Bayesian inference and failure analysis for risk assessment in quality engineering

Abstract

Failure is the state of not achieving a desired or intended goal. Failure analysis planning in the context of risk assessment is an approach that helps to reduce total cost, increase production capacity, and produce higher-quality products. One of the most common issues that businesses confront are defective products. This issue not only results in monetary loss, but also in a loss of status. Companies must improve their production quality and reduce the quantity of faulty products in order to continue operating in a healthy and profitable manner in today’s very competitive environment. On the other hand, there is the ongoing COVID-19 pandemic, which has thrown the world’s natural order into disarray, and has been designated a Public Health Emergency of International Concern by the World Health Organization. The demand for quality control is rapidly increasing. Failure analysis is thus an useful tool for identifying common failures, their likely causes, and their impact on the health system, as well as plotting strategies to limit COVID-19 transmission. It is now more vital than ever to enhance failure analysis methods. The traditional FMEA (Failure mode and effects analysis) is one of the most widely used approaches for identifying and classifying failure modes (FMs) and failure causes (FCs). It is a risk analysis tool for coping with possible failures and is widely used in the reliability engineering, safety engineering and quality engineering. To prioritize risks of different failure modes, FMEA uses the risk priority number (RPN), which is the product of three risk measures: severity (S), occurrence (O) and detection (D). Traditional FMEA, on the other hand, has drawbacks, such as the inability to cope with uncertain failure data, such as expert subjective evaluations, the failure events’ conditionality, RPN has a high degree of subjectivity, comparing various RPNs is challenging, potential errors may be ignored in the conventional FMEA process, etc. To overcome these limitations, I present an integrated Bayesian approach to FMEA in this thesis. In this proposed approach, I worked with experts in quality engineering and used Bayesian inference to estimate the FMEA risk parameters: S, O and D. The proposed approach is intended to become more practical and less subjective as more data is added. Bayesian statistics is a statistical theory that is based on the Bayesian interpretation of probability, which states that probability expresses a degree of belief or information (knowledge) about an event. Bayesian statistics addresses the issues with uncertainties found in frequentist statistics, such as the distribution of contributing factors, the implications of using specific distributions and specifies that there is some prior probability. A prior can be derived from previous information, such as previous experiments, but it can also be derived from a trained subject-matter expert’s purely subjective assessment. Frequentist statistics (also known as classical statistics) has several limitations, including a lack of uncertainty information in predictions, no built-in regularisation, and no consideration of prior knowledge. Due to the availability of powerful computers and new algorithms, Bayesian methods have seen increased use within statistics in the twenty-first century, and this thesis highlights the effective use of Bayesian analyses to address the shortcomings of the current FMEA with the revamped Bayesian FMEA. As a demonstration of the approach, three case studies are presented. The first case study is a Bayesian risk assessment approach of the modified SEIR (susceptible-exposed-infectious-recovered) model for the transmission dynamics of COVID-19 with an exponentially distributed. The effective reproduction number is estimated based on laboratory-confirmed cases and death data using Bayesian inference and analyse the impact of the community spread of COVID-19 across the United Kingdom. The value of effective reproduction number models the average number of infections caused by a case of an infectious disease in a population that includes not only susceptible people. The FMEA is then applied to evaluate the effectiveness of the action measures taken to manage the COVID-19 pandemic. In the FMEA, the focus was on COVID-19 infections and therefore the failure mode is taken as positive cases. The model is applied to COVID-19 data showing the effectiveness of interventions adopted to control the epidemic by reducing the effective reproduction number of COVID-19. The risk measures were estimated from the case fatality rate (S), the posterior median of the effective reproduction number (O) and the current corrective measures used by government policies (D). The second case study is a Bayesian risk assessment of a coordinate measuring machine (CMM) process using failure mode, effects and criticality analysis (FMECA) and an augmented form error model. The form error is defined as the deviation of a manufactured part from its design or ideal shape, and it is a key characteristic to evaluate in quality engineering and manufacturing. The form error is presented as a probabilistic model using symmetric unimodal distributions. Bayesian inference is then used to identify influence factors associated with the measurement process due to form error, environmental, human and random effects. A risk assessment is then performed by combining Bayesian inference, FMECA and conformity testing, to quantify and minimise the risk of wrong decisions. In the FMECA, the focus was on CMM measurement process and I identified four major FMs that can occur: probe, mechanical, environmental and measurement performance failure. Eleven FCs were also observed, each of which was linked to one of the four FMs. The risk measures were estimated from the posterior probability of failure causes associated with the CMM measurement process (O), the severity of a specific consumer’s risk (S) and the detectability of failures from the posterior standard deviation of the form error model (D). The third case study is a Bayesian risk assessment of a CMM measurement process using an autoregressive (AR) form error model and a combined Fault tree analysis (FTA) and FMEA approach to predict significant failure modes and causes. The main idea is to estimate and predict the form error based on CMM data using Gibbs sampling and analyse the impact of the CMM measurement process on product conformity testing. The FTA is used to compare the actual and predicted form error data from the Bayesian AR plot to determine the likelihood of the CMM measurement process failing using binary data. The acquired binary data is then classified into four states (true positive, true negative, false positive, and false negative) using a confusion matrix, which is subsequently utilized to calculate key classification measures (i.e., error rate, prediction rate, prevalence rate, sensitivity rate, etc). The classification measures were then used to assess the FMEA risk measures S, O, and D, which were critical for determining the RPN and making decisions. Analytical and numerical methods are used in all case studies to highlight the practical implications of our findings and are meant to be practical without complex computing. The proposed methodologies can find applications in numerous disciplines and wide quality engineering.