Methods and formulas for distribution characteristics in Parametric Distribution Analysis (Right Censoring)

In This Topic

Mean and standard deviation
Median
Quartiles and interquartile range
MTTF

Mean and standard deviation

Smallest extreme value

Mean: μ – cσ
Standard deviation

Weibull

Mean
Standard deviation

3-parameter Weibull

Mean

Standard deviation

Exponential

Mean: θ

Standard deviation: θ

2-parameter exponential

Mean: θ + λ

Standard deviation: θ

Normal

Mean: μ

Standard deviation: σ

Lognormal

Mean

Standard deviation

3-parameter lognormal

Mean

Standard deviation

Logistic

Mean: μ

Standard deviation

Loglogistic

Mean

Standard deviation

3-parameter loglogistic

Mean

Standard deviation

Notation

Term	Description
c	Euler's constant approximately equal to 0.5772
Γ	gamma function
μ	location parameter
β	shape parameter
σ	scale parameter
α	scale parameter (Weibull and 3-parameter Weibull)
θ	scale parameter (exponential and 2-parameter exponential)
λ	threshold parameter

Median

The 50th percentile. For more information, see the "Percentiles" topic.

Quartiles and interquartile range

First quartile (Q1) = the 25^th percentile

Third quartile (Q3) = the 75^th percentile

Interquartile range (IQR) = Q3 - Q1

For more information, see the "Percentiles" topic.

MTTF

In reliability analysis, the average lifetime of a product is the mean time to failure (MTTF).

Lognormal distribution

MTTF
Confidence interval

Notation

Term	Description
	location parameter

Term	Description
	scale parameter

Term	Description
z_α/2	value that corresponds to the upper α/2 percentile of the standard normal distribution

Term	Description
α	1 – (confidence level) where α is greater than or equal to 0 and less than or equal to 1

Term	Description
SE_{g_i}

Weibull Data

MTTF
Confidence interval

Notation

Term	Description
α	scale parameter

Term	Description
Γ	gamma function evaluated at r

Term	Description
β	shape parameter

Term	Description
g₁	log(MTTF)

Term	Description
SE_{g_i}