Chapter 7
Statistical Quality Control
Quality Control Approaches

Statistical process control (SPC)
Monitors the production process to prevent
poor quality
Statistical Process Control

Take periodic samples from a process

Plot the sample points on a control chart

Determine if the process is within limits

Correct the process before defects occur
Types Of Data

Attribute data

Product characteristic evaluated with a
discrete choice
–

Good/bad, yes/no
Variable data

Product characteristic that can be
measured
–
Length, size, weight, height, time, velocity
SPC Applied To Services

Nature of defect is different in services

Service defect is a failure to meet customer
requirements

Monitor times, customer satisfaction
Service Quality Examples

Hospitals
timeliness, responsiveness, accuracy

Grocery Stores
Check-out time, stocking, cleanliness

Airlines
luggage handling, waiting times, courtesy

Fast food restaurants
waiting times, food quality, cleanliness
Process Control Chart
Upper
control
limit
Process
average
Lower
control
limit
1
2
3
4
5
6
Sample number
7
8
9
10
Constructing a Control Chart





Decide what to measure or count
Collect the sample data
Plot the samples on a control chart
Calculate and plot the control limits on the control
chart
Determine if the data is in-control
 If non-random variation is present, discard the
data (fix the problem) and recalculate the control
limits
A Process Is In Control If

No sample points are outside control limits

Most points are near the process average

About an equal # points are above & below
the centerline

Points appear randomly distributed
The Normal Distribution
95 %
99.74 %
-3s
-2s
-1s
m = 0 1s 2s 3s
Area under the curve = 1.0
Control Charts and the Normal
Distribution
UCL
+3s
Mean
-3s
LCL
Types Of Data

Attribute data (p-charts, c-charts)
Product characteristics evaluated with a
discrete choice (Good/bad, yes/no, count)

Variable data (X-bar and R charts)
Product characteristics that can be measured
(Length, size, weight, height, time, velocity)
Control Charts For Attributes

p Charts
Calculate percent defectives in a sample;
an item is either good or bad

c Charts
Count number of defects in an item
p - Charts
Based on the binomial distribution
p = number defective / sample size, n
p = total no. of defectives
total no. of sample observations
UCL = p + 3 p(1-p)/n
LCL = p - 3 p(1-p)/n
p-Chart Example
The Western Jean Company produced denim jean.
The company wants to establish a p-chart to
monitor the production process and main high
quality. Western beliefs that approximately 99.74
percent of the variability in the production process
(corresponding to 3-sigma limits, or z = 3.00) is
random and thus should be within control limits,
whereas 0.26 percent of the process variability is
not random and suggest that the process is out of
control.
p-Chart Example
The company has taken 20 sample (one per day
for 20 days), each containing 100 pairs of jeans (n
= 100), and inspected them for defects, the results
of which are as follow.
Sample
1
2
3
4
5
6
7
8
9
10
# Defects
6
0
4
10
6
4
12
10
8
10
Sample
11
12
13
14
15
16
17
18
19
20
# Defects
12
10
14
8
6
16
12
14
20
18
p-Chart Calculations
Proportion
Sample Defect Defective
1
6
.06
2
0
.00
3
4
.04
..
20
..
18
200
UCL = p + 3 p(1-p) /n
..
= 0.190
.18
100 jeans in each sample
total defectives
p =
total sample observations
=
= 0.10 + 3 0.10 (1-0.10) /100
200 = 0.10
20 (100)
LCL = p - 3 p(1-p) /n
= 0.10 + 3 0.10 (1-0.10) /100
= 0.010
0.2
0.18
0.14
0.12
0.1
0.08
0.06
0.04
0.02
Sample number
20
18
16
14
12
..
10
8
6
4
2
0
0
Proportion defective
0.16
c - Charts

