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การสุ่มงานWorkStudy
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Doughnut Pho-ngam
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19
(Work Sampling)
Work Sampling
1
Dr. Pensuda Phanritdum
“
Dr. Pensuda Phanritdum
Work Sampling
1 M/C
3
2
RATING
Dr. Pensuda Phanritdum
3
Dr. Pensuda Phanritdum
1
40
(
)
36
20
∴
14
40
∴
36
4
(Working Time) = (36/40) x 100 = 90%
6
(Idle Time) = (4/40) x 100 = 10%
(Working Time) = (14/20) x 100 = 70%
(Idle Time) = (6/20) x 100 = 30%
8
480
(Working Time) = 480 x 0.9 = 432
∴
340 140
(Idle Time) = 480 x 0.1 = 48
= 70.83%
= 29.17%
Dr. Pensuda Phanritdum
5
Dr. Pensuda Phanritdum
7
Dr. Pensuda Phanritdum
(
Dr. Pensuda Phanritdum
:
)
(
/
Binomial Distribution
/
( Discrete Observation)
Discrete Observation ----
)
mean = p
2
n=
∴
p=
p(1 − p ) N
variance =
yes / no σ
p
=
⎛ → ⎜p= ⎝
c⎞ ⎟ n⎠
p(1 − p) N
x=
Standard deviation
n
p(x)
x
σ
p( x) = ⎛⎜⎜ n ⎞⎟⎟ p x (1 − p) n − x ⎝ x⎠
p
=
(pˆ)
p (1 − p ) N
x = 0,1,..., n
;
(
)
σ p
mean = np variance = npq = np(1 − p ) 9
Dr. Pensuda Phanritdum
Dr. Pensuda Phanritdum
2σ
95.45%
Dr. Pensuda Phanritdum
2σ p = 2
p (1 − p ) N
p
95%
±5%
95%
σ p
95%
*
±2
95%
95%
5%
± 2σp
95% Confidence Interval
±5% *
11
Dr. Pensuda Phanritdum
19.2
900
500
400
95%
S(
: Relative accuracy )
e
Absolute accuracy -------
e s = p
sp = e
0.555±0.0332
95%
2σ p = e = sp
p (1 − p ) = sp N
2
95%
8
N =
8× (0.555 ± 0.0332) = 4.44 ± 0.2656 4.1744
4(1 − p )
s2 p
4.7056
±5% → s = 0.05 13
Dr. Pensuda Phanritdum
95%
N
N= N=
±5%
Dr. Pensuda Phanritdum
19.3
(0.05) 2 p
p=
1600 (1 − p )
p
100
25 100
= 0 . 25 = 25 %
s = ± 5 % = 0 . 05
68%
±5%
sp = 2
1σ p = e = sp N =
p (1 − p ) = sp N N=
95%
25
4(1 − p )
N
% Idle time
N
±5%
4 (1 − p )
s2 p
N
(1 − p )
=
4 (1 − 0 . 25 )
N
2
s p
Dr. Pensuda Phanritdum
15
= 4,800 Observations
( 0 . 05 ) 2 ( 0 . 25 )
p (1 − p ) N
Dr. Pensuda Phanritdum
N
350
150
500
N
Alignment chart
∴
( p) =
150 500
sp = 2
N=
p
p
s
Precision interval
(0.05) 2 (0.30)
Precision interval
4(1 − 0.30)
chart)
Trial study
p(1 − p ) N
= 3733.3
N
( Alignment
= 0.30 = 30%
( N)
= 3734 observation
500
Dr. Pensuda Phanritdum
N
17
Dr. Pensuda Phanritdum
19.3
N
±5%
% Idle time
95%
25 p=
25 100
(
)
= 0 . 25 = 25 %
s = ± 5 % = 0 . 05
Precision Interval (
Absolute Accuracy
e = sp = 5 % × 0 . 25 = 1 . 25 %
Dr. Pensuda Phanritdum
19
Dr. Pensuda Phanritdum
(N)
p
Degree of accuracy
Dr. Pensuda Phanritdum
21
(N)
Dr. Pensuda Phanritdum
19.5
150
500
N
± 0.07
95%
∴
( p) = 150 = 0.30 = 30% 500
N
Dr. Pensuda Phanritdum
23
19.2
Dr. Pensuda Phanritdum
N = 1900
19.6
4,000
95%
sp = 2
p(1 − p) N
s= 2 p
p (1 − p ) = 2 (1 − p ) N Np
Dr. Pensuda Phanritdum
2,600
1,400
(S)
25
Dr. Pensuda Phanritdum
∴
= 1,400/4,000 = 0.35 = 35%
Control Chart
3 Sigma (3σ)
p(1 − p ) sp = 2 N 0.35s = 2
Control Chart
0.35(1 − 0.35) 4,000
95%
± 4.3%
35%
→ 35±(4.3x0.35)% Dr. Pensuda Phanritdum
p-chart
Control Limit = p ± 3
s = 0.043 = 4.3% (< ±5%)
4,000
p (1 − p ) n
n = number of daily observation
[33.5%
36.5%] 27
Dr. Pensuda Phanritdum
Assignable variable
19.7
100
/
12
%
/
1
100
9
9
2
100
10
10
3
100
12
12
4
100
8
8
5
100
6
6
6
100
9
9
7
100
23
23
8
100
9
9
9
100
8
8
10
100
9
9
11
100
9
9
12
100
8
8
1,200
120 29
Dr. Pensuda Phanritdum
Work Sampling random, unbias
Dr. Pensuda Phanritdum
(P.478)
17.00 .
