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

•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 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, Batbooti, Giannetti, and Ransing (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, Giannetti, Ransing, & James, 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 re-sampling 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.