建築工程品質管理案例研討

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蜃称钮
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4 ACI

6 1.1 ISO % 8 10%

7 4 4 EXCEL 1.2 4M statistical quality control SQC SQC

8 % ( ) ( purposive sampling random sampling (sample size) (random number) 2-3

9 [1] ASTM D3665 [ ] [2] 1 ASTM D

10 [3] 5 (1) CASIO fx-991 CASIO fx-3600p INV (RAN#) (2) CASIO fx-4500p CASIO fx-5500l SHIFT (RAN#) EXE

11 ASTM D3665

12 ASTM D3665

13 2.3 sample unit 320m m (simple random sampling) 2.2 [4] 320m [2] (1) (2) (3) (4) No. (1) (2)

14 stratified random sampling sublot [5] 320m / ( [2] ) (1) (2) (3) (4) (5) No. (1) (2) (3)+(4) (systematic random sampling) [6] 320m

15 80/ No ( ) 2-10

16 3.1 ( ) 5 28 fc 210 kgf/cm CNS 3090[ ] 2 test result 5 312No No ~

17 5 (kgf/cm 2 ) (1) (2) (3) (4) (5) (6) No P P P P P P P P P P P P C C C P P P S S S S S C C W G G G G [7] 2-12

18 [7] Sturges k13.32 log(n) 1 k n n k = 2 n30 k log(30) / 139/ /2 1731/

19 / / ~ / 100 2/ /

20 (histogram) kgf/cm

21 250 kgf/cm kgf/cm 2 16 % XY S kgf/cm kgf/cm kgf/cm

22 Microsoft EXCEL EXCEL 4 XY EXCEL 3 1 EXCEL A B B1B8 X A1A8 2-17

23 4 X,kgf/cm 2 Y EXCEL

24 Kgf\cm (mean) (arithmetic mean) x x,..., n 1, 2 x n 2-19

25 x = 1 ( x n 1 + x x ) = n n x i n i= 1 3 x = 1 x i = i1n n ( ) ( x x bar) (mu) 4 N 3 N 1 1 µ = ( x1 + x2 + + xn ) = x i N 4 N i= 1 100% () N/mm N/mm 2 [8] ,253,264,298,285 kgf/cm 2 x ( )/ kgf/cm 2 CNS 8905[ ] x S L +1.6σ 5, x 2-20

26 S L A S L 40 kgf/cm 2 B S L 60 kgf/cm 2 C S L 80 kgf/cm 2 x m x i xm / / / AB C A B C 7 7 ABC No. A B C

27 8 A B C (standard deviation) n x 1, x 2,..., x n n 2 ( xi x) i= 1 s = n 1 6 s

28 x i i1n x n ( ) (s) ( sigma) N 2 ( xi µ) i= 1 σ = 7 N x i i1n N 100% () s () kgf/cm 2 30 kgf/cm 2 [ ]CNS 2579[ ] standard deviation CNS [9] ,253,264,298,285 kgf/cm 2 x = 271 s = = ( ) + ( ) + ( ) + ( ) + ( ) = = 19.7kgf/cm

29 9 x i x i x 2 ( x i x ) /(5-1) = 19.7 kgf/cm coefficient of variation s s V = = 100% 8 x x V s x [10] 5 5 s19.7x 271 V 19.7 = = = 7.3% ACI 214R

30 5 1 overall variation 5 2 within-test variation precision CNS [12] 10ACI 214R-02 overall variation psi (kgf/cm 2 ) Excellent Very Good Good Fair Poor < >700 (<28.1) ( ) ( ) ( ) (>49.2) < >350 (<14.1) ( ) ( ) ( ) (>24.6) within-test variation % Excellent Very Good Good Fair Poor < >6.0 < > kgf/cm

31 4.5 (range) R = x max x min R x max x min 9 [11] 5 x i 2 255,253, 264, 298, 285 kgf/cm xmax = 298 x = min 253 R kgf/cm 2 n10 R n10 R k Ri i= R = 1 k 10 R s = d 2 11 R i i k k10 s d 2 d 2 (n) 11 n 2-26

32 11 d 2 (n) d [12] x 1 x 2 R R 147 R 147/ d 2 11 n s / x V 13/ % 5.3% 1 10 V 1 5.3% % 2-27

33 [13] ,253,264,298,285 kgf/cm 2 CASIO fx INV MODE SD 255 M+(x) M+(x) M+(x) M+(x) M+(x) 285 INV 6(n) 5 5 INV 7( x ) 271 INV 9(σ n 1 ) INV 8(σ n ) EXCEL 1 EXCEL A1A5 2 A6 AVERAGE(A1:A5)271 3 A7 STDEV(A1:A5) EXCEL 2-28

