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%.


. . . . . . . . . . . . . . . . . . . . . . . .


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).








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)


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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




Lot size: 500

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Use hypergeometric distribution to calculate probability of acceptance





Generated Plan(s)

Sample Size 171

Acceptance Number 3

Accept lot if defective items in 171 sampled 3; Otherwise reject.



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



Measurement type: Number of defects

Lot quality in defects per hundred

Use Poisson distribution to calculate probability of acceptance





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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, ).

2

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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Acceptance Sampling by Variables - Create/Compare


Upper Specification Limit (USL) 0,8

Historical Standard Deviation 0,02

Lot Size 1000

Acceptable Quality Level (AQL) 0,5




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.



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.


. . . . . . . . . . . . . . . . . . . . .

Generated Plan(s)

Sample Size 83


. . . . . . . . . . . . . . . . . . . . .

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


Upper Specification Limit (USL) 0,8

Z.USL 1


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, .



Lower Specification Limit (LSL) 5

Upper Specification Limit (USL) 30






Generated Plan(s)

Sample Size 50


Z.LSL = (mean - lower spec)/historical standard deviation


Accept lot if Z.LSL k and Z.USL k; otherwise reject.



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.



Lower Specification Limit (LSL) 90

Upper Specification Limit (USL) 100



Sample Size 7


Z.LSL = (mean - lower spec)/historical standard deviation


Accept lot if Z.LSL k and Z.USL k; otherwise reject.



2,27516 0,931 0,069

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