공정능력지수 PCI ( Process Capability Index ), 계수표, SQL예시

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관리 메뉴

DBILITY

공정능력지수 PCI ( Process Capability Index ), 계수표, SQL예시 본문

statistics/SPC

공정능력지수 PCI ( Process Capability Index ), 계수표, SQL예시

DBILITY 2017. 2. 26. 11:36

공정능력,검사관련 프로젝트에 들어갈때 아는게 일천하여 조사하고 정리한 것이다.

작은 도움이라도 되시길~

공정능력 ( Process Capability )
공정이 최상,즉 관리상태에 있을때 각 제품의 변동이 어느 정도인가를 표시하는 양
자연공차(Natural Tolerance)라는 용어를 사용하고 대개 6σ를 사용
잠재적 공정능력지수 ( Cp,Potential Capability Index )
동일한 일을 반복할 수 있는 공정의 잠재능력으로 공정이 관리되고 있을때 생산되는 제품의 품질변동을 나타내는 양
공정너비에 대한 공차의 너비의 비로 크면 클수록 좋다.

x̄ 평균 ( Mean )
S 표준편차 ( Standard Deviation ) - Sigma
R 범위 ( Range = Max - Min )
M 중앙값 ( Median )
UCL 관리상한선 ( Upper Control Line = +3σ)
LCL 관리하한선 ( Lower Control Line -3σ)
CL 중심선 ( Center Line = x̄)
USL 규격상한 ( Upper Specification Limit )
LSL 규격하한 ( Lower Specification Limit )
Tolerance 공차 USL-LSL

USL, LSL, 표준편차(σLT)를 구한다.
치우침(K)을 구한다.
　= ABS[(USL+LSL)/2-x̄ ]/[(USL-LSL)/2]
Pp 산출
　Pp = (USL-LSL)/(6*σLT)
Ppk산출
　Ppk = (1-K)*Pp , min(Ppl,Ppu)
　Ppu = (USL-x̄ )/(3*σLT)
　Ppl = (x̄ -LSL)/(3*σLT)

반응형

USL, LSL, 표준편차(σST)를 구한다.
치우침(K)을 구한다.
　= ABS[(USL+LSL)/2-x̄ ]/[(USL-LSL)/2]
Cp 산출
　Cp = (USL-LSL)/(6*σST)
Cpk산출
　Cpk = (1-K)*Cp, min(Cpl,Cpu)
　Cpu = (USL-x̄ )/(3*σST)
　Cpl = (x̄ -LSL)/(3*σST)

σST = 단기표준편차, σLT = 장기표준편차

합동표준편차 = SQRT(SUM((군내관측치-군내관측치평균)²)/(부분군개수*(부분군크기-1)))

부분군내 표준편차계산 = 합동표준편차 / c4((부분군개수*(부분군크기-1))+1)

A3 = 3 / (c4 √ n)
B4 = 1 + 3 / {c4 √ 2(n-1)}
B3 = 1 - 3 / {c4 √ 2(n-1)}
c4 = 4(n-1) / (4n-3)