Count the number of defects in an item

Based on the Poisson distribution
c = number of defects in an item
c=
total number of defects
number of samples
UCL = c + 3 c
LCL = c - 3 c
c-Chart Example
The Ritz Hotel has 240 rooms. The hotel’s
housekeeping department is responsible for
maintaining the quality of the room’s appearance
and cleanliness. Each individual housekeeper is
responsible for an area encompassing 20 rooms.
Every room in use is thoroughly clean and its
supplies, toiletries, and so on are restocked each
day. Any defects that the housekeeping staff
notice that are not part the normal housekeeping
service are supposed to be reported hotel
maintenance.
c-Chart Example
Every room is briefly inspected each day by a
housekeeping supervisor. However, hotel
management also conducts inspection for qualitycontrol purposes. The management inspector not
only check for normal housekeeping defects like
clean sheets, dust, room supplies, room literature,
or towels, but also for defects like an inoperative
or missing TV remote, poor TV picture quality or
reception, defective lamps, a malfunctioning clock,
tears or stains in bedcovers or curtain, or a
malfunctioning curtain pull.
c-Chart Example
An inspection sample include 12 rooms, i.e., one
room selected at random from each of the twelve
20-room blocks served by a housekeeper.
Following are the results from 15 inspection
samples conducted at random during a 1-month
period.
Sample
1
2
3
4
5
6
7
8
9
10
# Defects
12
8
16
14
10
11
9
14
13
15
Sample # Defects
11
12
12
10
13
14
14
17
15
15
c - Chart Calculations
Count # of defects per roll in 15 rolls of denim fabric
Sample Defects
1
12
2
8
3
16
.
.
.
15
.
15
190
c = 190/15 = 12.67
UCL = c + 3 c
= 12.67 + 3 12.67
= 23.35
LCL = c - 3 c
= 12.67 - 3 12.67
= 1.99
Example c - Chart
24
18
15
12
9
6
3
Sample number
14
12
10
8
6
4
2
0
0
.
Number of defects
21
Control Charts For Variables

Mean chart (X-Bar Chart)
Measures central tendency of a sample

Range chart (R-Chart)
Measures amount of dispersion in a sample

Each chart measures the process differently. Both
the process average and process variability must
be in control for the process to be in control.
Example: Control harts for
Variable Data
The Goliath Tool Company produces slip-ring
bearings, which look like flat doughnut or washer,
they fit around shafts or rods, such as drive shaft
in machinery or motor. In the production process
for a particular slip-ring bearing the employees
has taken 10 samples (during a 10 day period) of
5 slip-ring bearing (i.e., n = 5). The individual
observation from each sample are shown as
followed:
Example: Control Charts for Variable Data
Sample
1
2
3
4
5
6
7
8
9
10
Slip Ring Diameter (cm)
1
2
3
4
5
5.02 5.01 4.94 4.99 4.96
5.01 5.03 5.07 4.95 4.96
4.99 5.00 4.93 4.92 4.99
5.03 4.91 5.01 4.98 4.89
4.95 4.92 5.03 5.05 5.01
4.97 5.06 5.06 4.96 5.03
5.05 5.01 5.10 4.96 4.99
5.09 5.10 5.00 4.99 5.08
5.14 5.10 4.99 5.08 5.09
5.01 4.98 5.08 5.07 4.99
X
4.98
5.00
4.97
4.96
4.99
5.01
5.02
5.05
5.08
5.03
50.09
R
0.08
0.12
0.08
0.14
0.13
0.10
0.14
0.11
0.15
0.10
1.15
Constructing an Range Chart
UCLR = D4 R = (2.11) (.115) = 0.24
LCLR = D3 R = (0) (.115) = 0
where R = S R / k = 1.15 / 10 = .115
k = number of samples = 10
R = range = (largest - smallest)
Example R-Chart
0.25
UCL
Range
0.2
0.15
R
0.1
0.05
LCL
0
1
2
3
4
5
6
Sample number
7
8
9
10
Constructing A Mean Chart
UCLX = X + A2 R = 5.01 + (0.58) (.115) = 5.08
LCLX = X - A2 R = 5.01 - (0.58) (.115) = 4.94
where X = average of sample means = S X / n
= 50.09 / 10 = 5.01
R = average range = S R / k
= 1.15 / 10 = .115
Example X-bar Chart
5.10
UCL
5.06
5.04
5.02
X
5.00
4.98
4.96
LCL
4.94
Sample number
10
9
8
7
6
5
4
3
2
4.92
1
Sample average
5.08
Variation

Common Causes
Variation inherent in a process
Can be eliminated only through improvements
in the system

Special Causes
Variation due to identifiable factors
Can be modified through operator or
management action
Control Chart Patterns
UCL
UCL
LCL
LCL
Sample observations
consistently below the
center line
Sample observations
consistently above the
center line
Control Chart Patterns
UCL
UCL
LCL
LCL
Sample observations
consistently increasing
Sample observations
consistently decreasing
Sample Size Determination

Attribute control charts
50 to 100 parts in a sample

Variable control charts
2 to 10 parts in a sample