Classical and Generalized Process Capability Indices

Computes classical process capability indices (Cp, Cpk, Cpu, Cpl, Cpm, Cpmk, Pp, Ppk, Ppu, Ppl, Z) and the generalized process capability index Cpy (Maiti, Saha & Nanda, 2010) for any continuous or discrete quality characteristic. Users supply the probability density function (PDF) and cumulative distribution function (CDF) of the characteristic, and the package returns point estimates, bootstrap confidence intervals (percentile and BCa), and sensitivity tables/plots across ranges of short-term standard deviation (sigma), long-term standard deviation (s), desired yield (p0), and significance levels. Classical indices are recoverable as special cases under the normal distribution. The package follows the theory and notation of Kane (1986) , Chan, Cheng & Spiring (1988) , Pearn, Kotz & Johnson (1992) , Kotz & Johnson (2002) , Montgomery (2020, ISBN:978-1-119-39930-8), Juran (1974, ISBN:978-0-07-033176-1), Harry & Schroeder (2000, ISBN:978-0-385-49437-2), and the AIAG SPC Reference Manual (2005, ISBN:978-1-60534-026-3).

ProcessCapabilityR

Classical and Generalized Process Capability Indices for Any Distribution

Overview

ProcessCapabilityR computes Process Capability Indices (PCIs) for any quality characteristic — not just the normal distribution — by letting users supply the characteristic's PDF and CDF directly.

Features

• 11 classical indices: Cp, Cpk, Cpu, Cpl, Cpm, Cpmk, Pp, Ppk, Ppu, Ppl, Z (sigma level)
• Generalized index Cpy (Maiti, Saha & Nanda, 2010) for any continuous or discrete distribution
• Bootstrap confidence intervals — percentile and BCa methods, parametric or nonparametric
• Sensitivity grids across σ, s, p₀ values at multiple significance levels
• ggplot2 visualisation of sensitivity sweeps with confidence bands

Installation

# Install from GitHub
# devtools::install_github("shikhartyagi/ProcessCapabilityR")

# Or install locally from source
devtools::install("path/to/ProcessCapabilityR")

# Load the package
library(ProcessCapabilityR)

Quick Start

Classical Indices (Normal Process)

library(ProcessCapabilityR)

# Process: USL = 63, LSL = 57, μ = 60, σ = 1 (centered)
cp(LSL = 57, USL = 63, sigma = 1)                        # 1.0
cpk(LSL = 57, USL = 63, mu = 60, sigma = 1)              # 1.0
cpm(LSL = 57, USL = 63, mu = 60, sigma = 1, target = 60) # 1.0
z_level(LSL = 57, USL = 63, mu = 60, sigma = 1)          # 3.0

# Or use the generic interface
pci("Cp",  LSL = 57, USL = 63, sigma = 1)
pci("Cpk", LSL = 57, USL = 63, mu = 60, sigma = 1)

# Performance indices (long-term)
pp(LSL = 57, USL = 63, s = 1.5)                          # 0.667
ppk(LSL = 57, USL = 63, xbar = 60, s = 1.5)              # 0.667

Generalized Cpy (Non-Normal Distribution)

# Define a Weibull distribution
dist_weibull <- pci_dist(
  pdf    = function(x, shape, scale) dweibull(x, shape, scale),
  cdf    = function(x, shape, scale) pweibull(x, shape, scale),
  params = list(shape = 2, scale = 10),
  support = c(0, 50)
)

# Compute Cpy with desired yield p₀ = 0.95
pci("Cpy", dist = dist_weibull, LSL = 2, USL = 20, p0 = 0.95)

Bootstrap Confidence Intervals

dist_norm <- pci_dist_normal(mean = 60, sd = 1)
ci <- pci_ci("Cp", dist = dist_norm, n = 30,
             LSL = 57, USL = 63, alpha = 0.05, B = 2000)
print(ci)

Sensitivity Grid & Plot

grid <- pci_grid("Cp",
                 dist = pci_dist_normal(60, 1),
                 LSL = 57, USL = 63,
                 sigma_vals = seq(0.5, 2.0, by = 0.1),
                 mu = 60,
                 alpha_vals = c(0.10, 0.05, 0.01),
                 n = 30, B = 500)
plot(grid, x_axis = "sigma")

Cpy Sensitivity Grid

grid_cpy <- pci_grid("Cpy",
                     dist = pci_dist_normal(60, 1),
                     LSL = 57, USL = 63,
                     p0_vals = c(0.90, 0.95, 0.99),
                     alpha_vals = c(0.10, 0.05, 0.01),
                     n = 30, B = 500)
plot(grid_cpy, x_axis = "p0")

Available Indices

References

• Juran, J.M. (1974). Quality Control Handbook (3rd ed.). McGraw-Hill.
• Kane, V.E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41–52.
• Chan, L.K., Cheng, S.W., & Spiring, F.A. (1988). A new measure of process capability: Cpm. Journal of Quality Technology, 20(3), 162–175.
• Pearn, W.L., Kotz, S., & Johnson, N.L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24(4), 216–231.
• Harry, M., & Schroeder, R. (2000). Six Sigma: The Breakthrough Management Strategy. Doubleday.
• Kotz, S., & Johnson, N.L. (2002). Process capability indices — a review, 1992–2000. Journal of Quality Technology, 34(1), 2–19.
• AIAG (2005). Statistical Process Control (SPC) Reference Manual (2nd ed.).
• Maiti, S.S., Saha, M., & Nanda, A.K. (2010). On generalizing process capability indices. Quality Technology & Quantitative Management, 7(3), 279–300.
• Montgomery, D.C. (2020). Introduction to Statistical Quality Control (8th ed.). Wiley.

Authors

• Shikhar Tyagi — maintainer (ORCID) <[email protected]>
• Sumit Kumar <[email protected]>
• Vrijesh Tripathi <[email protected]>

License

MIT © 2025 Shikhar Tyagi, Sumit Kumar, Vrijesh Tripathi