Importance Sampling Estimation of Generalized Process Capability Indices

Introduction

The gpciImpSam package provides a generalized framework for parameter estimation and Generalized Process Capability Indices (GPCIs) under uncensored data using Importance Sampling (ImpSam).

Supported capability indices include: - \(C_{py}\) (Yield ratio) - \(C_p, C_{pk}, C_{pu}, C_{pl}, C_{pm}, C_{pmk}\) - \(C_{pTk}\) (Saha et al., 2019) - \(S_{pmk}\) (Dey & Saha, 2019) - \(C_{pc}\) (Saha et al., 2022) - \(CN_{pk}\) (Saha et al., 2018) - \(CN_{pmc}\) (Alotaibi et al., 2022) - \(CN_{pmkc}\) (Saha et al., 2024) - \(C_p(u, v)\) (Vännman’s generalized family)

Example: Importance Sampling Analysis with User Functions

In this example, we provide sample uncensored data and custom user PDF and CDF functions.

set.seed(123)
# Simulate 50 observations from a Normal process
process_data <- rnorm(50, mean = 10, sd = 1.2)

# Fit GPCIs using Importance Sampling
fit <- gpci_impsam(
  data = process_data,
  pdf = function(x, mean = 0, sd = 1) dnorm(x, mean = mean, sd = sd),
  cdf = function(x, mean = 0, sd = 1) pnorm(x, mean = mean, sd = sd),
  chain_length = 500,
  burn_in = 100,
  thinning = 1,
  USL = 13.5,
  LSL = 6.5,
  target = 10
)

# Print diagnostic summary table
summary_df <- summary(fit)
knitr::kable(summary_df[, c("Index", "Point_Estimate", "Posterior_Mean", "Bias", "MSE", "Risk_Value", "HPD95_Lower", "HPD95_Upper", "Convergence_Prob")])

Visualizing Posterior Distributions

plot(fit, type = "density", index = "Cpy")