nhpp: Non-Homogeneous Poisson Process Model for Repairable Systems.

In ReliaGrowR: Reliability Growth Analysis and Repairable Systems Modeling

Non-Homogeneous Poisson Process Model for Repairable Systems.

Description

Fits a parametric NHPP model to recurrent event data from repairable systems. Supported models include the Power Law process and the Log-Linear process. The Power Law model can also be fit as a piecewise (segmented) model with automatic change point detection or user-specified breakpoints.

Usage

nhpp(
  time,
  event = NULL,
  data = NULL,
  model_type = "Power Law",
  breaks = NULL,
  method = c("MLE", "LS"),
  conf_level = 0.95
)

Arguments

time	A numeric vector of cumulative event times, or a data frame containing columns time and optionally event. All values must be positive, finite, and strictly increasing.
event	An optional numeric vector of event counts at each time. If NULL (default), each time is treated as a single event.
data	An optional data frame containing columns time and optionally event.
model_type	Model type: "Power Law" (default) or "Log-Linear".
breaks	Optional vector of breakpoints for piecewise Power Law model.
method	Estimation method: "MLE" (default) or "LS". "LS" is not supported for "Log-Linear" models.
conf_level	Confidence level for bounds (default 0.95).

Details

The Power Law NHPP models the cumulative number of events as N(t) = \lambda t^\beta. The parameter \beta > 1 indicates a deteriorating system (increasing event rate), \beta < 1 an improving system, and \beta = 1 a constant rate (HPP).

The Log-Linear NHPP models the intensity as \lambda(t) = \exp(a + bt) with cumulative function \Lambda(t) = \frac{e^a}{b}(e^{bt} - 1).

Value

An object of class nhpp containing:

time	The input cumulative event times.
event	The event counts.
cum_events	Cumulative event counts.
n_obs	Number of observations.
model	Fitted model object (lm or segmented), or NULL for MLE.
model_type	"Power Law" or "Log-Linear".
method	"MLE" or "LS".
params	Named list of estimated parameters.
params_se	Named list of standard errors.
vcov	Variance-covariance matrix (MLE only).
fitted_values	Fitted cumulative events.
lower_bounds	Lower confidence bounds.
upper_bounds	Upper confidence bounds.
residuals	Model residuals.
logLik	Log-likelihood.
AIC	Akaike Information Criterion.
BIC	Bayesian Information Criterion.
breakpoints	Breakpoints (log scale) if piecewise model.
conf_level	Confidence level used.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
result <- nhpp(time, event)
print(result)
plot(result, main = "Power Law NHPP")

result_ll <- nhpp(time, event, model_type = "Log-Linear")
print(result_ll)

ReliaGrowR documentation built on May 22, 2026, 5:07 p.m.