3
independent
1
10
1
12.00 – 13.00
.
3 3
Dr. Pensuda Phanritdum
31
8.00
Dr. Pensuda Phanritdum
244
12
26
574
15.44 .
776
17.45 .
12.26
. -------(
)
10
33
Dr. Pensuda Phanritdum
2
)
3 1
(
Dr. Pensuda Phanritdum
1
2
2
Dr. Pensuda Phanritdum
35
244
9.44
574
13.74 .
.
776
15.76 .
Dr. Pensuda Phanritdum
3
(
)
2 8
.
8.00 – 17.00 .
13.00 .
480
10
(
2
2
≥ 48
)
10
.
37
Dr. Pensuda Phanritdum
44
= 44×10 = 440
= 7
20
= 15.20
.
16
17
Dr. Pensuda Phanritdum
8
18
9
10
= 18×10 = 180
11
12
= 3
13
14
15
= 11.00
.
Dr. Pensuda Phanritdum
39
random number
Dr. Pensuda Phanritdum
8.00 .
7
Column 1
25
/
1
25
8
./
0.20 → 8.00 + 0.20 = 08.20
.
0.55 → 8.00 + 0.55 = 08.55
.
2.30 → 8.00 + 2.30 = 10.30
.
3.05 → 8.00 + 3.05 = 11.05
.
3.25 → 8.00 + 3.25 = 11.25
.
4.00 → 8.00 + 4.00 = 12.00
.(
)
4.01 → 8.00 + 4.01 = 12.01
.(
)
4.55 → 8.00 + 4.55 = 12.55
.(
)
5.00 → 8.00 + 5.00 = 13.00
.
5.55 → 8.00 + 5.55 = 13.55
.
41
Dr. Pensuda Phanritdum
Dr. Pensuda Phanritdum
1.
-
-
-
-
-
4.
(Elements)
(
)
±5%
N=
)
(N)
4(1 − p )
s2 p
N=
2.
3.
p
(
p
95%
1600 (1 − p )
p
1–2 Dr. Pensuda Phanritdum
43
Dr. Pensuda Phanritdum
5.
-
-
-
-
-
(
(Design the study )
)
45
Dr. Pensuda Phanritdum
(
)
6. (Control
Chart)
Dr. Pensuda Phanritdum
7.
sp = 2
p(1 − p) N
s=
2
p
p(1 − p ) N
8.
Dr. Pensuda Phanritdum
47
Dr. Pensuda Phanritdum
(
)
10
•
19.9 (P.403) ----
---
1
•
5
1
8
1
1
•
20
= 6400/(20*10) = 32
49
Pensuda Phanritdum Random Dr.
8
.
480
5
96
2
95
34 ---
34*5 = 170
Work
= 2
50
= 10.50 .
9
10
11
12
(Rating)
%
Sampling
8
Independent
:
[
5
•
•
20
1 1
95
•
Dr. Pensuda Phanritdum
•
2
5
•
10
5
96
N = 6,400
.
480
13
14
Dr. Pensuda Phanritdum
15
16
17
51
Dr. Pensuda Phanritdum
(
)
3
Std . time =
total time spent × proportion production × performanc e index + allowances output during total time
Total time
Proportion production
Performance index Output during total time
Allowances
Rating (
)
Direct time study
Dr. Pensuda Phanritdum
53
Dr. Pensuda Phanritdum
Dr. Pensuda Phanritdum
55
Dr. Pensuda Phanritdum
Total time = 8
* (8
/
) * (60
/
)*3
= 11520
Proportion production = 431 / 480 = 0.898 Performance index = 47,350 / 431 = 109.9 Output during total time = 314 Allowances = 15%
57
Dr. Pensuda Phanritdum
Dr. Pensuda Phanritdum
1.
2.
Work
1
3.
4.
Direct time study
2. 3.
(Man hours) 4.
Work sampling
Dr. Pensuda Phanritdum
59
7.
Performance rating
6.
5.
8.
1.
sampling
1
Direct time study
Dr. Pensuda Phanritdum
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