The gpciProgTyII package provides a unified statistical
framework for evaluating classical and Generalized Process Capability
Indices (GPCIs) under Progressive Type-II Censored Data.
Key features include: 1. Parameter estimation for progressive Type-II
censored data using the MleCensoR package
(mle_progressive_type2). 2. Evaluation of GPCIs including
\(C_{py}\), \(S_{pmk}\), \(C_{pTk}\), \(C_{pc}\), \(C_{Npmc}\), \(C_{Npmkc}\), \(C_{Npk}\), and Vännman’s \(C_p(u,v)\) family. 3. Computation of
parametric and non-parametric bootstrap confidence intervals at 90%,
95%, and 99% levels of significance. 4. Calculation of Standard Errors
(SE), Mean Squared Error (MSE), Bias, and empirical coverage
probabilities for model parameters and capability indices.
# Load distribution and define progressive data
dist_w <- dist_weibull(shape = 1.5, scale = 4.0)
# Observed failure times under progressive censoring
x <- c(0.8, 1.5, 2.3, 3.1, 4.2)
r_scheme <- c(1, 0, 2, 0, 1)
# Fit model parameters and compute capability indices
fit <- capability_prog(
x = x, r_removals = r_scheme,
distribution = dist_w,
USL = 6.0, LSL = 0.5, target = 3.25,
indices = c("Cpy", "Cp", "Cpk", "Cpm", "CpTk", "Spmk", "CNpmc")
)
print(fit)
#> --- Progressive Type-II GPCI Analysis (Class: gpc_prog_fit) ---
#> Distribution: Weibull
#> Parameters: shape = 2.1242, scale = 3.5655
#> Spec Limits: LSL = 0.5 , USL = 6 , Target = 3.25
#> Mode: moments
#> Expected Nonconforming (p_hat): 6.4045 %
#>
#> Point Estimates of Capability Indices:
#> Cpy Cp Cpk Cpm CpTk Spmk CNpmc
#> 0.9385 0.6460 0.5874 0.6362 0.8667 0.6080 0.5227
# Compute Bootstrap Confidence Intervals at 90%, 95%, and 99%
ci <- boot_ci_prog(fit, B = 50, alpha = c(0.10, 0.05, 0.01), method = "percentile")
print(ci)
#> --- Progressive Type-II Bootstrap Confidence Intervals ---
#> Bootstrap Type: parametric
#> CI Method: percentile
#> Replicates (B): 50
#>
#> Performance Summary (Standard Error, Bias, MSE):
#> Parameters:
#> item estimate se bias mse
#> shape shape 2.1242 1.5975 1.0983 3.7072
#> scale scale 3.5655 0.6925 -0.2083 0.5134
#>
#> Capability Indices:
#> item estimate se bias mse
#> Cpy Cpy 0.9385 0.0794 0.0068 0.0062
#> Cp Cp 0.6460 0.5900 0.3599 0.4707
#> Cpk Cpk 0.5874 0.3725 0.1784 0.1678
#> Cpm Cpm 0.6362 0.2897 0.1288 0.0988
#> CpTk CpTk 0.8667 0.2637 -0.2422 0.1268
#> Spmk Spmk 0.6080 0.2954 0.0817 0.0922
#> CNpmc CNpmc 0.5227 0.1332 0.0361 0.0187
#>
#> Confidence Intervals (90%, 95%, 99%):
#> type index estimate method bootstrap_type alpha conf_level lower
#> 1 GPCI Cpy 0.9385 percentile parametric 0.10 90% 0.7663
#> 2 GPCI Cpy 0.9385 percentile parametric 0.05 95% 0.7498
#> 3 GPCI Cpy 0.9385 percentile parametric 0.01 99% 0.7075
#> 4 GPCI Cp 0.6460 percentile parametric 0.10 90% 0.3850
#> 5 GPCI Cp 0.6460 percentile parametric 0.05 95% 0.3449
#> 6 GPCI Cp 0.6460 percentile parametric 0.01 99% 0.2684
#> 7 GPCI Cpk 0.5874 percentile parametric 0.10 90% 0.2954
#> 8 GPCI Cpk 0.5874 percentile parametric 0.05 95% 0.2648
#> 9 GPCI Cpk 0.5874 percentile parametric 0.01 99% 0.2186
#> 10 GPCI Cpm 0.6362 percentile parametric 0.10 90% 0.3791
#> 11 GPCI Cpm 0.6362 percentile parametric 0.05 95% 0.3385
#> 12 GPCI Cpm 0.6362 percentile parametric 0.01 99% 0.2651
#> 13 GPCI CpTk 0.8667 percentile parametric 0.10 90% 0.1242
#> 14 GPCI CpTk 0.8667 percentile parametric 0.05 95% 0.0272
#> 15 GPCI CpTk 0.8667 percentile parametric 0.01 99% 0.0000
#> 16 GPCI Spmk 0.6080 percentile parametric 0.10 90% 0.3232
#> 17 GPCI Spmk 0.6080 percentile parametric 0.05 95% 0.3055
#> 18 GPCI Spmk 0.6080 percentile parametric 0.01 99% 0.1816
#> 19 GPCI CNpmc 0.5227 percentile parametric 0.10 90% 0.3501
#> 20 GPCI CNpmc 0.5227 percentile parametric 0.05 95% 0.3175
#> 21 GPCI CNpmc 0.5227 percentile parametric 0.01 99% 0.2541
#> 22 Parameter shape 2.1242 percentile parametric 0.10 90% 1.4309
#> 23 Parameter shape 2.1242 percentile parametric 0.05 95% 1.2899
#> 24 Parameter shape 2.1242 percentile parametric 0.01 99% 1.1224
#> 25 Parameter scale 3.5655 percentile parametric 0.10 90% 2.3337
#> 26 Parameter scale 3.5655 percentile parametric 0.05 95% 2.2808
#> 27 Parameter scale 3.5655 percentile parametric 0.01 99% 1.6561
#> upper width
#> 1 1.0027 0.2364
#> 2 1.0027 0.2529
#> 3 1.0027 0.2952
#> 4 1.7206 1.3356
#> 5 2.8879 2.5430
#> 6 3.2836 3.0152
#> 7 1.3591 1.0637
#> 8 1.4415 1.1767
#> 9 1.8864 1.6679
#> 10 1.2861 0.9071
#> 11 1.3115 0.9731
#> 12 1.3552 1.0901
#> 13 0.9513 0.8271
#> 14 0.9923 0.9651
#> 15 0.9986 0.9986
#> 16 1.2472 0.9241
#> 17 1.2559 0.9504
#> 18 1.3891 1.2075
#> 19 0.7464 0.3963
#> 20 0.7513 0.4339
#> 21 0.7592 0.5051
#> 22 5.8099 4.3789
#> 23 6.0860 4.7961
#> 24 8.5446 7.4222
#> 25 4.4129 2.0792
#> 26 4.9230 2.6422
#> 27 5.2383 3.5822