Abstract
During the past three decades, PCIs – process capability indices – have inspired hundreds of pages of scientific research. The trade-off between simplicity and precision in reproducing an overall process quality prediction is both the reason behind the criticism for Cp and Cpk and the motive for their widespread use. Indeed, their strength in simplifying the assessment of a process control status compensates for some of the statistical shortcomings largely recognized in the literature, amongst which is the normality assumption. Hence, this article aims at overcoming the main statistical problems of Cp and Cpk indices by proposing a new indicator, still compliant with the traditional PCIs approach, but applicable for cases of non-normal processes while being simple to implement and easy to interpret. The proposed indicator is composed of three sub-indices, each related to a specific process characteristic: how the process is repeatable, how much the data distribution is skewed about the mean value and how much the process data comfortably lies between the specifications limits. On top of this, a specific parameter allows designers or quality engineers to modify the index value range in order to finetune the effect of the cost of Taguchi's loss function. The article presents the theoretical structure of the new indicator and an extensive numerical test on several different processes with different distributions upon multiple specification limit combinations, along with a comparison to the Cpk index, in order to demonstrate how the new index provides a clearer indication of the process criticalities.
Highlights
1.1 Literature review on PCIsThe importance of process capability indices (PCIs) mirrors their strategic role in the quality control activities, especial‐ ly in the manufacturing processes
Their structure creates a relation between process data indices and the specification limits, upper specification limit (USL) and lower specification limit (LSL) [1,2]
The following examples show how Cpk index fails to discriminate between two different cases, while PuSH provides a clearer indication on the process criticalities
Summary
The importance of process capability indices (PCIs) mirrors their strategic role in the quality control activities, especial‐ ly in the manufacturing processes. PCIs provide a numer‐ ical value of whether or not a manufacturing process is capable of meeting a specified level of tolerances Their structure creates a relation between process data indices (mean, median standard deviation, etc.) and the specification limits, upper specification limit (USL) and lower specification limit (LSL) [1,2]. Considering that not all workers in the manufacturing industry master statistics, the indices structures must be as close as possible to their understanding This is one of the reasons behind the widespread choice in industry of sampling PCIs values into intervals (e.g., 1 < Cpk < 1.33) rather than presenting them with their bare absolute values in order to quickly obtain a mark, linked with a certain risk prediction. PCIs should be able to quickly and clearly tell the factors that influence performances
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