Package {csbewma}

Apply multiple testing corrections

Description

Applies Bonferroni, Holm, or Benjamini-Hochberg corrections.

Usage

apply_multiple_testing(pvals, method = "BH", alpha = 0.05)

Arguments

Value

List with adjusted_pvals and flags

Examples

pvals <- c(0.001, 0.01, 0.03, 0.10, 0.50)
result <- apply_multiple_testing(pvals, method = "BH", alpha = 0.05)

Calculate p-values for all streams

Description

Computes exact binomial p-values for each stream based on successes.

Usage

calculate_pvalues(bin_matrix, p0 = 0.5)

Arguments

Value

Numeric vector of p-values

Examples

bin_mat <- matrix(rbinom(500, 1, 0.5), nrow = 10, ncol = 50)
pvals <- calculate_pvalues(bin_mat, p0 = 0.5)

CSB-EWMA Control Chart

Description

Runs the Cumulative Standardized Binomial EWMA control chart on multiple stream data.

Usage

csb_ewma(
  data,
  lambda,
  L,
  p0 = 0.5,
  max_time = NULL,
  posthoc_method = "BH",
  alpha = 0.05,
  verbose = TRUE
)

Arguments

Value

A list of class "csb_ewma" containing chart results and flagged streams

Examples

{
set.seed(123)
bin_data <- matrix(rbinom(10*100, 1, 0.5), nrow = 10, ncol = 100)
for(i in 1:3) bin_data[i, ] <- rbinom(100, 1, 0.8)
result <- csb_ewma(bin_data, lambda = 0.175, L = 1.375)
message(result)
plot(result)
}

Dichotomize Continuous Data to Binary Indicators

Description

Converts continuous observations to binary indicators based on whether each observation exceeds the in-control median or specified quantile.

Usage

dichotomize_data(data, distribution, p0 = 0.5)

Arguments

Value

Integer vector of binary indicators (0 or 1)

Examples

x <- rnorm(100)
binary <- dichotomize_data(x, distribution = "normal", p0 = 0.5)

Summarize flagged streams

Description

Creates a summary of which streams were flagged.

Usage

flagged_streams_summary(flagged_results, verbose = TRUE)

Arguments

Value

List with flagged streams and summary table

Examples

bin_mat <- matrix(rbinom(10*100, 1, 0.5), nrow = 10, ncol = 100)
for(i in 1:3) bin_mat[i, ] <- rbinom(100, 1, 0.8)
result <- identify_ooc(bin_mat)
summary <- flagged_streams_summary(result)
print(summary$flagged_streams)

Generate Continuous Data from Specified Distribution

Description

Generates continuous observations from normal, Laplace, uniform, or exponential distributions with optional shift parameter for out-of-control simulation.

Usage

generate_continuous_data(distribution, n, shift = 0, p0 = 0.5)

Arguments

Value

A numeric vector of length n containing the generated data

Examples

data <- generate_continuous_data("normal", n = 100, shift = 0.2)

Identify out-of-control streams Main function for post-hoc identification using multiple testing corrections.

Description

Identify out-of-control streams Main function for post-hoc identification using multiple testing corrections.

Usage

identify_ooc(bin_matrix, alpha = 0.05, method = "BH", p0 = 0.5, verbose = TRUE)

Arguments

Value

Data frame with p-values and flags for each stream

Examples

set.seed(123)
bin_mat <- matrix(rbinom(10*100, 1, 0.5), nrow = 10, ncol = 100)
for(i in 1:3) bin_mat[i, ] <- rbinom(100, 1, 0.8)
result <- identify_ooc(bin_mat, p0 = 0.5)
print(result[result$flagged, ])

Plot CSB-EWMA Control Chart

Description

Creates a professional control chart showing EWMA statistic and limits.

Usage

## S3 method for class 'csb_ewma'
plot(x, title = "CSB-EWMA Control Chart", show_signal = TRUE, ...)

Arguments

Value

A ggplot object (invisibly) and displays the plot

Examples

# See csb_ewma() for examples

Combined Diagnostic Dashboard

Description

Creates a combined plot showing both the CSB-EWMA control chart and the flagged streams bar plot side by side or stacked.

