1 | 15

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. ,

2 | 15

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),

3 | 15

(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

4 | 15

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

5 | 15

- 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.

6 | 15

(-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)

7 | 15

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

8 | 15

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

9 | 15

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

10 | 15

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

11 | 15

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%.

12 | 15

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

13 | 15

(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% ;

14 | 15

: , 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.

15 | 15

=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