Download - Minitab Sampling
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ME TO 17
T 17 (Acceptance Sampling) .
. Stat > Quality Tools > Acceptance Sampling by Attributes,
. Stat > Quality Tools > Acceptance Sampling by Variables.
.
(Help)
, Help > Methods and Formulas > Quality and process
improve-ment > Acceptance Sampling.
.
Stat > Quality Tools > Acceptance Sampling by Attributes / , .
, Create a sampling plan, (n, c) , Compare user defined sampling plans, .
.1. Create a sampling plan -
Measurement type Go/no go (defectives) (units) , Number of defects .
Units for quality levels :
Go/no go (defectives), Percent defective (0-100), Proportion defective (0-1), Defectives per million (0-1.000.000).
Number of defects, Defects per unit, Defects per hundred, Defects per million.
Acceptable quality level (AQL) AQL. H AQL Units for quality levels.
Rejectable quality level (RQL or LTPD) RQL LTPD. AQL < LTPD. LTPD Units for quality levels.
Producer's risk (Alpha) o (0-1).
Consumer's risk (Beta) o (0-1). 1 > .
Lot Size . (AOQ), (), Options.
.2. Compare user defined sampling plans -
Measurement type, Units for quality levels, Acceptable quality level (AQL), Rejectable quality level (RQL or LTPD) Lot Size, .1. ,
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Acceptable quality level (AQL) Rejectable quality level (RQL or LTPD) . Sample sizes Acceptance numbers.
Sample sizes , Acceptance numbers .
(n) (c1, c2, , cr),
(c) (n1, n2, , nr),
(n1, n2, , nr) (c1, c2, , cr), (n1, c1), (n2, c2), , (nr, cr).
. Go/no go (defectives). (Lot Size) Use hypergeometric distribution for isolated lot Options. , Number of defects, Poisson.
B.
Stat > Quality Tools > Acceptance Sampling by Variables > Create/Compare / , . , Create a sampling plan, (n, k) , Compare user defined sampling plans .
Stat > Quality Tools > Acceptance Sampling by Variables > Accept/Reject Lot .
B.1. Create a sampling plan -
Units for quality levels, Acceptable quality level (AQL), Rejectable quality level (RQL or LTPD), Producer's risk (Alpha), Consumer's risk (Beta) Lot Size, . Lower spec, Upper spec Historical standard deviation (Optional).
Lower spec Upper spec , ( ). ,
Historical standard deviation (Optional) , .
.2. Compare user defined sampling plans -
Units for quality levels, Acceptable quality level (AQL), Rejectable quality level (RQL or LTPD), Sample sizes, Lower spec, Upper spec, Historical standard deviation (Optional), Lot Size . Acceptable quality level (AQL) Rejectable quality level (RQL or LTPD) .
Critical distances (k values) . Sample sizes :
(n) (k1, k2, , kr),
(k) (n1, n2, , nr),
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(n1, n2, , nr) (k1, k2, , kr) (n1, k1), (n2, k2), , (nr, kr).
.3. Accept/Reject Lot
Stat > Quality Tools > Acceptance Sampling by Variables > Accept/Reject . Measurement data . Critical distance (k values), Lower spec, Upper spec Historical standard deviation (Optional) .
1
N = 500. 90% 1% , 95% 4% .
() (n,c) .
() , Q-po -po. (AOQL);
() 2% 4% :
(i) n () c=2, c=3, c=4.
(ii) c () n=177, n=227, n=277.
;
() (n,c)
(i) ,
(ii) Poisson.
(i) (ii).
: () , p1=AQL=1%, p2=LTPD=4%, =0.10 =0.05. Stat > Quality ols > Acceptance Sampling by Attributes
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o MINITAB session window
Acceptance Sampling by Attributes
Measurement type: Go/no go
Lot quality in percent defective
Use binomial distribution to calculate probability of acceptance
Acceptable Quality Level (AQL) 1
Producers Risk () 0,1
Rejectable Quality Level (RQL or LTPD) 4
Consumers Risk () 0,05
Generated Plan(s)
Sample Size 227
Acceptance Number 4
Accept lot if defective items in 227 sampled 4; Otherwise reject.
Percent Probability Probability
Defective Accepting Rejecting
1 0,921 0,079
4 0,049 0,951
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- n=227 c=4. 0.079 0.049 ( ). session window .
( ).
