# Methods and formulas for planning values in Estimation Test Plan

## Two distributional parameters specified

If you specify the planning values for both μ and σ (θ and β for the Weibull model), then Minitab calculates the percentile or the reliability.

• The planning value for the pth percentile is calculated as follows:
• for location-scale models (normal, logistic and extreme value)
• for log-location-scale models (Weibull, lognormal, loglogistic)
• The planning value for reliability at a given time is calculated as follows:
• for location-scale models (normal, logistic, extreme value)
• for log-location-scale models (Weibull, lognormal, loglogistic)

### Notation

TermDescription
μmean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
σscale parameter
θscale parameter for Weibull
βshape parameter for Weibull
ttime
tp,planplanning value for the pth percentile at time t
Rplan(t)planning value for reliability at time t
Φ CDF for the corresponding distribution
Φ-1 inverse CDF for the corresponding distribution

## Percentile and shape (or scale) specified

If you specify the planning values for β (or σ) and a percentile tp0, then Minitab calculates the planning value for μ as follows:

• For location-scale models (normal, logistic and extreme value)
• For log-location-scale models (Weibull, lognormal and loglogistic)

To obtain the planning value for the percentile or the reliability, use the calculations for when two parameters are specified. For more information, see the section "Two distributional parameters specified".

### Notation

TermDescription
μmean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
μplanplanning value for mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
σscale parameter
σplanplanning value for scale parameter
βshape parameter for Weibull
ttime
tppercentile at time t
Φ-1 inverse CDF for the corresponding distribution

## Percentile and scale (or location) specified

If you specify the planning values for μ (or θ) and a percentile tp0 then Minitab calculates the planning value for σ as follows:

• For location-scale models (normal, logistic and extreme value)
• For log-location-scale models (Weibull, lognormal and loglogistic)

To obtain the planning value for the percentile or the reliability, use the calculations for when two parameters are specified. For more information, see the section "Two distributional parameters specified".

### Notation

TermDescription
μmean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
μplanplanning value for mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
σscale parameter
σplanplanning value for scale parameter
βshape parameter for Weibull
ttime
tppercentile at time t
Φ-1 inverse CDF for the corresponding distribution

## Two percentiles specified

If you specify the planning values for two percentiles, then Minitab calculates the planning values for both μ and σ.

• The planning value for μ is calculated as follows:
• For location-scale models (normal, logistic and extreme value)
• For log-location-scale models (Weibull, lognormal, loglogistic)
• The planning value for σ is calculated as follows:
• For location-scale models (normal, logistic, extreme value)
• For log-location-scale models (Weibull, lognormal, loglogistic)

To obtain the planning value for the percentile or the reliability, use the calculations for when two parameters are specified. For more information, see the section "Two distributional parameters specified".

### Notation

TermDescription
μmean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
μplanplanning value for mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic)
σscale parameter
σplanplanning value for scale parameter
βshape parameter for Weibull
ttime
tppercentile at time t
Φ-1 inverse CDF for the corresponding distribution
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