMA chart based on Bayes‐conditional pivotal quantity for Weibull percentiles under complete data and type‐II censoring

AbstractBayes‐conditional control chart has been used for monitoring the Weibull percentiles with complete data and type‐II censoring. Firstly, the Weibull data are transformed to the smallest extreme value (SEV) distribution. Secondly, the posterior median of quantiles is used as a monitoring statistic. Finally, a pivotal quantity based on the monitoring statistic with its conditional distribution function is derived for obtaining the control limits. This control chart is denoted as Shewhart‐SEV‐ . In this study, we extend this work based on an exponential weighted moving average model named exponential weighted moving average‐SEV‐ for monitoring the Weibull percentiles. We provide the statistical properties of the monitoring statistic. The average run length and the standard deviation of run lengths, computed by the integral equation approach, are used as performance measures. The results indicate that the proposed chart performs better than the Shewhart‐SEV‐ . The breaking strength of carbon fibers is used to illustrate the application of the proposed control chart.

A Modified Replacement Model for Items That Fail Suddenly with Variable Replacement Costs

Several researches have been done to provide better alternative to the existing replacement models, but the research works did not adequately address the replacement problem for items that fail suddenly. Hence, a modified replacement model for items that fail suddenly has been proposed using the knowledge of probability distribution of failure times as well as that of variable replacement cost. The modified cost functions for implementing both individual and group replacements were derived. The modified cost functions were minimized using the principle of classical optimization in order to find the age at which replacement of items would be appropriate. Conditions under which the individual and group replacement policies should be adopted were derived. Two real data sets on failure time of LED bulbs and their replacement costs were used to validate the theoretical claims of this work. In essence, goodness-of-fit test was used to select appropriate probability distribution of failure times as well as that of replacement costs for data sets I and II respectively. The goodness-of-fit results showed that failure times of LED bulbs follow the Smallest Extreme Value and Laplace distributions for data sets I and II respectively. Similarly, it was observed that individual replacement cost followed the two-parameter Gamma and Largest Extreme Value distributions for data sets I and II respectively. Further, the group replacement cost was found to follow the log-normal and two-parameter Weibull distributions for data sets I and II respectively. Based on the empirical study, we observed that individual replacement policy is better than group replacement policy in terms of cost minimization for both existing model and the proposed model. In view of the results, the proposed replacement policy was recommended over the existing one because it yielded lower replacement costs than the existing replacement model.

Statistical Distribution Analysis of Mechanical Properties of a Welded Pipeline Steel API X70 and Correlation between Hardness and other Mechanical Characteristics

The aim of this study is to model the distribution patterns of the different mechanical properties of a submerged arc welded pipeline steel API X70 and to investigate the relationship between Vickers hardness and other mechanical properties of API X70. In this study, serial mechanical properties of 70 pipes, formed by spiral submerged arc welding of high strength low alloy steel (HSLA) API X70, were measured in base metal and weldments. Four main statistical distributions: Normal, Log-normal, Weibull and smallest extreme value distributions were chosen to test the goodness of fit to the experimental data. As a result, normal and lognormal distributions can equally model the distribution patterns of the whole experimental data of studied mechanical properties except for the hardness and toughness of the base metal that can be approximated by Weibull and smallest extreme value distributions, respectively. Using the current data, a weak but statistically significant correlation is obtained only between the toughness of the fusion zone and the hardness of both the base metal and the heat affected zone. Consequently, the calculated regression models were unable to estimate impact toughness values based on future measures of Vickers hardness components.

Application of Mixture Models for Analyzing Reliability Data: A Case Study

Whenever purchasing durable goods, customers expect it to perform properly at least for a reasonable period of time. Over the last 30 years there has been a heightened interest in improving quality, productivity and reliability of manufactured products. As discussed by Murthy, Xie and Jiang, [1] analyzed “Aircraft windshield failure data” and fitted 2-fold Weibull mixture model for this data set. They estimated the model parameters from WPP plot. In this study, a set of competitive 2-fold mixture models (including Weibull, Exponential, Normal, Lognormal, Smallest extreme value distribution) are applied to find out the suitable statistical models. The data consist of both failure and censored lifetimes of the windshield. In the existing literature, there are many uses of mixture models for the complete data, but very limited literature available about it uses for the censored data case. Maximum likelihood estimation method is used to estimate the model parameters and the Akaike Information Criterion (AIC), Anderson-Darling (AD) and Adjusted Anderson Darling (AD*) test statistics are applied to select the suitable models among a set of competitive models. Various characteristics of the mixture models, such as the cumulative distribution function, reliability function, mean time to failure, B10 life, etc. are estimated to assess the reliability of the component.

Total-Probability Method in Reliability Design of Gear Strength

Total probability method is based on stress-strength interference theory. There are four acceptable distribution types for gear (strength, stress), which are normal distribution, lognormal distribution, Weibull distribution and the smallest extreme value distribution. Based on the four distribution types, 16 different stress-strength distributions were obtained through permutation respectively. The results show that they summarize the mathematical model of reliability calculation for the gear actual failure mode and get the exact solutions of gear reliability.

Comparisons of approximate confidence intervals for the smallest extreme value distribution simple linear regression model under time censoring

Exact confidence interval estimation for accelerated life regression models with censored smallest extreme value (or Weibull) data is often impractical. This paper evaluates the accuracy of approximate confidence intervals based on the asymptotic normality of the maximum likelihood estimator, the asymptotic X2distribution of the likelihood ratio statistic, mean and variance correction to the likelihood ratio statistic, and the so-called Bartlett correction to the likelihood ratio statistic. The Monte Carlo evaluations under various degrees of time censoring show that uncorrected likelihood ratio intervals are very accurate in situations with heavy censoring. The benefits of mean and variance correction to the likelihood ratio statistic are only realized with light or no censoring. Bartlett correction tends to result in conservative intervals. Intervals based on the asymptotic normality of maximum likelihood estimators are anticonservative and should be used with much caution.