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# Contributions to industrial statistics

 dc.contributor.author Leung, Bartholomew Ping Kei en_US dc.date.accessioned 2007-05-25T18:30:59Z dc.date.available 2007-05-25T18:30:59Z dc.date.issued 1999-02-01T00:00:00Z en_US dc.identifier.uri http://hdl.handle.net/1993/2178 dc.description.abstract The main theme of this dissertation deals with the impact and consequences of non-normal distribution on the process capability index Cpm. In this thesis, much work has been done in this area including the properties of C^pm, the estimate of Cpm, under normality, its sensitivity to non-normality and also the relationship of Cpm to squared error loss. Related to Cpm is the unifying measure of process capability index Cpw. Several properties of C^pw are investigated. Much of the controversy surrounding the Cp index involves 6[sigma] in the denominator. It carries particular physical meaning when the process characteristic is normally distributed. A new index Cpo is proposed which is based on the difference between two order statistics. The sampling distribution of C^po is obtained for those cases where the process characteristic is uniform, exponential and normal distributions. The behavior of C^p, when n = 2, under non-normal situations such as uniform and exponential distributions is also investigated as a special case of C^po. Another major issue addressed in this dissertation is the Inverted Probability Loss Functions (IPLFs). It is a modified loss function found by inverting a probability density function which was first invented by my supervisor Dr. F.A. Spiring in 1993. The first loss function I studied is the inverted beta loss function (IBLF). I have found certain interesting properties that this class of loss function possesses such as the shape, the loss function and its associated risk function of the IBLF are scale invariant under linear transformation. Finally, I have investigated a few more IPLFs satisfying the usual loss function properties and developed some theorems in this portion of the study. en_US dc.format.extent 7072426 bytes dc.format.extent 184 bytes dc.format.mimetype application/pdf dc.format.mimetype text/plain dc.language en en_US dc.language.iso en_US dc.rights info:eu-repo/semantics/openAccess dc.title Contributions to industrial statistics en_US dc.type info:eu-repo/semantics/doctoralThesis dc.type doctoral thesis en_US dc.degree.discipline Statistics en_US dc.degree.level Doctor of Philosophy (Ph.D.) en_US
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