34 A AVERAGE(A1:A5) STDEV(A1:A5) normal distribution curve 8 (12) 1 x µ 1 ( ) 2 σ ( x) = e 2 f - x 2πσ 12 x e ( ) 2-29

35 X XN (, 2 ) 13 X kgf/cm kgf/cm 2 XN (250.3, ) (1) () (2) x () 9 σ σ µ 9 XN(300,20 2 ) (3) - + (4) () () a. ()

36 XN(300,20 2 ) XN(320,20 2 ) 10 XN(300,20 2 )XN(320,20 2 ) b. () 11 XN(300,20 2 ) XN(300,30 2 ) 11 XN(300,20 2 )XN(300,30 2 ) (5) x x a b Px Xx 12 a b P[260X320] 12 XN(300,20 2 ) X P[260X320] 2-31

37 2 (6) X ~ N( µ, σ ) Z ~ N(0,1) P[260X320] P[-2Z1] PWL X n ( x ) (s) x P[ x X x ] b a 1 ( x ) () 2 (s) () x a b 2-32

38 3 x b x a 4 a b x x () x µ z = a a σ 14 x µ z = b b σ z a z b P[ Z za ] z z a P Z z ] z [ b z b 6 P [ xa b b a X x ] = P[ Z z ] P[ Z z ] 16 P[ Z za ] (15) P [ Z z a ] = F ( z a ) = z a 1 2 π e 1 2 t 2 dt 17 F(z a ) - z a (z 0 )z<0 -z a F( za) za 1 F z ) (16) ( a a ( a F z ) = 1 F( z )

39 F ( z ) = z π e 1 2 t 2 z dt F(z) 0 z Z 2-34

40 [14] kgf/cm kgf/cm 2 x (1)Px300 (2)Px (3)P210x ()250.3 kgf/cm 2 ()34.2 kgf/cm 2 2 Px z( )/ Px300 PZ ( ) Pz % P[x 300] 14 P[x 300]( kgf/cm 2 ) 3 Px z( )/ Px210 Pz 1.18 Pz 1.18 Pz

41 1 Pz1.18 1Pz ( ) Pz Pz % P[x 210] 15 P[x 210]( kgf/cm 2 ) 4 P210x P210x300 Px300 Px % P[210 x 300] 16 P[210 x 300]( kgf/cm 2 ) EXCEL NORMDISTx,,, 1 x F(x)[14] NORMDIST300,250.3,34.2,1 2-36

42 NORMDIST210,250.3,34.2,1 NORMDIST300,250.3,34.2,1 NORMDIST210,250.3,34.2,1 0 x f(x) x150 NORMDIST150,250.3,34.2,0 EXCEL x100400x Y XY XY 15 14x X x Y f(x) EXCEL 4 EXCEL ( ) P[ x ] P[-1z1] ( ) P[ 2 x 2] 2-37

43 P[-2z2] ( ) P[ 3 x 3] P[-3z3] natural tolerance limit 99% %68 [15] X 2.0mm 3 tolerance limit (2.0) 6.0mm X 5000 mm 5, mm 5.3 n x x 18 (19)(20) 2-38

44 µ = µ x 19 σ σ = 20 x n µ x σ x 2 X ~ N( µ, σ ) 21 σ 2 X ~ N( µ,( ) ) n 22 n σ x ( x ) 4 x x X ~ N(300,( ) ) X ~ N(300,30 ) X ~ N(300,30 ) 4 X ~ N(300,( ) ) 4 3 [16] 6.0mm 4 σ 2.0 ± 3 σ = ± 3 = ± 3 = ± 3. mm x n mm 19[15][16]

45 20 3 ±6.0 ± [15] [16]4 [17]CNS 3090[ ] fc -35 kgf/cm 2 3 fc fc 210 kgf/cm 2 () 30 kgf/cm 2 CNS 3090 (fcr ) 1 1% 2 (14) 0.99 z ( 20) Pz z2.33 z2.326 CNS 12891[ ] z ( 20) fcr fc

46 fcr (2.33)(30) kgf/cm fcr 245 S L S L 175, fcr 245 kgf/cm 2 4 (20) 3 σ σ = x σ fcr fc +2.33σ x fc fc fcr 210+(1.34)(30) kgf/cm 2 6 (23)(25) fcr 250 kgf/cm 2 S L σ x fcr S L 210, fcr 250 kgf/cm 2 (23)(25) CNS 12891[ ] CNS 3090[ ] 2-41

