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Life Distribution Mathematical Functions - Page 2 of 2

             

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Table 3. Lognormal Distribution

Probability Density Function

f(t) = e^{-0.5[(ln(t)-µ)/s]2} / (stÖ2p)

Cumulative Density Function

F(t) = (1/[(2p)]) ò0t (1/x) e^{-0.5[(ln(x)-µ)/s]2}dx

Instantaneous Failure Rate

l(t) = f(t)/(1-F(t))

Median

t = t50% = eµ

Mean

t = e^(µ+s2/2)

Mode

t = e^(µ-s2)

Location Parameter

eµ

Shape Parameter s

s - s,estimate of s, may be calculated as ln(t50%/t16%)

                    

Table 4. Weibull Distribution

Probability Density Function

f(t) = ([b(t-g)b-1]/[ab]) (e^{-[(t-g)/a]b})

Cumulative Density Function

F(t) = 1 - e^{-[(t-g)/a]b}

Instantaneous Failure Rate

l(t) = [b(t-g)b-1]/[ab]

Location Parameter

a = t at 63.2% failure

Shape Parameter

b

Time Delay Parameter

g, not used unless data do not fit the distribution without time delay

       

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Reference:  D.S. Peck & O.D. Trapp, Accelerated Testing Handbook, Technology Associates   

   

 

      

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