A new trigonometric modification of the Weibull distribution: Control chart and applications in quality control

Abstract

In the most recent era, the extensions of the probability models via trigonometry methods have received great attention. This paper also offers a novel trigonometric version of the Weibull model called a type-I cosine exponentiated Weibull (for short “TICE-Weibull”) distribution. The identifiability properties for all three parameters of the TICE-Weibull model are derived. The estimators of the TICE-Weibull model are derived by implementing the maximum likelihood approach. To demonstrate the effectiveness of the TICE-Weibull model, two applications from real-world phenomena are analyzed. In addition, the proposed statistical model is established for an attribute control chart based on a time-truncated life test. The advantage of the developed charts is examined based on the average run length (ARL). The necessary tables of shift sizes and various sample sizes are offered for numerous values of the distribution parameters, as well as specified ARL and shift constants. Some numerical examples are discussed for various scheme parameters to study the performance of the new TICE-Weibull attribute control charts. According to our search and a brief study of the statistical literature, there is no published work on the development of a control chart using new probability models that are introduced using the cosine function. This is the key motivation of this work, which fills this amazing and interesting research gap.

Weibull analysis of ceramics and related materials: A review

“…WA is a widely utilized distribution in the analysis of reliability and durability data. The Weibull distribution may describe diminishing, cumulative, or constant risk functions, allowing it to define any stage of the item's life cycle [ [88] , [89] , [90] , [91] , [92] , [93] ]. Waloddi Weibull introduced a statistical distribution in 1939 that frequently defines identified failures.…”

A New Sine-Based Distributional Method with Symmetrical and Asymmetrical Natures: Control Chart with Industrial Implication

“…Several authors have investigated the attribute control chart for the time-truncated life test for various distributions; refer to [31][32][33][34]. Recently, Alomair et al [35] studied a control chart using the trigonometrically generated distribution. They studied a new trigonometric modification of the Weibull distribution, control chart, and applications in quality control.…”