관리도 계수표

N	c4	c5	d2	d3	d4
1	*	*	1	0.82	1
2	0.797885	0.603	1.128	0.8525	0.954
3	0.886227	0.463	1.693	0.8884	1.588
4	0.921318	0.389	2.059	0.8794	1.978
5	0.939986	0.341	2.326	0.8641	2.257
6	0.951533	0.308	2.534	0.848	2.472
7	0.959369	0.282	2.704	0.8332	2.645
8	0.96503	0.262	2.847	0.8198	2.791
9	0.969311	0.246	2.97	0.8078	2.915
10	0.972659	0.232	3.078	0.7971	3.024
11	0.97535	0.22	3.173	0.7873	3.121
12	0.977559	0.21	3.258	0.7785	3.207
13	0.979406	0.202	3.336	0.7704	3.285
14	0.980971	0.194	3.407	0.763	3.356
15	0.982316	0.187	3.472	0.7562	3.422
16	0.983484	0.181	3.532	0.7499	3.482
17	0.984506	0.175	3.588	0.7441	3.538
18	0.98541	0.17	3.64	0.7386	3.591
19	0.986214	0.166	3.689	0.7335	3.64
20	0.986934	0.161	3.735	0.7287	3.686
21	0.987583	0.157	3.778	0.7242	3.73
22	0.98817	0.153	3.819	0.7199	3.771
23	0.988705	0.15	3.858	0.7159	3.811
24	0.989193	0.147	3.895	0.7121	3.847
25	0.98964	0.144	3.931	0.7084	3.883
26	0.990052		3.965
27	0.990433		3.997
28	0.990786		4.028
29	0.991113		4.058
30	0.991418		4.086
31	0.991703		4.113
32	0.991969		4.139
33	0.992219		4.164
34	0.992454		4.189
35	0.992675		4.213
36	0.992884		4.236
37	0.99308		4.258
38	0.993267		4.28
39	0.993443		4.301
40	0.993611		4.322
41	0.99377		4.342
42	0.993922		4.361
43	0.994066		4.38
44	0.994203		4.398
45	0.994335		4.415
46	0.99446		4.432
47	0.99458		4.449
48	0.994695		4.466
49	0.994806		4.482
50	0.994911		4.498
51	0.995013
52	0.99511
53	0.995204
54	0.995294
55	0.995381
56	0.995465
57	0.995546
58	0.995624
59	0.995699
60	0.995772
61	0.995842
62	0.99591
63	0.995976
64	0.99604
65	0.996102
66	0.996161
67	0.996219
68	0.996276
69	0.99633
70	0.996383
71	0.996435
72	0.996485
73	0.996534
74	0.996581
75	0.996627
76	0.996672
77	0.996716
78	0.996759
79	0.9968
80	0.996841
81	0.99688
82	0.996918
83	0.996956
84	0.996993
85	0.997028
86	0.997063
87	0.997097
88	0.997131
89	0.997163
90	0.997195
91	0.997226
92	0.997257
93	0.997286
94	0.997315
95	0.997344
96	0.997372
97	0.997399
98	0.997426
99	0.997452
100	0.997478

