The development of mathematical models for evaluating the quality risk of product with multi-correlated characteristics

Abstract

Quality is an important aspect in today’s business, regardless of the nature of the industry, whether it is manufacturing or services and without exemption to large or small and medium-sized enterprises. In the context of the manufacturing industry, most products today are valued by more than one key quality characteristics and in many cases correlations exist among these quality characteristics. In the presence of correlation, evaluating quality using classical univariate techniques may provide inaccurate conclusion about the actual process performance. Furthermore, when a product or process quality is measured by a large number of key quality characteristics with different specifications type, evaluating the process performance can be a difficult task. A comprehensive review on past researches related to techniques of multivariate capability analysis and multivariate loss functions has been conducted. However, most of these models are insufficient in dealing with these aspects of multivariate process data: correlated variables, departure from normality and mixed type of specifications. The present research is motivated by the need to address these concerns. Subsequently, the core objective of this research is to answer the following questions: How can we measure the risk of quality failure for correlated multivariate quality characteristics effectively? Does the quality risk information assists in quality improvement efforts? In evaluating quality based on sample data, the work presented in this thesis considers both the multivariate normal and multivariate non-normal distributions. The Modified Tolerance Region (MTR) model and the Target Distance (TD) models are developed to evaluate the proportion of non-conformance in the presence of joint normal distributions with a combination of nominal-the-best (NTB) specifications type. When quality characteristic is governed by unilateral type of specifications such as smaller-the-better (STB) and larger-the-better (LTB), the assumption of normal distribution is ineffective. Largely, the distribution of data in unilateral type of specifications tends to cluster towards the extreme end of the specification length. Furthermore, the setting of process mean to the target mean value as done in the NTB type cannot be extended to unilateral type of specifications. Thus, in the presence of skewed marginal distributions in correlated data, the Gaussian copula approach and the zero-centred Target Distance (TD0) model are introduced. The models developed in this study are demonstrated in numerical examples and compared to other existing models in the literature. The results obtained highlight that these models are very promising and are effective in estimating the performance of the multivariate process. An application of the TD0 model to a medical case study is also included. When non-conformance is detected within the vicinity of the manufacturing site, costs associated to activities that attempt to rectify the non-conformance are categorised as internal failure costs. On the other hand, poor quality products which passed the engineering specification may leave undetected and received by the customer, which consequently gives rise to the external failure cost. External failure costs such as warranty claim, product recall, etc. can be difficult to estimate and are often neglected by manufacturers. In this thesis, it is shown that the internal failure costs and the external failure costs for multivariate processes can be estimated based on the probability of non-conformance and expected loss due to quality failure. The probability of non-conformance is evaluated using one of the presented models (MTR, TD, TD0 or Gaussian copula) and the expected loss is estimated using multivariate loss functions. Numerical examples for cases of bilateral and unilateral type of specification are provided. Comparison to other model shows that the quality failure costs are greatly underestimated when correlation among quality characteristics is not considered. The final part of this thesis highlights the feasibility of the presented models for the quality improvement of processes with multivariate quality characteristics. A new 6-step quality improvement framework i.e. Define, Measure, Analyse, Prioritise, Improve and Control (DMAPIC) is introduced. The DMAPIC framework integrates the prioritisation of unfavourable risk from the risk assessment process into the widely known problem-solving methodology DMAIC. Unacceptable risks are identified based on the estimated quality failure costs. The application of the DMAPIC framework is demonstrated using a case study conducted on an Australian manufacturing company. From the case study, it is evident that the prioritisation of risk in processes with multiple key quality characteristics provides an important advantage especially when resources are limited.