Demonstration test plans are of two types: substantiation tests and reliability tests.
For a substantiation test, the hypotheses are as follows.
 H_{0}: The redesigned system is no different than the current system.
 H_{1}: The redesigned system is better than the current system.
For a reliability test, the hypotheses are as follows.
 H_{0}: The system reliability is equal to a specified value.
 H_{1}: The system reliability is greater than a specified value.
The hypotheses can be defined in terms of the following values:
 Scale (Weibull or exponential distribution) or location (other distributions)

 H_{0}: Location (Scale for Weibull/Exponential) = T
 H_{1}: Location (Scale for Weibull/Exponential) > T
 Percentile

 H_{0}: P^{th} percentile = T
 H_{1}: P^{th} percentile > T
 Reliability at a particular time

 H_{0}: Reliability at time T = p
 H_{1}: Reliability at time T > p
 Mean time to failure (MTTF)

 H_{0}: MTTF = T
 H_{1}: MTTF > T
If you pass the demonstration test (the number of failures ≤ M), then you reject H_{0} at the confidence level that you selected for the demonstration test plan (default is 95%).
If you fail the demonstration test (the number of failures > M), then you fail to reject H_{0}. M is the maximum number of failures allowed according to the demonstration test plan.