1) Process variability and its impact on key performance indicator (e.g quality) of a manufactured product (1000 words)
(Note: Discussion should include; what variation in processes is, types of variation, why it is important to understand variation concepts, how variation in processes results in variation in quality of products. Also you are required to use a diagram to depict variation in parameters of two or more processes and how it could lead to failure in output)
2) The use of probability distribution in quantifying outcomes of a random variable X (Process Variable) and derivations of probability density function (pdf) and cummulative dendity function (cdf) formulations (from integral function) for various continuous probability distributions (normal, lognormal, weibull, gamma, exponential). (1500)
3) How methods for uncertainty quantification can be used to determine probability distribution of an output with uncertain inputs. Discussion should include description (using statistical and mathematical formulations) of uncertainty quantification methods (i.e sampling methods and mean value approximation methods). (1450)
Note: uncertainty quantification methods and their formulations should be for monte carlo simulation, latin hypercube and first order second moment.
4) Process capability modelling in manufacturing and its various measures (capability indices). Illustrate, with diagram, process distribution with Cp values (Cp = 1, Cp = 1.33, Cp = 1.66 and Cp = 2.0) (750)
5) Process capability modelling for non-normal processes
Transformation of non-normal data with johnson transformation method. Identification of parameters for the three distributions: Bounded, Semi-Unbounded and Unbounded must also be included. (750 words)