WITH T1 (ACTVALUE) AS (
    SELECT 0.529  FROM DUAL UNION ALL
    SELECT 0.55  FROM DUAL UNION ALL
    SELECT 0.555  FROM DUAL UNION ALL
    SELECT 0.541  FROM DUAL UNION ALL
    SELECT 0.559  FROM DUAL UNION ALL
    SELECT 0.543  FROM DUAL UNION ALL
    SELECT 0.557  FROM DUAL UNION ALL
    SELECT 0.559  FROM DUAL UNION ALL
    SELECT 0.581  FROM DUAL UNION ALL
    SELECT 0.551  FROM DUAL UNION ALL
    SELECT 0.493  FROM DUAL UNION ALL
    SELECT 0.534  FROM DUAL UNION ALL
    SELECT 0.527  FROM DUAL UNION ALL
    SELECT 0.511  FROM DUAL UNION ALL
    SELECT 0.565  FROM DUAL UNION ALL
    SELECT 0.559  FROM DUAL UNION ALL
    SELECT 0.519  FROM DUAL UNION ALL
    SELECT 0.562  FROM DUAL UNION ALL
    SELECT 0.551  FROM DUAL UNION ALL
    SELECT 0.53  FROM DUAL UNION ALL
    SELECT 0.545  FROM DUAL UNION ALL
    SELECT 0.588  FROM DUAL UNION ALL
    SELECT 0.544  FROM DUAL UNION ALL
    SELECT 0.561  FROM DUAL UNION ALL
    SELECT 0.573  FROM DUAL UNION ALL
    SELECT 0.607  FROM DUAL UNION ALL
    SELECT 0.532  FROM DUAL UNION ALL
    SELECT 0.562  FROM DUAL UNION ALL
    SELECT 0.542  FROM DUAL UNION ALL
    SELECT 0.549  FROM DUAL UNION ALL
    SELECT 0.577  FROM DUAL UNION ALL
    SELECT 0.526  FROM DUAL UNION ALL
    SELECT 0.546  FROM DUAL UNION ALL
    SELECT 0.557  FROM DUAL UNION ALL
    SELECT 0.548  FROM DUAL UNION ALL
    SELECT 0.546  FROM DUAL UNION ALL
    SELECT 0.56  FROM DUAL UNION ALL
    SELECT 0.53  FROM DUAL UNION ALL
    SELECT 0.564  FROM DUAL UNION ALL
    SELECT 0.514  FROM DUAL UNION ALL
    SELECT 0.527  FROM DUAL UNION ALL
    SELECT 0.545  FROM DUAL UNION ALL
    SELECT 0.513  FROM DUAL UNION ALL
    SELECT 0.557  FROM DUAL UNION ALL
    SELECT 0.525  FROM DUAL UNION ALL
    SELECT 0.557  FROM DUAL UNION ALL
    SELECT 0.559  FROM DUAL UNION ALL
    SELECT 0.529  FROM DUAL UNION ALL
    SELECT 0.539  FROM DUAL UNION ALL
    SELECT 0.591  FROM DUAL UNION ALL
    SELECT 0.538  FROM DUAL UNION ALL
    SELECT 0.557  FROM DUAL UNION ALL
    SELECT 0.517  FROM DUAL UNION ALL
    SELECT 0.521  FROM DUAL UNION ALL
    SELECT 0.568  FROM DUAL UNION ALL
    SELECT 0.544  FROM DUAL UNION ALL
    SELECT 0.55  FROM DUAL UNION ALL
    SELECT 0.562  FROM DUAL UNION ALL
    SELECT 0.54  FROM DUAL UNION ALL
    SELECT 0.537  FROM DUAL UNION ALL
    SELECT 0.558  FROM DUAL UNION ALL
    SELECT 0.548  FROM DUAL UNION ALL
    SELECT 0.532  FROM DUAL UNION ALL
    SELECT 0.57  FROM DUAL UNION ALL
    SELECT 0.567  FROM DUAL UNION ALL
    SELECT 0.56  FROM DUAL UNION ALL
    SELECT 0.533  FROM DUAL UNION ALL
    SELECT 0.538  FROM DUAL UNION ALL
    SELECT 0.567  FROM DUAL UNION ALL
    SELECT 0.557  FROM DUAL UNION ALL
    SELECT 0.541  FROM DUAL UNION ALL
    SELECT 0.534  FROM DUAL UNION ALL
    SELECT 0.544  FROM DUAL UNION ALL
    SELECT 0.537  FROM DUAL UNION ALL
    SELECT 0.574  FROM DUAL UNION ALL
    SELECT 0.572  FROM DUAL UNION ALL
    SELECT 0.556  FROM DUAL UNION ALL
