Bathtub curve and Allan-Plaȋt chart: two problematic graphs in reliability engineering

• Published in: IOP conference series. Materials Science and Engineering 2024-09, Vol.1311 (1), p.12033
• Main Authors: Andrei-Alexandru, Boroiu, Ionel, Vieru, Tiberiu-Aurelian, Udma, Alexandru, Boroiu
• Format: Article
• Language: English
• Subjects: Distribution functions; Failure rates; Graphical representations; Graphs; Regression models; Reliability engineering
• ISSN: 1757-8981; 1757-899X
• DOI: 10.1088/1757-899X/1311/1/012033

In the reliability literature, there are completely different representations for two of the most common graphs: the graph that expresses the failure rate over the life of a product (bathtub curve) and the one that graphically identifies the Weibull triparametric model (linear regression of the Weibull curve using the Allan-Plaît graph). Even if the identification of the Weibull model is no longer done graphically, but with the help of dedicated calculation programs, the mathematical bases of the linearization of the F(t) fault distribution function by logarithm remain equally important. The present paper aims to establish which of the graphic variants are the correct ones and to identify the causes that led to the incorrect graphic representations. Based on an extensive theoretical documentation (analysis of numerous works in the field of reliability, published over the last decades, in the country and abroad) it is concluded that in foreign literature these graphs are always correct and that they were taken correctly in Romanian works from the 70’s to the 80’s of the last century, but starting with the 90’s there are fundamentally different representations, especially in the field of reliability engineering. Finally, the causes that led to these non-compliant graphical representations are identified. As these misrepresentations seem to persist, this paper is intended to be a signal of this issue.