Development and application of process capability indices

In order to measure the performance of manufacturing processes, several process capability indices have been proposed. A process capability index (PCI) is a unitless number used to measure the ability of a process to continuously produce products that meet customer specifications. These indices have since helped practitioners understand and improve their production systems, but no single index can fully measure the performance of any observed process. Each index has its own drawbacks which can be complemented by using others. Advantages of commonly used indices in assessing different aspects of process performance have been highlighted. Quality cost is also a function of shift in mean, shift in variance and shift in yield. A hybrid is developed that complements the strengths of these individual indices and provides the set containing the smallest number of indices that gives the practitioner detailed information on the shift in mean or variance, the location of mean, yield and potential capability. It is validated that while no single index can fully assess and measure the performance of a univariate normal process, the optimal set of indices selected by the proposed hybrid can simultaneously provide precise information on the shift in mean or variance, the location of mean, yield and potential capability. A simulation study increased the process variability by 100% and then reduced by 50%. The optimal set managed to pick such a shift. The asymmetric ratio was able to detect both the 10% decrease and 20% increase in µ but did not alter significantly with a 50% decrease or a 100% increase in σ, which meant it was not sensitive to any shift in σ. The implementation of the hybrid provides the quality practitioner, or computer-aided manufacturing system, with a guideline on prioritised tasks needed to improve the process capability and reduce the cost of poor quality. The author extended the proposed hybrids to fully measure the performance of a process with multiple quality characteristics, which follow normal distribution and are correlated. Furthermore, for multivariate normal processes with correlated quality characteristics, process capability analysis is not complete without fault diagnostics. Fault diagnostics is the identification and ranking of quality characteristics responsible for multivariate process poor performance. Quality practitioners desire to identify and rank quality characteristics, responsible for poor performance, in order to prioritise resources for process quality improvement tasks thereby speeding up the process and minimising quality costs. To date, none of the existing commonly used source identification approaches can classify whether the process behaviour is caused by the shift in mean or change in variance. The author has proposed a source identification algorithm based on mean and variance impact factors to address this shortcoming. Furthermore, the author developed a novel fault diagnostic hybrid based on the proposed optimal set selection algorithm, principal component analysis, machine learning, and the proposed impact-factor. The novelty of this hybrid is that it can carry out a full multivariate process capability analysis and provides a robust tool to precisely identify and rank quality characteristics responsible for the shifts in mean, variance and yield. The fault diagnostic hybrid can guide the practitioners to identify and prioritise quality characteristics responsible for the poor process performance, thereby reducing the quality cost by effectively speeding up the multivariate process improvement tasks. Simulated scenarios have been generated to increase/decrease some components of the mean vector (µ2/µ4) and in increase/reduce the variability of some components (σ1 reduced to close to zero/σ6 multiplied by 100%). The hybrid ranked X2 and X6 as the most contributing variables to the process poor performance and X1 and X4 as the major contributors to process yield. There is a great challenge in carrying out process capability analysis and fault diagnostics on a high dimensional multivariate non-normal process, with multiple correlated quality characteristics, in a timely manner. The author has developed a multivariate non-normal fault diagnostic hybrid capable of assessing performance and perform fault diagnostics on multivariate non-normal processes. The proposed hybrid first utilizes the Geometric Distance (GD) approach, to reduce dimensionality of the correlated data into fewer number of independent GD variables which can be assessed using univariate process capability indices. This is followed by fitting Burr XII distribution to independent GD variables. The independent fitted distributions are used to estimate both yield and multivariate process capability in a time efficient way. Finally, machine learning approach, is deployed to carry out the task of fault diagnostic by identifying and ranking the correlated quality characteristics responsible for the poor performance of the least performing GD variable. The results show that the proposed hybrid is robust in estimating both yield and multivariate process capability, carrying out fault diagnostics beyond GD variables, and identifying the original characteristic responsible for poor performance. The novelty of the proposed non-normal fault diagnostic hybrid is that it considers quality characteristics related to the least performing GD variable, instead of investigating all the quality characteristics of the multivariate non-normal process. The efficacy of the proposed hybrid is assessed through a real manufacturing examples and simulated scenarios. Variables X1,, X2 and X3 shifted away from the target by 25%, 15% and 35%, respectively, and the hybrid was able to select variables X3 to be contributing the most to the corresponding geometric distance variable's poor performance