The reliability of a system during operation can be expressed quantitatively through different time functions. Mathematical procedures and statistical laws allow to assess the precise analytical relations between these functions. Referring to a generic system or component is a common experience that its duration in-service is not predictable in a deterministic way. This consideration identifies the lifetime (or time to failure) of the component as a continuous random variable, susceptible to a statistical description, whose estimate is crucial in the design phase, or in any case before the commissioning of equipment. In a second stage, the actual values of reliability must be compared with the forecast values arising from the theoretical statistical model used. This comparison allows assessment of the goodness-of-fit level and the confidence level of the prediction model, in order to validate it for any future equipment redesigns or for similar equipment. In this context, the present work is aimed at identifying the most appropriate statistical tools for the comparison above, and then to assess the reliability of the forecast data, compared to the real performance of a reliability system. For this purpose, a literature analysis was conducted, with a dual purpose: The identification of statistical models most commonly used to describe the reliability function of a system; to provide a choice of appropriate indicators and effective tests for assessing the confidence of the statistical models for reliability scopes. The models identified were then applied, as an example, to the real case of a catalytic cracking catalyst with the fluidized bed of a petrochemical plant. The results obtained from the case study, discussed in the final section of the work, offer many points of comparison between the various statistical models as well as a first overview of their reliability.
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