Reliability Demonstration Test Planning
In ReliaGrowR: Reliability Growth Analysis and Repairable Systems Modeling

knitr::opts_chunk$set(collapse = TRUE, comment = "#>")

library(ReliaGrowR)

Overview

A Reliability Demonstration Test (RDT) provides statistical evidence that a product meets its reliability requirement. The rdt() function computes either:

the required test time given a fixed sample size, or
the required sample size given a fixed test duration.

The calculation uses the Weibull distribution; setting beta = 1 (the default) gives the exponential special case.

Test Time

For a zero-failure test plan (f = 0), the required cumulative test time $T$ for $n$ units satisfying reliability $R$ at mission time $t_m$ with confidence $C$ is:

$$T = t_m \left(\frac{-\ln C}{-\ln R}\right)^{1/\beta}$$

When allowable failures $f > 0$, the chi-squared quantile replaces $-\ln C$:

$$T = \frac{t_m}{(-\ln R)^{1/\beta}} \cdot \left(\frac{\chi^2_{1-C,\,2(f+1)}}{2n}\right)^{1/\beta}$$

Solving for Test Time

Suppose you need to demonstrate 90% reliability at 500 hours with 90% confidence, and you have 20 units available for testing:

plan <- rdt(
  target       = 0.90,   # 90% reliability
  mission_time = 500,    # hours
  conf_level   = 0.90,   # 90% confidence
  n            = 20      # 20 test units
)
print(plan)

Each unit must be tested for Required_Test_Time hours (or failure, whichever comes first) with zero failures allowed.

Solving for Sample Size

Alternatively, fix the test duration at 800 hours per unit:

plan2 <- rdt(
  target       = 0.90,
  mission_time = 500,
  conf_level   = 0.90,
  test_time    = 800
)
print(plan2)

Effect of Weibull Shape

For products with wear-out (beta > 1) or infant mortality (beta < 1), the Weibull shape parameter changes the required test time. Here we compare three scenarios:

betas <- c(0.8, 1.0, 1.5)
for (b in betas) {
  p <- rdt(target = 0.90, mission_time = 500, conf_level = 0.90, n = 20, beta = b)
  cat(sprintf("beta = %.1f  ->  required test time = %.1f hours\n",
              b, p$Required_Test_Time))
}

Higher beta (wear-out) demands shorter tests because failures concentrate near end-of-life; lower beta (infant mortality) demands longer tests.

Allowing Failures

A zero-failure plan is conservative. Allowing a small number of failures can substantially reduce the test burden:

for (f in 0:3) {
  p <- rdt(target = 0.90, mission_time = 500, conf_level = 0.90, n = 20, f = f)
  cat(sprintf("f = %d  ->  required test time = %.1f hours\n",
              f, p$Required_Test_Time))
}

Summary

| Parameter | Role | |---|---| | target | Required reliability R(t_m) | | mission_time | The time at which reliability is evaluated | | conf_level | Statistical confidence in the demonstration | | beta | Weibull shape (1 = exponential) | | f | Allowable failures (0 = most conservative) | | n | Sample size → solves for test time | | test_time | Test duration per unit → solves for sample size |