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arxiv: 2604.15544 · v1 · submitted 2026-04-16 · 📊 stat.AP · stat.ME

Practical Process Capability Indices Workflows

Fei Jiang , Lei Yang This is my paper

Pith reviewed 2026-05-10 09:20 UTC · model grok-4.3

classification 📊 stat.AP stat.ME
keywords process capability indicesunivariate analysisoutlier detectionnormality testdistribution fittingquality controlmanufacturing processesworkflows
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The pith

This paper develops practical procedural workflows for univariate process capability analysis by integrating outlier detection, normality testing, and best distribution fitting.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews univariate process capability indices and constructs step-by-step workflows for their application in manufacturing quality assessment. These workflows address different preconditions by first detecting and handling outliers, then testing for normality, and finally fitting the best distribution when data deviates from normal. A sympathetic reader would care because incorrect index selection or ignored data issues can produce misleading conclusions about whether a process meets customer specifications. The review evaluates a range of methodologies to offer concrete selection guidance for specific process conditions. This structure aims to reduce the complexity of capability analysis while improving its reliability in quality control settings.

Core claim

The paper claims that comprehensive procedural workflows, which embed outlier detection, normality tests, and best distribution fitting as standard steps, enable accurate and robust assessments of process capability under varied preconditions and provide guidance for choosing the most suitable univariate PCI for given process conditions.

What carries the argument

Practical procedural workflows that combine outlier detection, normality testing, and distribution fitting before selecting and applying the appropriate process capability index.

If this is right

  • Researchers and practitioners receive systematic guidance for choosing PCIs matched to specific data conditions and process types.
  • Non-normal data no longer forces reliance on approximate indices because best-fitting distributions can be substituted.
  • Outlier removal becomes a routine first step that prevents distorted capability estimates.
  • The overall process of capability analysis is simplified into repeatable procedures that enhance precision in quality control decisions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The workflows could be encoded into software tools that automate the sequence of tests and index selection.
  • Similar integration of preprocessing steps might be tested for extending the approach to multivariate process capability measures.
  • The review's identification of less common scenarios suggests targeted empirical studies to quantify accuracy gains from the proposed procedures.

Load-bearing premise

That embedding standard statistical steps like outlier detection and distribution fitting into the workflows will automatically yield more accurate capability assessments, even absent new comparative case studies or empirical validations in the review.

What would settle it

A side-by-side comparison on a real manufacturing dataset with known outliers and non-normality, measuring whether indices computed via the proposed workflows predict the actual proportion of conforming items more accurately than indices computed without these preprocessing steps.

Figures

Figures reproduced from arXiv: 2604.15544 by Fei Jiang, Lei Yang.

Figure 1
Figure 1. Figure 1: Practical workflow for calculating various PCIs across [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: PCIs-related parameters for a non-normally distributed [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: presents a practical workflow outlining the step￾by-step process for calculating both within standard deviaiton and overall standard deviation using different methodologies, which will be illustrate in the following sections. Standard Deviation subgroup size=1 Overall ￾overall = vuut 1 N ￾ 1 X N i=1 (xi ￾ x¯)2 ￾within = MR d4 Within subgroup size≥2 Median moving range Average moving range Square root of MS… view at source ↗
Figure 4
Figure 4. Figure 4: Histogram with density of  Cpk Ppk  across the 9 dimen￾sions, based on Cpk and Ppk values in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: PCIs workflow VIII. CONCLUSIONS This case study highlights the considerable variation in Process Capability Indices (PCIs) that arises solely from using different methods to calculate standard deviation. Notably, this variation occurs even before accounting for other critical factors, such as the type of tolerance (unilateral or bilateral, with or without a defined target), the nature of the data distri￾bu… view at source ↗
read the original abstract

This paper presents a comprehensive review of univariate process capability indices (PCIs), which are critical metrics for assessing how effectively a manufacturing process satisfies customer specifications based on a single quality characteristic. The primary objective of this review is to develop practical procedural workflows for conducting process capability analysis under various preconditions, including those less frequently addressed scenarios in existing literature. Key analytical components, such as outlier detection, normality test, and best distribution fitting, are integrated into the proposed framework to ensure accurate and robust capability assessments. By systematically evaluating a range of methodologies, this study offers guidance for researchers and practitioners in selecting the most appropriate PCIs for specific process conditions. Ultimately, the work aims to simplify the complexity of PCI analysis while enhancing its precision and utility in quality control and process improvement efforts.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper provides a review of univariate process capability indices (PCIs) and develops practical procedural workflows that integrate outlier detection, normality testing, and best distribution fitting to guide PCI selection under varied process conditions, with the stated aim of simplifying analysis while ensuring accurate and robust assessments for quality control applications.