47 (23)(25) 3 1 (23) fc -35(25) fc σ 2 (23) (25) x CNS (23)(25) 1% Dr. Shewhart Chart 1 process control chart 6.2 CL UCL LCL 2 acceptance control chart 6.3 ACI 1 control chart for variable control chart for attribute 2-42

48 (1) random causes (2) assignable causes CL 3 CL 3 ( 99%) CL 2 1% 3 22 (1) (2) (3) 2-43

49 UCL CL LCL UCL CL LCL UCL CL LCL

50 6.2 - x R Chart x R Chart n210 [18] [18] x R No.,% x 1 x 2 x R ( )/ 2 x = x 1 + x 2 x R max min = x 3 ( x ) (R 2-45

51 k 1 x = xi = /10 = k i= 1 k 1 R = R i = 2.56/10 = k i= 1 k 4 56 CL = x = UCL = x + A R = ( 1.880)( 0.256) = LCL = x A2 R = 5.56 ( 1.880)( 0.256) = CL = R = UCL = D ( )( ) 4 R = = LCL = D R ( 0)( 0.256) 0. 3 = = (28)(33) A 2 D 3 D n A 2 D 3 D

52 UCL=6.04 CL=5.56 CL=5.08 UCL=0.84 CL= x R 6.3 ACI ACI 214 ACI 3 [19] ACI ACI 214 CNS x Chart 2-47

53 ACI 214 fc fcr CNS 3090 fc -35 kgf/cm 2 2 x m Chart ACI CNS ACI 214 fcr CNS fc 3 3 R m Chart 10 ACI % 10 Max. R m = σ 1 d 2 = ( V1 fcr') d 2 = V1 d 2 fcr' (34) m Max. R 1 fcr V 1 d 2 (n) 11 2 n2d Max. R m = V1 ( 1.128) fcr' (35) V % [19] 5 ACI (1) fc 210 kgf/cm 2 (2) fcr 250 kgf/cm 2 [17] ACI

54 a. fc 210 kgf/cm 2 fcr 250 kgf/cm 2 S L fc 35 kgf/cm 2 175kgf/cm 2 b. fcr 250 kgf/cm 2 S L fc 210 kgf/cm 2 c. Max. R m = V1 ( 1.128) fcr' 10 fcr 250 Max. R m = V1 ( 1.128) fcr' = V1 ( 1.128)( 250) = 282 V1 V 1 V 1 Max. R m (1)(2) 4 (3) 24 ( )/ (5) (4) 24 ( )/ (6) 24 ( )/ EXCEL

55 a. 1 fc -35kgf/cm b. 4 fc c

56 18ACI (1) (2) (3) (4) (5) (6) 3 10 No. x 1 x 2 x x m R R m

57 fc =210 fcr =250 fc -35=175 fc =210 fcr =250 V 1 >6% V 1 56% V 1 45% V 1 34% V 1 <3% 24ACI 2-52

58 mm 2 2 gono go gauge mm, 29.9mm D=30.1 D=

59 X EXCEL

60 n 2 d 2-55

61 d 3 p = 36 n 4 k n 1,n 2, n k d 1,d 2, d k p d + d d 1 2 k i= 1 = = k n1 + n nk ( 1 p) k i= 1 d n i i 37 p σ p = 38 n p chart pn chart c chart [20][21] 1 2 [20]

62 n d p p=d/n 2 CL 33 CL = p = = CL = p = = UCL ( 1 p) ( ) p UCL = p + 3 = n = = LCL 2-57

63 ( 1 p) ( ) p LCL = p 3 = n = = = [21] CL n = 400 CL = pn = = UCL 2-58

64 p = = UCL = pn + 3 = = 6.6 pn ( 1 p) = ( ) 44 LCL UCL = pn 3 pn p = = 2.2 = 0 ( 1 ) = ( )

65 [1],2005," ", [2]," ", [3],2006," ", [4],"EXCEL ", [5],2005," ", [6],1988," ", [7]CNS 3090," " [8]CNS 9042," " [9]CNS 12891," " [10]D.C.Montgomery,G.C.Runger and N.F. Hubele,2004,"Engineering Statistics " [11]ACI ,2002,"Recommended Practice for Evaluation of Strength Test Results of Concrete" [12]ACI ,"Building Code Requirement for Reinforced Concrete" [13]ASTM D3665,"Standard Practice for Random Sampling of Construction Materials" 2-60

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