기초통계의개념과이해 - promoim.co.kr

1 1 e-mail: 2 Review Reliability & Confidence Level 3 Review: (Reliablity) 1. (reliability) 2. (Faliure rate or hazard rate): t 1 , 1 . 10 ( ) . )(1)()(tFtXPtR = =)(1)()()()(tFtftXPtft = = (t) (t, t+ t ) .3. MTTF(Mean time to Failure): ( ) 4 Review1. (reliability) 2. (Confidence level)- (parameter= , , ) . ( ) 100 sampling 100 , 100 95 ( ) 95% . 51.

2 Descriptive Statistics - Point Estimation( )2. Probability Distribution( )3. Interval Estimation( )4. 61. Descriptive Statisticsparameters2, nXXX,..,,21populationsample2,sXestimates inference Parameter : , 2 Estimates point estimates : ,interval estimates : X2s 7 Point Estimation ( ) ==+++== ===niiXXns1222)(11 (1) Mean( )(2) Median( )(3) Mode ( ) Measure for Variation Measure for Location(1) Variance ( )(2) Standard Deviation( )s( ) 2, 3, 3, 4, 38 =10, =3, =3 8 by Minitab5153555759616395% Confidence Interval for Confidence Interval for MedianVariable: BPA-Squared:P-Value:MeanStDevVarianceSke wnessKurtosisNMinimum1st QuartileMedian3rd Normality Test95% Confidence Interval for Mu95% Confidence Interval for Sigma95% Confidence Interval for MedianDescriptive Statistics 9e222)(21)( =xxf2.

3 Probability Distribution ( ) (Normal Distribution) 3 2 + +2 +3 10 The normal distribution with parameter values = 0 and =1 is called a standard normal distribution. A random variable that has a standard normal distribution is called a standard normal random variableand will be denoted by Z. The pdf of Z isthe cdf of Z is , which we will denote by . << = zezfz,21)1,0;(2/2 = zdyyfzZP)1,0;()()(z (Standard Normal Distribution)2. Probability Distribution(cont d) 112. Probability Distribution(cont d) (Exponential Distribution) - ( =1 ) (lognormal Distribution) - , 2 (Weibull Distribution) :(shape parameter) : (scale parameter).

4 123. Interval Estimation( )An Interval Estimates statesthe range within which a population parameter probably lies. ( )nzX 2/ , .nstXn)1(2/ (Confidence Level) : 90%, 95%, 99% 13 (parameter= , ) . ( ) 100 sampling 100 , 100 95 ( ) 95% . Confidence Interval 14 , . 90%, 95%, 99% . 95% 99% 4% ..( 2) 7.

5 , , , , , , 95% . ( )X= , z /2 = = XznXzn + ( / 7 ) ( / 7 ) + 83 386 111183 386 + , ( , ) . ( , ) 95% . dX d{}. + = 09595% nzX 2/ 3 2 + +2 +3 16( ) 174. step2 :( ) : ( ) 18( ) : 243km , ( ) 2 . 2 confidence level( ) 90% ?Step1 : MTTF= [( +1)/ ]= (3/2) Step2 : MTTF =243 . = TF/ (3/2) = 243 = Step3.

6 2( ,2)= /12)22;(1~}/2{+= =rCniiT2)2; (~12 = =niiT 2( ,2)= 0 n=2, =2 . (t1=t2)2)2; (~2221)(2 =+ ~22 =t ) () (212~212=== t (Confidence level) 90% 243km MTTF 2 . 20 : H-AKCW1 16,585 25,868 11,786 13,217 25,172 19,966 21,067 12,601 41,55516,969H-BKCW1 21,549 3,534 11,262 18,937 69,713H-CKCW1 2,993 6,642 55,985H-DKCW1 6,401 37,424 43,029 23,986 28,805 50,264 27,762 25,383 19,836 ( , H-C ) : ( ) : ( ) , MTTF= 24782 : MTTF , Lognormal 2. MTTF - 20000 3. (confidence level) 90%, 95%, 99%4. 3 1.

7 , . 21 (( )) 22 MTTF 20000 3 90% . i) 3 19399 90% 20000 .ii) , 1 19399 18000 2 29323 ( ) 90% 20000 . iii) 2 1 29323 28000 , 1 42803 20000 . (( )) , 3 19398 , 90% MTTF 20000 . 90% random 10000 10% MTTF 20000 . 23(1) 100$ 95%.

8 Error Bound 100 = 100 . n=[( *s)/100]2 . s=1000$ n=385 ( ) (2) A 24% ( 2%, 95% ) , n random 100 95 22%~26% . (Ref : Scheaffer, Mendenhall and Ott, Elementary Survey Sampling, 1990)n= Npq/((N-1)D+pq) n=sample size, N=population size p, q=1-p D=(bound error)2/( )2 : Confidence Level & bound Error ( )nzX 2/ nz 2/