If you specify the reliability goal in terms of a time and a reliability, Minitab first calculates the parameter to be demonstrated using the formula for the specified distribution in the following table.
Next, Minitab calculates the testing time or sample size the same way as in the substantiation testing case.
Distribution (parameter)  Parameter to be demonstrated 

Weibull (scale)  
Exponential (mean)  
Smallest extreme value (location) Normal (mean) Logistic (mean) 

Lognormal (loglocation) Loglogistic (loglocation) 

Term  Description 

t  time 
R(t)  reliability function 
θ  scale (Weibull) or mean (exponential) 
β  shape parameter (Weibull) 
σ  scale parameter (lognormal, loglogistic, logistic, normal, smallest extreme value) 
μ  mean (normal, logistic) or loglocation (lognormal, loglogistic) 
Φ^{1 }  inverse CDF for the corresponding distribution 
If you specify the reliability goal in terms of the P^{th} percentile (t_{p}), Minitab first calculates the parameter to be demonstrated using the formula for the specified distribution in the following table.
Next, Minitab calculates the testing time or sample size the same way as in the substantiation testing case.
Distribution (parameter)  Parameter to be demonstrated 

Weibull (scale)  
Exponential (mean)  
Smallest extreme value (location) Normal (mean) Logistic (mean) 

Lognormal (loglocation) Loglogistic (loglocation) 

Term  Description 

t  time 
R(t)  reliability function 
p  percentile 
α  scale (Weibull) 
θ  mean (exponential) 
μ  mean (normal, logistic), location (smallest extreme value), or loglocation (lognormal, loglogistic) 
Φ^{1 }  inverse CDF for the corresponding distribution 
If you specify the reliability goal in terms of the MTTF, Minitab first calculates the parameter to be demonstrated using the formula for the specified distribution in the following table.
Next, Minitab calculates the testing time or sample size the same way as in the substantiation testing case.
Distribution (parameter)  Parameter to be demonstrated 

Weibull (scale)  
Exponential (mean)  
Normal (mean) Logistic (mean) 

Lognormal (loglocation) 

Loglogistic (loglocation) 

Smallest extreme value (location) 

Term  Description 

α  scale (Weibull) 
σ  scale (lognormal, loglogistic, smallest extreme value distribution) 
β  shape (Weibull) 
θ  mean (exponential) 
μ  mean (normal, logistic), location (smallest extreme value), or loglocation (lognormal, loglogistic) 
MTTF  mean time to failure 
c  Euler's constant ≈ 0.5772 
Γ  gamma function 