Significance. If the workflows accurately compile and structure existing methods without overclaiming empirical gains, the paper could serve as a useful reference for practitioners in manufacturing statistics by organizing standard tools into procedural steps; however, its significance is constrained by the absence of any new validation demonstrating measurable improvements in PCI accuracy or decision-making over unintegrated approaches already available in the literature.

major comments (1)
  1. [Abstract] Abstract: the central claim that the integrated components 'ensure accurate and robust capability assessments' is load-bearing for the paper's objective but receives no support from new empirical evidence, as the manuscript is described as a methodological review that sketches workflows without providing case studies, simulated data, or quantitative comparisons showing that the combined steps alter PCI values or improve outcomes relative to standard practice.
minor comments (1)
  1. [Abstract] The abstract would be strengthened by specifying the exact range of methodologies evaluated and the less frequently addressed preconditions covered, rather than leaving these as general statements.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our review paper. We agree that the manuscript synthesizes existing methods without new empirical validation and will revise the abstract to ensure its claims accurately reflect this scope.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the integrated components 'ensure accurate and robust capability assessments' is load-bearing for the paper's objective but receives no support from new empirical evidence, as the manuscript is described as a methodological review that sketches workflows without providing case studies, simulated data, or quantitative comparisons showing that the combined steps alter PCI values or improve outcomes relative to standard practice.

    Authors: We agree that the paper is a methodological review synthesizing established techniques and does not contain new case studies, simulations, or quantitative comparisons. The original phrasing was intended to describe the intended purpose of the integrated workflow based on prior literature showing benefits of individual components (e.g., outlier removal and distribution fitting improving PCI reliability). However, we recognize that 'ensure' may imply unsupported empirical gains from the integration itself. We will revise the abstract to state that the components are integrated 'to support accurate and robust capability assessments by following established practices in the literature.' This revision aligns the wording with the review nature of the work while preserving the practical guidance offered. revision: yes

Circularity Check

0 steps flagged

No circularity detected; paper is a methodological review compiling existing PCI techniques without derivations or self-referential predictions.

full rationale

The manuscript is a review that integrates standard statistical components (outlier detection, normality testing, distribution fitting) into procedural workflows for process capability analysis. It offers guidance by evaluating methodologies from the literature but contains no equations, predictions, or claims that reduce by construction to fitted inputs, self-citations, or renamed known results. The central objective of providing practical workflows rests on descriptive compilation rather than any load-bearing derivation chain, rendering the work self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper introduces no new free parameters, axioms, or invented entities; it relies entirely on standard statistical tools such as normality tests and distribution fitting drawn from prior literature.

pith-pipeline@v0.9.0 · 5412 in / 1061 out tokens · 42912 ms · 2026-05-10T09:20:37.273117+00:00 · methodology

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Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

  1. [1]

    Process capability: a total quality management tool,

    F. A. Spiring, “Process capability: a total quality management tool,” Total Quality Management, vol. 6, no. 1, pp. 21–34, 1995

    work page 1995

  2. [2]

    Distributional and Inferential Properties of Process Capability Indices,

    W. L. Pearn, S. Kotz, and N. L. Johnson, “Distributional and Inferential Properties of Process Capability Indices,”Journal of Quality Technology, vol. 24, no. 4, pp. 216–231, Oct. 1992

    work page 1992

  3. [3]

    Process Capability Indices—A Review, 1992–2000,

    S. Kotz and N. L. Johnson, “Process Capability Indices—A Review, 1992–2000,”Journal of Quality Technology, vol. 34, no. 1, pp. 2–19, Jan. 2002

    work page 1992

  4. [5]

    A review and interpretations of process capability indices,

    K. Palmer and K.-L. Tsui, “A review and interpretations of process capability indices,” 1999

    work page 1999

  5. [6]

    Process capability analysis for an entire product,

    K. S. Chen, M. L. Huang, and R. K. Li, “Process capability analysis for an entire product,”International Journal of Production Research, vol. 39, no. 17, pp. 4077–4087, Jan. 2001

    work page 2001

  6. [7]

    The Taguchi Capability Index,

    R. A. Boyles, “The Taguchi Capability Index,”Journal of Quality Technology, vol. 23, no. 1, pp. 17–26, Jan. 1991

    work page 1991

  7. [8]