() () 500 Lot size ( )
session window () :
(i) (Q ATI),
(ii) AOQL=0.612% 1.599%.
Acceptance Sampling by Attributes
. . . . . . . . . . . . . . . . . . . . . . . .
Percent Probability Probability
Defective Accepting Rejecting AOQ ATI
1 0,921 0,079 0,503 248,6
4 0,049 0,951 0,107 486,6
Average outgoing quality limit (AOQL) = 0,612 at 1,599 percent defective.
Q-po -po.
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(-i) Stat > Quality Tools > Acceptance Sampling by Attributes ( Options).
o MINITAB session window
Acceptance Sampling by Attributes
Measurement type: Go/no go
Lot quality in percent defective
Use binomial distribution to calculate probability of acceptance
Acceptable Quality Level (AQL) 1
Rejectable Quality Level (RQL or LTPD) 4
Compare User Defined Plan(s)
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Sample Acceptance Percent Probability Probability
Size(n) Number(c) Defective Accepting Rejecting
227 2 1 0,604 0,396
227 2 2 0,166 0,834
227 2 4 0,005 0,995
227 3 1 0,806 0,194
227 3 2 0,333 0,667
227 3 4 0,018 0,982
227 4 1 0,921 0,079
227 4 2 0,523 0,477
227 4 4 0,049 0,951
Accept lot if defective items in n sampled c; Otherwise reject.
( ).
session window. , n=227 c=3, p0=0.02 0.333. c, .
(-ii) Stat > Quality Tools > Acceptance Sampling by Attributes ( Options)
o MINITAB session window
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Acceptance Sampling by Attributes
Measurement type: Go/no go
Lot quality in percent defective
Use binomial distribution to calculate probability of acceptance
Acceptable Quality Level (AQL) 1
Rejectable Quality Level (RQL or LTPD) 4
Compare User Defined Plan(s)
Sample Acceptance Percent Probability Probability
Size(n) Number(c) Defective Accepting Rejecting
177 4 1 0,967 0,033
177 4 2 0,719 0,281
177 4 4 0,160 0,840
227 4 1 0,921 0,079
227 4 2 0,523 0,477
227 4 4 0,049 0,951
277 4 1 0,853 0,147
277 4 2 0,349 0,651
277 4 4 0,013 0,987
Accept lot if defective items in n sampled c; Otherwise reject.
session window. , n=277 c=4, p0=0.02 0.349. n, .
(-i) (), Options Use hypergeometric distribution for isolated lot. o MINITAB session window
Acceptance Sampling by Attributes
Measurement type: Go/no go
Lot quality in percent defective
Lot size: 500
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Use hypergeometric distribution to calculate probability of acceptance
Acceptable Quality Level (AQL) 1
Producers Risk () 0,1
Rejectable Quality Level (RQL or LTPD) 4
Consumers Risk () 0,05
Generated Plan(s)
Sample Size 171
Acceptance Number 3
Accept lot if defective items in 171 sampled 3; Otherwise reject.
Percent Probability Probability
Defective Accepting Rejecting AOQ ATI
1 0,951 0,049 0,626 187,1
4 0,048 0,952 0,127 484,1
Average outgoing quality limit (AOQL) = 0,763 at 1,600 percent defective.
n=171 c=3. session window .
(-ii) Stat > Quality Tools > Acceptance Sampling by Attributes
o MINITAB session window
Acceptance Sampling by Attributes
Measurement type: Number of defects
Lot quality in defects per hundred
Use Poisson distribution to calculate probability of acceptance
Acceptable Quality Level (AQL) 1
Producers Risk () 0,1
Rejectable Quality Level (RQL or LTPD) 4
Consumers Risk () 0,05
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Generated Plan(s)
Sample Size 229
Acceptance Number 4
Accept lot if number of defects in 229 items 4; Otherwise reject.
Defects
Per Probability Probability
Hundred Accepting Rejecting
1 0,917 0,083
4 0,050 0,950
n=229 c=4. session window Poisson. 1.29 ( . 92, ).
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chlorpyrifos 0.80 mg/Kg. 98% 0.5% 0.80 mg/Kg, 92% 3% 0.80 mg/Kg. .
() (n,k) . , Q-po -po =1000. (AOQL); 0.02 mg/Kg.
() (n,k) . .
() n=25 chlorpyrifos ( mg/Kg)
(), ;
: () , p1=AQL=0.5%, p2=LTPD=3%, =0.02, =0.08, =0.02 USL=0.8. Stat > Quality Tools > Acceptance Sampling by Variables > Create/Compare .
