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Exponential Distribution (Constant Hazard)

Source: R/distributions.R
dfr_exponential.Rd

Creates a DFR distribution with constant failure rate (exponential). The exponential distribution is "memoryless" - the hazard does not depend on time, making it appropriate for random failures unrelated to age.

Usage

dfr_exponential(lambda = NULL)

Arguments

lambda

Rate parameter (failure rate). If NULL, must be provided when calling methods or fitting. Must be positive.

Value

A dfr_dist object with analytical rate, cumulative hazard, and score function.

Details

The exponential distribution has:

  • Hazard: \(h(t) = \lambda\)

  • Cumulative hazard: \(H(t) = \lambda t\)

  • Survival: \(S(t) = e^{-\lambda t}\)

  • Mean time to failure: \(1/\lambda\)

Reliability Interpretation

Use exponential for:

  • Electronic components during useful life (random failures)

  • Systems with redundancy where failures are independent

  • As a baseline model to test against more complex alternatives

Examples

# Component with MTBF of 1000 hours (lambda = 0.001)
comp <- dfr_exponential(lambda = 0.001)

# Survival probability at 500 hours
S <- surv(comp)
S(500)  # ~60.6%
#> [1] 0.6065307

# Fit to failure data
set.seed(42)
failures <- data.frame(t = rexp(50, rate = 0.001), delta = 1)
solver <- fit(comp)
result <- solver(failures, par = c(0.002))
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
coef(result)  # Should be close to 0.001
#> [1] 0.0008808454