Pallotta, Giuliana (2008) ADVANCES IN BAYESIAN CHARTS FOR RELIABILITY CONTROL. [Tesi di dottorato] (Unpublished)

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The general objective of the research study underlying this thesis was to develop innovative charts able to support reliability control by monitoring over time a critical-to-quality characteristic of interest within a Bayesian framework. The proposed control charts use the Bayes Theorem to directly produce and effectively update information about the parameters of the reliability distributions involved in the problem. For this peculiar feature, the charts can fit in a recent stream of research in the area of Statistical Process Control (SPC) dealing with Bayesian Process Monitoring and Control. However, the developed methodology differs from the available techniques where Bayesian inference is combined to the traditional Shewhart control charts as a supplementary tool to compute the expected loss relating to the state of the process. Only in the latest literature some interesting new approaches can be found where Bayesian inference is used as the working engine to sequentially estimate the probability of occurrence of an assignable cause responsible for the change in the process state. More specifically, the charts were designed exploiting some Bayesian reliability estimators known as Practical Bayes Estimators (PBE) which resulted very suitable for this specific application. Thanks to the specific properties of the PBE, new charts to monitor Weibull percentiles are developed when very small samples are available (say 2, 3). As a matter of fact, the charts are able to integrate the sample information together with the prior technological knowledge into the estimation process. So, the proposed charts can support the analyst in facing some critical scenarios where, based on very few experimental data, prompt decisions are needed (and both the Weibull parameters are unknown). In practice, this environment is typical in short production runs (parts with a long cycle time, just-in-time production, prototype parts, destructive testing of parts) and in low volume production. The proposed methodology was investigated via numerical simulations and two real examples are presented in order to show how to operatively implement the proposed charts in two specific application areas.

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