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Quality Control Using Inferential Statistics in Weibull Analyses for Components Fabricated from Monolithic Ceramics
Parikh, Ankurben H.

2012, Master of Science in Civil Engineering, Cleveland State University, Fenn College of Engineering.

This work presents the mathematical constructs for certain statistical elements that when combined properly produce a quality control program that can be used to accept or reject ceramic materials based on mechanistic strength information. Due to the high tensile strength and low fracture toughness of ceramic materials the design engineer must consider a stochastic design approach. Critical flaws with lengths that cannot be detected by current non-destructive evaluation methods render a distribution of defects in ceramics that effectively requires that the tensile strength of the material must be treated as a random variable. The two parameter Weibull distribution (an extreme value distribution) with size scaling is adopted for tensile strength in this work.


Typically the associated Weibull distribution parameters are characterized through the use of four-point flexure tests. The failure data from these tests are used to determine the Weibull modulus (m) and a Weibull characteristic strength (σθ). To determine an estimate of the true Weibull distribution parameters maximum likelihood estimators are used. The quality of the estimated parameters relative to the true distribution parameters depends fundamentally on the number of samples taken to failure and the component under design. The statistical concepts of “confidence intervals” and “hypothesis testing” are discussed here relative to their use in assessing the “goodness” of the estimated distribution parameters. Both of these inferential statistics tools enable the calculation of likelihood confidence rings. Work showing how the true distribution parameters lie within a likelihood ring with a specified confidence is presented.


A material acceptance criterion is defined here and the criterion depends on establishing an acceptable probability of failure of the component under design as well as an acceptable level of confidence associated with estimated distribution parameter determined using failure data from a specific type of strength test. A standard four point bend bar was adopted although the procedure is not limited to only this type of specimen. This work shows how to construct likelihood ratio confidence rings that establishes an acceptance region for distribution parameters relative to a material performance curve. Combining the two elements, i.e., the material performance curve based on an acceptable component probability of failure and a likelihood ratio ring based on an acceptable confidence level, allows the design engineer to determine if a material is suited for the component design at hand – a simple approach to a quality assurance criterion.

Stephen Duffy, PhD (Committee Chair)
Lutful Khan, PhD (Committee Member)
Jacqueline Jenkins, PhD (Committee Member)
51 p.

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Parikh, A. (2012). Quality Control Using Inferential Statistics in Weibull Analyses for Components Fabricated from Monolithic Ceramics. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Parikh, Ankurben. "Quality Control Using Inferential Statistics in Weibull Analyses for Components Fabricated from Monolithic Ceramics." Electronic Thesis or Dissertation. Cleveland State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 23 Oct 2017.

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Parikh, Ankurben "Quality Control Using Inferential Statistics in Weibull Analyses for Components Fabricated from Monolithic Ceramics." Electronic Thesis or Dissertation. Cleveland State University, 2012. https://etd.ohiolink.edu/

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