Interval-valued Uncertainty Capability Indices with South African Industrial Applications

Includes bibliographical references.Since the advent of statistical quality control and process capability analysis, its study and application has gained tremendous attention both in academia and industry. This attention is due to its ability to describe the capability of a complex process adequately, simply (i.e. using a unitless index) and also in some instances to compare different manufacturing processes. However, the application of statistical quality control has come under intense criticism, notably in one car manufacturing industry where the actual number of non-conforming units considerably exceeded expectation, although probabilistic control measures were in place. This failure led to a large recall of their vehicles and also left a dent on the image of the company. One of the reasons for this unfortunate instance is that in classical quality control measures, human judgement is ignored and since in process engineering there is considerable expert intuition in decision making, this element cannot be undermined. Hence the research study applies the uncertainty theory proposed by Baoding Liu (2007) to enable us to incorporate human judgement into process capability analysis. The major findings of the thesis is that the uncertain process capability indices under an uncertainty environment are interval-valued and their relevant characteristics. The study further developed the "sampling" uncertainty distributions and thus the "sampling" impacts on the newly defined uncertain process capability indices under Liu's uncertain normal distribution assumptions. In order to reach the main purpose of the thesis, a thoroughgoing literature review on probabilistic process capability indices is necessary