Transcript Managing Quality

CHAPTER SIX
Managing
Quality
Statistical Process
control
McGraw-Hill/Irwin
Basics of Statistical Process
Control
• Statistical Process Control
(SPC) developed by
Walter A. Shewhart at Bell
Lab in 1920.
UCL
– monitoring production process
to detect and prevent poor
quality
• Sample
– subset of items produced to use
for inspection
• Control Charts
– process is within statistical
control limits
LCL
SPC in TQM
• SPC
–tool for identifying problems and make
improvements
–contributes to the TQM goal of
continuous improvements
• Real world Example: Honda
Control Chart
• Control Chart
–Purpose: to monitor process output to see if it is
random deciding whether the process is in control
or not
–A time ordered plot represents sample statistics
obtained from an ongoing process (e.g. sample
means)
–Upper and lower control limits define the range of
acceptable variation
Variability
• Random
–common causes
–inherent in a process
–can be eliminated only
through improvements
in the system
• Non-Random
–special causes
–due to identifiable
factors
–can be modified
through operator or
management action
Process Control
Chart
Out of control
Upper
control
limit
Process
average
Lower
control
limit
1
2
3
4
5
6
Sample number
7
8
9
10
Quality Measures
• Variable
–a product characteristic that is continuous and can be
measured
–weight - length
• Attribute
–a product characteristic that can be evaluated with a
discrete response
–good – bad; yes - no
Control Charts
• Types of charts
–Variables
• mean (x bar – chart)
• range (R-chart)
*Note: mean and range charts
are used together
–Attributes
• p-chart
• c-chart
Control Charts for Variables
• Mean control charts
–Used to monitor the central tendency of a process.
–X bar charts
• Range control charts
–Used to monitor the process variability
–R charts
Using x- bar and R-Charts Together
 Process average and process variability
must be in control
 It is possible for samples to have very
narrow ranges, but their averages are
beyond control limits
 It is possible for sample averages to be in
control, but ranges might be very large
Mean and Range Charts
(process mean is
shifting upward)
Sampling
Distribution
UCL
Detects shift
x-Chart
LCL
UCL
R-chart
LCL
Does not
detect shift
Mean and Range Charts
Sampling
Distribution
(process variability is increasing)
UCL
x-Chart
LCL
Does not
reveal increase
UCL
R-chart
Reveals increase
LCL
10-12
x-bar Chart
x1 + x2 + ... xk
x= = k
UCL = x= + A2R
LCL = x= - A2R
Where
=
x = average of sample means
R- Chart
UCL = D4R
LCL = D3R
R
R= k
where
R = range of each sample
k = number of samples
Example
• measuring the weight/packet in grams
•
Packet
• Sample
1
2
3
Ri x-bari
•
1
42
40
44
•
2
35
40
45
•
3
44
44
44
•
4
40
40
43
•
5
41
41
38
Total
___
___
Average
___ ___
Example (cont.)
• # of samples = k =
• Sample size = n =
Example (cont.)
• X-bar chart
Example (cont.)
• R chart
Example (cont.)
R Chart
|
|
|
|
|
|
|
x-bar Chart
|
|
|
Appendix:
Determining Control Limits for x-bar and R-Charts
SAMPLE SIZE
n
FACTOR FOR x-CHART
A2
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1.88
1.02
0.73
0.58
0.48
0.42
0.37
0.44
0.11
0.99
0.77
0.55
0.44
0.22
0.11
0.00
0.99
0.99
0.88
Fa
cto
rs
FACTORS FOR R-CHART
D3
D4
0.00
0.00
0.00
0.00
0.00
0.08
0.14
0.18
0.22
0.26
0.28
0.31
0.33
0.35
0.36
0.38
0.39
0.40
0.41
3.27
2.57
2.28
2.11
2.00
1.92
1.86
1.82
1.78
1.74
1.72
1.69
1.67
1.65
1.64
1.62
1.61
1.61
1.59
Control Charts for Attributes
 p-charts
 uses portion defective in a sample
 c-charts
 uses number of defects in an item
p-Chart
UCL = p + zp
LCL = p - zp
z = number of standard deviations from
process average
p = sample proportion defective; an estimate
of process average
p = standard deviation of sample proportion
p =
p(1 - p)
n
p-Chart Example
(assume the sample size of
100)
SAMPLE
1
2
3
4
5
total
average
NUMBER OF
DEFECTIVES
13
7
20
0
10
PROPORTION
DEFECTIVE
P-Chart Example (cont.)
Step 1: get
sigma
p 

p 1 p
n

Step 2: get UCL
UCL p  p  3 p
and LCL
LCL p  p  3 p
C-Chart
UCL = c + zc
LCL = c - zc
c =
c
where
c = number of defects per sample
C-Chart (cont.)
Measuring number of fouls called on a team per game
SAMPLE
1
2
3
4
5
Total
Avg.
NUMBER
OF
FOULS
37
9
22
25
32
C-Chart (cont.)
UCL = c + zc
LCL = c - zc
Control Chart Patterns
UCL
UCL
LCL
Sample observations
consistently below the
center line
LCL
Sample observations
consistently above the
center line
Control Chart Patterns (cont.)
UCL
UCL
LCL
Sample observations
consistently increasing
LCL
Sample observations
consistently decreasing
Homework for Ch 6-II
• Computer upgrade problem
Computer upgrades take 80 minutes. Six samples of five
observations each have been taken, and the results are as listed.
Determine if the process is in control. You have to use appropriate
chart(s)
•
•
•
•
•
•
1
79.2
78.8
80.0
78.4
81.0
2
80.5
78.7
81.0
80.4
80.1
3
79.6
79.6
80.4
80.3
80.8
4
78.9
79.4
79.7
79.4
80.6
5
80.5
79.6
80.4
80.8
78.8
6
79.7
80.6
80.5
80.0
81.1
6–30
Homework for Ch 6-II
• Wrong account problem
•
The operations manager of the booking services department of
hometown bank is concerned about the number of wrong customer
account numbers recorded by hometown personnel. Each week a
random sample of 2,500 deposits is taken, and the number of incorrect
account numbers is recorded. The results for the past 12 weeks are
shown in the following table. Is the process out of control? Use
appropriate control chart and use three sigma control limit, ie. Z=3.
• Sample number 1
• wrong account 15
2
12
3 4
19 2
5
19
6
4
7 8 9 10 11
24 7 10 17 15
12
3
6–31