    The Views of Long Term and Short Term Process Capability Indices- A Comparison,

    Y . Wooluru, D. R. Swamy, and P. Nagesh, “The Views of Long Term and Short Term Process Capability Indices- A Comparison,” 2015

    work page 2015

  8. [9]

    J. M. Juran, F. M. Gryna, and R. S. Bingham,Quality control handbook. McGraw-hill New York, 1979, vol. 3

    work page 1979

  9. [10]

    Capability index-enough for process industries,

    J. T. Herman, “Capability index-enough for process industries,” inASQC Ann. Qual. Congress Trans, Toronto, 1989, pp. 670–675

    work page 1989

  10. [11]

    Quality engineering in japan,

    G. Taguchi, “Quality engineering in japan,”Communications in Statistics-Theory and Methods, vol. 14, no. 11, pp. 2785–2801, 1985

    work page 1985

  11. [12]

    Process Capability Indices,

    V . E. Kane, “Process Capability Indices,”Journal of Quality Technology, vol. 18, no. 1, pp. 41–52, Jan. 1986

    work page 1986

  12. [13]

    A tutorial on quality control and assurance-the taguchi methods,

    T. C. Hsiang, “A tutorial on quality control and assurance-the taguchi methods,” inASA Annual Meeting LA, 1985, 1985

    work page 1985

  13. [14]

    Optimal design for a linear log contrast model for ex- periments with mixtures,

    L.-Y . Chan, “Optimal design for a linear log contrast model for ex- periments with mixtures,”Journal of statistical planning and inference, vol. 20, no. 1, pp. 105–113, 1988

    work page 1988

  14. [15]

    Estimation of pmk c process capability index based on bootstrap method for weibull distribution: A case study,

    B. Sadeghpour, “Estimation of pmk c process capability index based on bootstrap method for weibull distribution: A case study,”International journal for quality research, vol. 8, no. 2, pp. 255–264, 2014

    work page 2014

  15. [16]

    A New Measure of Process Capability:C pm ,

    L. K. Chan, S. W. Cheng, and F. A. Spiring, “A New Measure of Process Capability:C pm ,”Journal of Quality Technology, vol. 20, no. 3, pp. 162–175, Jul. 1988

    work page 1988

  16. [17]

    A class of process capa- bility indices for asymmetric tolerances,

    Z. Abbasi Ganji and B. Sadeghpour Gildeh, “A class of process capa- bility indices for asymmetric tolerances,”Quality Engineering, vol. 28, no. 4, pp. 441–454, Oct. 2016

    work page 2016

  17. [18]

    Estimating process capability index C

    W. L. Pearn, P. C. Lin, and K. S. Chen, “Estimating process capability index C”pmk for asymmetric tolerances: Distributional properties,” 2002. 11

    work page 2002

  18. [19]

    The asymptotic distribution of the process capability indexC pmk ,

    Sy-Mien Chen and Nai-Feng Hsu, “The asymptotic distribution of the process capability indexC pmk ,”Communications in Statistics - Theory and Methods, vol. 24, no. 5, pp. 1279–1291, Jan. 1995

    work page 1995

  19. [20]

    Estimating capability index cpk for processes with asymmetric tolerances,

    W. L. Pearn and G. H. Lin, “Estimating capability index cpk for processes with asymmetric tolerances,”Communications in Statistics - Theory and Methods, vol. 29, no. 11, pp. 2593–2604, Jan. 2000

    work page 2000

  20. [21]

    Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances,

    Y . Chang and C.-W. Wu, “Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances,”European Journal of Operational Research, vol. 190, no. 1, pp. 205–227, Oct. 2008

    work page 2008

  21. [22]

    Incapability index with asymmetric tolerances,

    K. S. Chen, “Incapability index with asymmetric tolerances,”Statistica Sinica, pp. 253–262, 1998

    work page 1998

  22. [23]

    Capability indices for processes with asymmetric tolerances,

    K.-S. Chen and W.-L. Pearn, “Capability indices for processes with asymmetric tolerances,”Journal of the Chinese Institute of Engineers, vol. 24, no. 5, pp. 559–568, Jul. 2001

    work page 2001

  23. [24]

    An application of non-normal process capability indices,

    K. S. Chen and W. L. Pearn, “An application of non-normal process capability indices,”Quality and Reliability Engineering International, vol. 13, no. 6, pp. 355–360, 1997

    work page 1997

  24. [25]

