Process Capability and Process Performance Metrics in Six Sigma: A Unified Framework Integrating Taguchi Quadratic Loss Function with Application to the Spinning Industry
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2026
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| _version_ | 1866902023682654208 |
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| author | Balasubramaniam, Sujai |
| author_facet | Balasubramaniam, Sujai |
| contents | <p><em><span lang="EN-US">This paper presents a rigorous, comprehensive exposition of Process Capability and Process Performance Metrics employed within the Six Sigma improvement methodology, and their mathematical integration with the Taguchi Quadratic Loss Function as a unified quality economics framework. The study meticulously derives and interprets the metrics Cp, Cpk, Pp, Ppk, Cr, Cpm, and Ppm from first principles, illustrating each with a real-world VMC machined shaft diameter dataset (n=40 observations, subgroup size=4). By coupling the loss-function approach with process sigma and process performance sigma, a financially quantifiable model is constructed that enables practitioners to evaluate the cost of deviation from nominal in monetary terms — bridging the gap between statistical quality control and management decision-making. Three process improvement options are analysed using Return on Investment (ROI), Benefit-Cost Ratio, and Payback Period, demonstrating payback periods as low as 140 days. The article extends the framework to the textile spinning industry, identifying critical quality characteristics — yarn count (Ne), tenacity (cN/tex), elongation, twist per inch (TPI), and hairiness index — where these metrics deliver maximum impact. The paper argues that spinners who institutionalise process capability measurement as a continuous discipline, coupled with Taguchi loss-function economics, gain a measurable competitive advantage through reduced waste, improved first-pass yield, and demonstrable quality cost reduction.</span></em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19177570 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Process Capability and Process Performance Metrics in Six Sigma: A Unified Framework Integrating Taguchi Quadratic Loss Function with Application to the Spinning Industry Balasubramaniam, Sujai Process Capability (Cp); Capability Index (Cpk); Process Performance (Pp); Performance Index (Ppk); Capability Ratio (Cr); Cpm; Voice of Customer; Voice of Process; Taguchi Quadratic Loss Function; Six Sigma; Statistical Process Control; Shewhart Sigma; Spinning Industry Quality; Cost of Poor Quality; ROI; Variation Reduction <p><em><span lang="EN-US">This paper presents a rigorous, comprehensive exposition of Process Capability and Process Performance Metrics employed within the Six Sigma improvement methodology, and their mathematical integration with the Taguchi Quadratic Loss Function as a unified quality economics framework. The study meticulously derives and interprets the metrics Cp, Cpk, Pp, Ppk, Cr, Cpm, and Ppm from first principles, illustrating each with a real-world VMC machined shaft diameter dataset (n=40 observations, subgroup size=4). By coupling the loss-function approach with process sigma and process performance sigma, a financially quantifiable model is constructed that enables practitioners to evaluate the cost of deviation from nominal in monetary terms — bridging the gap between statistical quality control and management decision-making. Three process improvement options are analysed using Return on Investment (ROI), Benefit-Cost Ratio, and Payback Period, demonstrating payback periods as low as 140 days. The article extends the framework to the textile spinning industry, identifying critical quality characteristics — yarn count (Ne), tenacity (cN/tex), elongation, twist per inch (TPI), and hairiness index — where these metrics deliver maximum impact. The paper argues that spinners who institutionalise process capability measurement as a continuous discipline, coupled with Taguchi loss-function economics, gain a measurable competitive advantage through reduced waste, improved first-pass yield, and demonstrable quality cost reduction.</span></em></p> |
| title | Process Capability and Process Performance Metrics in Six Sigma: A Unified Framework Integrating Taguchi Quadratic Loss Function with Application to the Spinning Industry |
| topic | Process Capability (Cp); Capability Index (Cpk); Process Performance (Pp); Performance Index (Ppk); Capability Ratio (Cr); Cpm; Voice of Customer; Voice of Process; Taguchi Quadratic Loss Function; Six Sigma; Statistical Process Control; Shewhart Sigma; Spinning Industry Quality; Cost of Poor Quality; ROI; Variation Reduction |
| url | https://doi.org/10.5281/zenodo.19177570 |