S1 Appendix -

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.</div

Visual illustration of the 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.</div

The graphical illustration of the simulation results using <i>δ</i> = 0.8 (green curve), <i>α</i> = 1.0 (blue curve), and λ = 1.4 (red curve).

The graphical illustration of the simulation results using δ = 0.8 (green curve), α = 1.0 (blue curve), and λ = 1.4 (red curve).</p

The survival times data set and summary statistics (Lee and Wang [19]).

The survival times data set and summary statistics (Lee and Wang [19]).</p

ARLs of attribute control charts for NTS-Weibull and Weibull distributions for <i>ARL</i>₀ = 370 and <i>n</i> = 20.

ARLs of attribute control charts for NTS-Weibull and Weibull distributions for ARL0 = 370 and n = 20.</p

The ARLs of the proposed chart for <i>δ</i> = 2.5, λ = 1.5, and <i>n</i> = 20.

The ARLs of the proposed chart for δ = 2.5, λ = 1.5, and n = 20.</p

The profiles of the LLF of and of the NTS-Weibull distribution using the survival times data.

The profiles of the LLF of and of the NTS-Weibull distribution using the survival times data.</p

The simulation results using <i>δ</i> = 0.8, <i>α</i> = 1.0, and λ = 1.4.

The simulation results using δ = 0.8, α = 1.0, and λ = 1.4.</p

Visual display of the best-fitting ability of the NTS-Weibull distribution.

Visual display of the best-fitting ability of the NTS-Weibull distribution.</p

The ARLs of the proposed chart for <i>δ</i> = 4.1, λ = 1.3, and <i>n</i> = 30.

The ARLs of the proposed chart for δ = 4.1, λ = 1.3, and n = 30.</p