0.80 0.81 0.86 0.89 0.79
0.60 0.76 0.74 0.81 0.81
0.78 0.71 0.84 0.82 0.78
0.75 0.71 0.74 0.73 0.83
0.74 0.75 0.88 0.83 0.74
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o MINITAB session window
Acceptance Sampling by Variables - Create/Compare
Lot quality in percent defective
Upper Specification Limit (USL) 0,8
Historical Standard Deviation 0,02
Lot Size 1000
Acceptable Quality Level (AQL) 0,5
Producers Risk () 0,02
Rejectable Quality Level (RQL or LTPD) 3
Consumers Risk () 0,08
Generated Plan(s)
Sample Size 25
Critical Distance (k Value) 2,16344
Z.USL = (upper spec - mean)/historical standard deviation
Accept lot if Z.USL k; otherwise reject.
Percent Probability Probability
Defective Accepting Rejecting AOQ ATI
0,5 0,980 0,020 0,478 44,1
3,0 0,079 0,921 0,230 923,2
Average outgoing quality limit (AOQL) = 0,796 at 1,194 percent defective
n=25 k=2.16344. 0.02 0.079 ( ). 2.16 ( . 101, ). ZUSLk, . AOQL=0.796% 1.194%.
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Q-po -po.
() () 0.02 Historical standard deviation . MINITAB n=83 k=2.16314.
Acceptance Sampling by Variables - Create/Compare
. . . . . . . . . . . . . . . . . . . . .
Generated Plan(s)
Sample Size 83
Critical Distance (k Value) 2,16314
. . . . . . . . . . . . . . . . . . . . .
k , .
() C1 MINITAB. Stat > Quality Tools > Acceptance Sampling Variables > Accept/ Reject Lot
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(Decision : Reject Lot) session window .
Acceptance Sampling by Variables - Accept/Reject Lot
Make Accept or Reject Decision Using C1
Sample Size 25
Mean 0,78
Historical Standard Deviation 0,02
Upper Specification Limit (USL) 0,8
Z.USL 1
Critical Distance (k Value) 2,16344
Decision: Reject lot.
3
, 5 30 mm. 0.6 mm.
95%, 4% , , 95%, 10% ;
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: , p1=AQL=4%, p2=LTPD=10%, =0.05, =0.05, =0.6, LSL=5 USL=30. Stat > Quality ls > Acceptance Sampling by Variables > Create/Compare .
To MINITAB session window n=50 k=1.51612. 2.23 (. 108, ). LSLk ZUSLk, .
Acceptance Sampling by Variables - Create/Compare
Lot quality in percent defective
Lower Specification Limit (LSL) 5
Upper Specification Limit (USL) 30
Historical Standard Deviation 0,6
Acceptable Quality Level (AQL) 4
Producers Risk () 0,05
Rejectable Quality Level (RQL or LTPD) 10
Consumers Risk () 0,05
Generated Plan(s)
Sample Size 50
Critical Distance (k Value) 1,51612
Z.LSL = (mean - lower spec)/historical standard deviation
Z.USL = (upper spec - mean)/historical standard deviation
Accept lot if Z.LSL k and Z.USL k; otherwise reject.
Percent Probability Probability
Defective Accepting Rejecting
4 0,951 0,049
10 0,049 0,951
4
, 90 100 . =1.5 .
: n=7, k=1.44.
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=93 , ;
: (93, 1.5).
= ( < ) + ( > ) = (
) = (
) +(
).
LSL=90, USL=100, =93 =1.5
= (2) + (4.666667) = 0.0227501 + 0.0000015 = 0.0227516.
Stat > Quality ls > Acceptance Sampling by Variables > Create/Compare
To MINITAB session window 0.931.
Acceptance Sampling by Variables - Create/Compare
Lot quality in percent defective
Lower Specification Limit (LSL) 90
Upper Specification Limit (USL) 100
Historical Standard Deviation 1,5
Compare User Defined Plan(s)
Sample Size 7
Critical Distance (k Value) 1,44
Z.LSL = (mean - lower spec)/historical standard deviation
Z.USL = (upper spec - mean)/historical standard deviation
Accept lot if Z.LSL k and Z.USL k; otherwise reject.
Percent Probability Probability
Defective Accepting Rejecting
2,27516 0,931 0,069