A control chart for time truncated life tests using Pareto distribution of second kind

Control charts using half-normal and half-exponential power distributions using repetitive sampling

This manuscript presents the development of an attribute control chart (ACC) designed to monitor the number of defective items in manufacturing processes. The charts are specifically tailored using time-truncated life test (TTLT) for two lifetime data distributions: the half-normal distribution (HND) and the half-exponential power distribution (HEPD) under a repetitive sampling scheme (RSS). To assess the effectiveness of the proposed control charts, both in-control (IC) and out-of-control (OOC) scenarios are considered by deriving the average run length (ARL). Various factors, including sample sizes, control coefficients, and truncated constants for shifted phases, are taken into account to evaluate the performance of the charts in terms of ARL. The behavior of ARLs is analyzed in the shifted process by introducing shifts in its parameters. The superiority of the HEPD-based chart is highlighted by comparing it with both the HND-based ACC and the ACC based on the Exponential distribution (ED) under TTLT using RSS. The results showcase the superior performance of the proposed HEPD-based chart, indicated by smaller ARL values. Additionally, the benefits of another proposed ACC using HND are compared with the ED-based ACC under RSS, further confirming the effectiveness of the HND-based approach through smaller ARLs Finally, the proposed control charts are evaluated through simulation testing and real-life implementation, emphasizing their practical applicability in real-world manufacturing settings.

A new statistical methodology using the sine function: Control chart with an application to survival times data

Statistical methodologies have a wider range of practical applications in every applied sector including education, reliability, management, hydrology, and healthcare sciences. Among the mentioned sectors, the implementation of statistical models in health sectors is very crucial. In the recent era, researchers have shown a deep interest in using the trigonometric function to develop new statistical methodologies. In this article, we propose a new statistical methodology using the trigonometric function, namely, a new trigonometric sine-G family of distribution. A subcase (special member) of the new trigonometric sine-G method called a new trigonometric sine-Weibull distribution is studied. The estimators of the new trigonometric sine-Weibull distribution are derived. A simulation study of the new trigonometric sine-Weibull distribution is also provided. The applicability of the new trigonometric sine-Weibull distribution is shown by considering a data set taken from the biomedical sector. Furthermore, we introduce an attribute control chart for the lifetime of an entity that follows the new trigonometric sine-Weibull distribution in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested chart is investigated using the average run length. A comparative study and real example are given for the proposed control chart. Based on our study of the existing literature, we did not find any published work on the development of a control chart using new probability distributions that are developed based on the trigonometric function. This surprising gap is a key and interesting motivation of this research.

Control chart for half normal and half exponential power distributed process

In this manuscript, we construct an attribute control chart (ACC) for the number of defective items using time-truncated life tests (TTLT) when the lifetime of a manufacturing item follows two lifetime data distributions: the half-normal distribution (HND) and the half-exponential power distribution (HEPD). To assess the potential of the proposed charts, necessary derivations are made to obtain the value of the average run length (ARL) when the production process is in-control and out-of-control. The performance of the presented charts is evaluated for different sample sizes, control coefficients, and truncated constants for shifted phases in terms of ARL. The behavior of ARLs is studied for the shifted process by introducing shifts in its parameters. The advantages of the proposed HEPD-based chart are discussed in the form of ARLs with HND and Exponential Distribution (ED) based ACCs under TTLT, showing the excellent assessment of the proposed chart. Additionally, the advantages of another proposed ACC using HND are compared with ED-based ACC, and the findings support the HND in the form of smaller ARLs. Finally, simulation testing and real-life implementation are also discussed for functional purposes.

An attribute control chart for the inverse Weibull distribution under truncated life tests

Statistical Process Control (SPC) is applied to monitor production processes in order to discover any problems or issues that may arise during the production process and to help in finding solutions for these issues. In this paper, we consider a situation in which the product's quality, as measured by its lifetime, is monitored. Since the monitoring requires life tests to be performed and this may take relatively long time, the test time is truncated at some pre-specified time t 0 , chosen to be related to the product's target mean life. This results in a truncated life test. The number of failures during the life test is used as an indicator of the quality of the product. We consider the situation in which the lifetimes follow the Inverse Weibull distribution. A control chart is proposed for this specific situation, thus extending the applicability of control charts methodology to situations involving truncated life tests. Simulation techniques has been employed to obtain the quantities needed for constructing the control chart with the aim that the average run length (ARL) is close to its target value. The control chart is evaluated by obtaining the ARL values when the process is out-of-control for various values of the shift coefficient. We obtained the coefficients of the control limit and the truncation coefficient for different sample sizes and average run length target values. An example on the application of the proposed control chart is provided.

Attribute Control Chart for Rayleigh Distribution Using Repetitive Sampling under Truncated Life Test

A control chart is an important tool in statistical process monitoring that is useful to monitor and improve production process quality. In this article, an attribute control chart using repetitive sampling under a truncated life test is proposed for monitoring the mean life of the product where the lifetime follows the Rayleigh distribution. The repetitive sampling parameters and the control limit coefficients of the chart are determined so that the in-control average run length (ARL) is very close to the target ARL. Tables of ARL values for various shift sizes in the scale parameter were presented, and the performance of the proposed chart is compared with the existing attribute control charts using the out-of-control ARL. The proposed control chart is shown to outperform the existing control charts in terms of ARL. An illustrative example is given to demonstrate the application of the proposed chart.

Control Chart for Failure-Censored Reliability Tests under Uncertainty Environment

Existing control charts based on failure-censored (Type-II) reliability tests were designed using classical statistics. Classical statistics was applied for the monitoring of the process when observations in the sample or the population were determined. Neutrosophic statistics (NS) are applied when there is uncertainty in the sample or population. In this paper, a control chart for failure-censored (Type-II) reliability tests was designed using NS. The design of a control chart for the Weibull distribution, which is applied when there is a lack of symmetry using neutrosophic statistics, is given. The proposed control chart was used to monitor the neutrosophic mean and neutrosophic variance, which are related to the neutrosophic scale parameter. The advantages of the proposed control chart over the existing control chart are discussed.