Usage

plot_chart_with_flagged(chart_result, flagged_results, layout = "side")

Arguments

Value

A combined ggplot object (invisibly) and displays the plot

Direct Plot for CSB-EWMA Results

Description

Creates a professional control chart showing EWMA statistic and limits. This function can be called directly without S3 dispatch.

Usage

plot_csb_ewma_direct(
  result,
  title = "CSB-EWMA Control Chart",
  show_signal = TRUE
)

Arguments

Value

A ggplot object (invisibly) and displays the plot

Plot Flagged Streams Bar Chart

Description

Creates a bar plot showing -log10(p-values) for each stream. Flagged streams appear in red, others in gray.

Usage

plot_flagged_streams(flagged_results, alpha = 0.05, title = "Stream P-values")

Arguments

Value

A ggplot object (invisibly) and displays the plot

Precompute variance vector for all time points

Description

This function precomputes the exact variance for all time points from 1 to max_t. For efficiency, it computes exact variances up to a convergence threshold (converge_t) and then sets remaining values to 1 (asymptotic). Based on the derivation, variance reaches 99% of asymptotic value by t=227, so converge_t = 500 is safe and efficient.

Usage

precompute_variance(lambda, max_t, converge_t = 500)

Arguments

Value

A numeric vector of length max_t containing variance at each time point

Examples

# Precompute variance for lambda = 0.175, up to t = 1000
var_cache <- precompute_variance(lambda = 0.175, max_t = 1000, converge_t = 500)

Prints a formatted summary of CSB-EWMA chart results.

Description

Prints a formatted summary of CSB-EWMA chart results.

Usage

## S3 method for class 'csb_ewma'
print(x, ...)

Arguments

Value

Invisibly returns the object

Generate Laplace (Double Exponential) Random Variables

Description

Generates random numbers from the Laplace distribution using inverse transform sampling.

Usage

rlaplace(n, location = 0, scale = 1)

Arguments

Value

A numeric vector of length n containing Laplace random variables

Examples

{
x <- rlaplace(100, location = 0, scale = 1)
}

Run CSB-EWMA Chart on Binary Data

Description

This function implements the core CSB-EWMA monitoring algorithm exactly as implemented in the original simulation code.

Usage

run_csb_ewma(bin_matrix, lambda, L, var_cache, max_time = NULL, p0 = 0.5)

Arguments

Details

The algorithm works as follows:

1. Initialize cumulative sum (cum_sum = 0) and EWMA (r_prev = 0)

2. For each time point t = 1, 2, ..., max_time:

   • Get binary vector for current time point

   • Calculate C_t = sum of binary indicators

   • Update cumulative sum: cum_sum = cum_sum + C_t

   • Compute standardized statistic: W_t = (cum_sum - mu0t) / sqrt(tsigma2_0)

   • Update EWMA: r_t = lambda * W_t + (1 - lambda) * r_prev

   • Get exact variance from precomputed cache: v_t = var_cachet

   • Compute control limits: UCL_t = L * sqrt(v_t), LCL_t = -L * sqrt(v_t)

   • If r_t > UCL_t or r_t < LCL_t, signal at time t and break

   • Otherwise, update r_prev = r_t and continue

Value

A list of class "csb_ewma" containing chart results

Examples

bin_matrix <- matrix(rbinom(10*200, 1, 0.5), nrow = 10, ncol = 200)
for(i in 1:3) bin_matrix[i, ] <- rbinom(100, 1, 0.8)
var_cache <- precompute_variance(0.175, max_t = 200)
result <- run_csb_ewma(bin_matrix, lambda = 0.175, L = 1.375, var_cache)
message(paste("Signal at time:", result$signal_time))

Compute exact CSB-EWMA variance for a single time point

Description

This function implements the exact variance formula derived in Theorem 2. The variance is computed using double summation over the covariance structure of the standardized statistics. For a given smoothing parameter lambda and time point t, this returns Var(r_t) as defined in Equation (19) of the supplementary material.

Usage

var_rt_exact_single(lambda, t)

Arguments

Value

The exact variance Var(r_t) at time t. For t = 0, returns 0.

Examples

# Compute variance at time 10 for lambda = 0.175
var_rt_exact_single(lambda = 0.175, t = 10)

# Compute variance at time 50 for lambda = 0.15
var_rt_exact_single(lambda = 0.15, t = 50)