Development of finite mixture models to assess the adequacy of non-identical multiple tooled manufacturing processes

The objective of this research was to identify, develop, and evaluate a methodology to better assess the adequacy of Non-identical Multiple Tooled (NIMT) manufacturing processes, such as multiple cavity injection molding. The objective was effectively accomplished by implementation of Finite Mixture Distribution (FMD) Modeling and Statistics. A stepwise methodology was developed, along with supporting mathematics and statistics. The methodology was validated by actual application of the methodology to two sets of real multi-cavity injection molding data. The methodology appeared to be quite applicable and useful, and it is expected that the methodology could be applied to more processes than just injection molding. The method allowed better examination of the fraction of parts nonconforming or better setting of the specification level.; The research produced the following: (1) a general methodology and application of FMD models to NIMT processes, along with examples, (2) statistical considerations and sound statistical methods for FMD models of NIMT processes (where the number and weighting of component distributions are known), (3) rationale and guidelines for the decision to use an FMD model versus simpler normal distribution models and ways to examine extreme tail probabilities (including the Ratio of Tail Probabilities and log p.d.f. comparisons), and (4) sample sizes needed to generate adequate normal distribution tail probabilities including Tail Probability Factors (an extension of Statistical Tolerance Intervals).; Other developments included methods of estimating the overall mean and variance by way of the FMD component distribution parameters (including the efficiency of such statistics).