    SELECT 0.56  FROM DUAL UNION ALL
    SELECT 0.52  FROM DUAL UNION ALL
    SELECT 0.578  FROM DUAL UNION ALL
    SELECT 0.543  FROM DUAL UNION ALL
    SELECT 0.544  FROM DUAL UNION ALL
    SELECT 0.541  FROM DUAL UNION ALL
    SELECT 0.526  FROM DUAL UNION ALL
    SELECT 0.518  FROM DUAL UNION ALL
    SELECT 0.521  FROM DUAL UNION ALL
    SELECT 0.532  FROM DUAL UNION ALL
    SELECT 0.524  FROM DUAL UNION ALL
    SELECT 0.544  FROM DUAL UNION ALL
    SELECT 0.523  FROM DUAL UNION ALL
    SELECT 0.55  FROM DUAL UNION ALL
    SELECT 0.544  FROM DUAL UNION ALL
    SELECT 0.545  FROM DUAL UNION ALL
    SELECT 0.571  FROM DUAL UNION ALL
    SELECT 0.527  FROM DUAL UNION ALL
    SELECT 0.536  FROM DUAL UNION ALL
    SELECT 0.554  FROM DUAL UNION ALL
    SELECT 0.569  FROM DUAL UNION ALL
    SELECT 0.531  FROM DUAL UNION ALL
    SELECT 0.534  FROM DUAL
), T2 (SPECVAL, SPEC_USL, SPEC_LSL) AS (
    SELECT 0.55, 0.6, 0.5 FROM DUAL
), T3 (STDDEV_WITHIN) AS (
    SELECT
        ROUND(SQRT(SUM(B)/(COUNT(*)-(COUNT(*)/5)))/0.996880,7)
    FROM
    (
        SELECT
         POWER(ACTVALUE-AVG(ACTVALUE) OVER(PARTITION BY CEIL(ROWNUM/5)),2) B
        FROM T1
    )
 ) 
SELECT
      TRUNC(AVG(ACTVALUE),5) AVG
    , TRUNC(VAR_POP(ACTVALUE),5) POP
    , T3.STDDEV_WITHIN
    , ROUND(STDDEV_SAMP(ACTVALUE),7) STDDEV_OVERALL
    , SPECVAL
    , SPEC_USL
    , SPEC_LSL
    , ABS( (SPEC_USL+SPEC_LSL)/2-AVG(ACTVALUE) ) / ( (SPEC_USL-SPEC_LSL)/2 ) K
    , TRUNC((SPEC_USL-SPEC_LSL)/(6*ROUND(STDDEV_SAMP(ACTVALUE),4)),2) PP        
    , TRUNC((AVG(ACTVALUE)-SPEC_LSL)/(3*ROUND(STDDEV_SAMP(ACTVALUE),4)),2) PPL
    , TRUNC((SPEC_USL-AVG(ACTVALUE))/(3*ROUND(STDDEV_SAMP(ACTVALUE),4)),2) PPU
    , TRUNC((1-ABS( (SPEC_USL+SPEC_LSL)/2-AVG(ACTVALUE) ) / ( (SPEC_USL-SPEC_LSL)/2 ))*ROUND((SPEC_USL-SPEC_LSL)/(6*ROUND(STDDEV_SAMP(ACTVALUE),4)),4),2) PPK
    , TRUNC(LEAST((SPEC_USL-AVG(ACTVALUE))/(3*ROUND(STDDEV_SAMP(ACTVALUE),4)),(AVG(ACTVALUE)-SPEC_LSL)/(3*ROUND(STDDEV_SAMP(ACTVALUE),4))),2) PPK2    
    , TRUNC((SPEC_USL-SPEC_LSL)/(6*ROUND(T3.STDDEV_WITHIN,4)),2) CP    
    , TRUNC((AVG(ACTVALUE)-SPEC_LSL)/(3*ROUND(T3.STDDEV_WITHIN,4)),2) CPL
    , TRUNC((SPEC_USL-AVG(ACTVALUE))/(3*ROUND(T3.STDDEV_WITHIN,4)),2) CPU
    , TRUNC((1-ABS( (SPEC_USL+SPEC_LSL)/2-AVG(ACTVALUE) ) / ( (SPEC_USL-SPEC_LSL)/2 ))*ROUND((SPEC_USL-SPEC_LSL)/(6*ROUND(T3.STDDEV_WITHIN,4)),4),2) CPK
    , TRUNC(LEAST((SPEC_USL-AVG(ACTVALUE))/(3*ROUND(T3.STDDEV_WITHIN,4)),(AVG(ACTVALUE)-SPEC_LSL)/(3*ROUND(T3.STDDEV_WITHIN,4))),2) CPK2 
    , SUM(CASE WHEN ACTVALUE BETWEEN SPEC_LSL AND SPEC_USL THEN 1 ELSE 0 END)/COUNT(1)*100 PASS_RATE
    , COUNT(*) OBS
FROM T1,T2,T3 GROUP BY 0,T3.STDDEV_WITHIN;

PCI_공정능력지수_ORACLE.sql

0.01MB

관리도계수표.txt

0.00MB

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DBILITY

공정능력지수 PCI ( Process Capability Index ), 계수표, SQL예시 본문

공정능력지수 PCI ( Process Capability Index ), 계수표, SQL예시

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