A bootstrap method for uncertainty estimation in quality correlation algorithm for risk based tolerance synthesis

Abstract

A risk based tolerance synthesis approach is based on ISO9001:2015 quality standard's risk based thinking. It analyses in-process data to discover correlations among regions of input data scatter and desired or undesired process outputs. Recently, Ransing et al. (2016) proposed a quality correlation algorithm (QCA) for risk based tolerance synthesis. The quality correlation algorithm is based on the principal component analysis (PCA) and a co-linearity index concept (Ransing et al. 2013). The uncertainty in QCA results on mixed data sets is quantified and analysed in this paper.The uncertainty is quantified using a bootstrap sampling method with bias-corrected and accelerated confidence intervals. The co-linearity indices use the length and cosine angles of loading vectors in a p-dimensional space. The uncertainty for all p-loading vectors is shown in a single co-linearity index plot and is used to quantify the uncertainty in predicting optimal tolerance limits. The effects of resampling distributions are analysed. The QCA tolerance limits are revised after estimating the uncertainty in limits via bootstrap sampling. The proposed approach has been demonstrated by analysing in-process data from a previously published case study. and in-process quality improvement. Highlights An approach to embed ISO 9001:2015's risk based thinking for in-process quality improvement is proposed. The uncertainty in the quality correlation algorithm has quantified using an enhanced bootstrap method. The algorithm determines robust optimal and avoid ranges within the process variation including process interactions.

A Novel Imputation Based Predictive Algorithm for Reducing Common Cause Variation from Small and Mixed Datasets with Missing Values

“…A Nickel based alloy data set used by Ransing et al (2016) and Batbooti et al (2017) to estimate the optimal limits is discussed here. In the current simulation, the QCA algorithm with six principal components is used.…”

“…After discussions with foundry process engineers, it was discovered that they do try to reduce the common cause variation by further fine tuning the process manually using their experience and expertise. A quality correlation algorithm has been developed recently (Batbooti, Ransing, & Ransing, 2017;Ransing, Batbooti, Giannetti, & Ransing, 2016) to fine tune the process inputs to reduce a deviation from the desired process response (output) values. The developed algorithm is based using the co-linearity index (Giannetti et al, 2014;Ransing, Giannetti, Ransing, & James, 2013) as a measure to discover correlated variables.…”

Manufacturing Process Causal Knowledge Discovery using a Modified Random Forest-based Predictive Model

“…The author could not conduct a comparison with other externally published work because the nickel-based superalloy dataset is Swansea-centric. In addition, a comparison with the author's previous work [8] could not be undertaken because the QCA algorithm is unable to deal with non-linear interactions [12]. Furthermore, the use of the QCA algorithm produces poor results.…”

“…The sample size depends on the prevalence of rejection rates and the minimum magnitude of process improvement required to demonstrate success. For studies based on design of experiment guidelines, a very small sample size (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) is also sufficient as the magnitude of process improvement demonstrated is usually high. However, the algorithms developed in this thesis are based on the observational studies.…”

“…As discussed in the literature review, the prediction model introduced in [8,12,88] is affected by significant limitations in terms of its regression capability when compared to the Neural Network model; this was found to be especially true for problems involving non-linear datasets. This particular drawback, which affects the algorithms discussed above, can be attributed to the underlying assumption that the dataset is linear, which does not hold true for the dataset under investigation in this thesis (i.e.…”