    A new process capability index for non- normal distributions,

    J.-P. Chen and C. G. Ding, “A new process capability index for non- normal distributions,”International Journal of Quality & Reliability Management, vol. 18, no. 7, pp. 762–770, Oct. 2001

    work page 2001

  25. [26]

    Basic Process Capability Indices: An Expository Review,

    M. Z. Anis, “Basic Process Capability Indices: An Expository Review,” International Statistical Review, vol. 76, no. 3, pp. 347–367, Dec. 2008

    work page 2008

  26. [27]

    Process Capability Indices for Non-Normal Data,

    M. Kov ´aˇr´ık and L. Sarga, “Process Capability Indices for Non-Normal Data,” vol. 11, 2014

    work page 2014

  27. [28]

    A unified approach to capability indices,

    K. V ¨annman, “A unified approach to capability indices,”Statistica Sinica, pp. 805–820, 1995

    work page 1995

  28. [29]

    A process incapability index,

    M. Greenwich and B. L. Jahr-Schaffrath, “A process incapability index,” International Journal of Quality & Reliability Management, vol. 12, no. 4, pp. 58–71, 1995

    work page 1995

  29. [30]

    A comparison of various tests of normality,

    B. Yazici and S. Yolacan, “A comparison of various tests of normality,” Journal of statistical computation and simulation, vol. 77, no. 2, pp. 175–183, 2007

    work page 2007

  30. [31]

    Comparisons of various types of normality tests,

    B. W. Yap and C. H. Sim, “Comparisons of various types of normality tests,”Journal of Statistical Computation and Simulation, vol. 81, no. 12, pp. 2141–2155, 2011

    work page 2011

  31. [32]

    The shapiro–wilk test for normality,

    R. Dudley, “The shapiro–wilk test for normality,” 2023

    work page 2023

  32. [33]

    Kolmogorov–smirnov test: Overview,

    V . W. Berger and Y . Zhou, “Kolmogorov–smirnov test: Overview,”Wiley statsref: Statistics reference online, 2014

    work page 2014

  33. [34]

    The anderson-darling test for normality,

    L. S. Nelson, “The anderson-darling test for normality,”Journal of Quality Technology, vol. 30, no. 3, pp. 298–299, 1998

    work page 1998

  34. [35]

    Aic, bic and recent advances in model selection,

    A. Chakrabarti and J. K. Ghosh, “Aic, bic and recent advances in model selection,”Philosophy of statistics, pp. 583–605, 2011

    work page 2011

  35. [36]

    Process Capability Analysis With GD&T Specifications,

    J. Liu, W. Huang, Z. Kong, and Y . Zhou, “Process Capability Analysis With GD&T Specifications,” inVolume 2A: Advanced Manufacturing. San Diego, California, USA: American Society of Mechanical Engi- neers, Nov. 2013, p. V02AT02A063

    work page 2013

  36. [37]

    The box–cox transforma- tion: Review and extensions,

    A. C. Atkinson, M. Riani, and A. Corbellini, “The box–cox transforma- tion: Review and extensions,” 2021

    work page 2021

  37. [38]

    Estimating the Standard Deviation in Quality-Control Applications,

    M. A. Mahmoud, G. R. Henderson, E. K. Epprecht, and W. H. Woodall, “Estimating the Standard Deviation in Quality-Control Applications,” Journal of Quality Technology, vol. 42, no. 4, pp. 348–357, Oct. 2010

    work page 2010

  38. [39]

    Methodological insights for industrial quality control manage- ment: The impact of various estimators of the standard deviation on the process capability index,

    E. ´Alvarez, P. J. Moya-F ´ernandez, F. J. Blanco-Encomienda, and J. F. Mu˜noz, “Methodological insights for industrial quality control manage- ment: The impact of various estimators of the standard deviation on the process capability index,”Journal of King Saud University - Science, vol. 27, no. 3, pp. 271–277, Jul. 2015

    work page 2015

  39. [40]

    Oakland and J

    J. Oakland and J. S. Oakland,Statistical process control. Routledge, 2007

    work page 2007

  40. [41]

    Estimating the standard deviation for statistical process control,

    D. W. Marquardt, “Estimating the standard deviation for statistical process control,”International Journal of Quality & Reliability Man- agement, vol. 10, no. 8, 1993

    work page 1993

  41. [42]

    Calculating the exact pooled variance,

    J. W. Rudmin, “Calculating the exact pooled variance,”arXiv preprint arXiv:1007.1012, 2010. 12

    work page arXiv 2010