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
1 2 3 4 5 6 7 8 9 10
Sample number
Uppercontrollimit
Processaverage
Lowercontrollimit
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
99.74 %
The Normal Distribution
95 %
= 0 1 2 3-1-2-3
Area under the curve = 1.0
Control Charts and the Normal Distribution
Mean
UCL
LCL
+ 3
- 3
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 ChartsCalculate percent defectives in a sample;
an item is either good or bad
c ChartsCount 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 # Defects Sample # Defects1 6 11 122 0 12 103 4 13 144 10 14 85 6 15 66 4 16 167 12 17 128 10 18 149 8 19 20
10 10 20 18
p-Chart Calculations Proportion
Sample Defect Defective 1 6 .06 2 0 .00 3 4 .04
. . .
. . .20 18 .18 200
= 0.10
=
total defectives total sample observations 200 20 (100)
p =
100 jeans in each sample
LCL = p - 3 p(1-p) /n
= 0.10 + 3 0.10 (1-0.10) /100
= 0.010
UCL = p + 3 p(1-p) /n
= 0.10 + 3 0.10 (1-0.10) /100
= 0.190
. .
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 2 4 6 8
10 12 14 16 18 20
Prop
ortio
n de
fect
ive
Sample number
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 ExampleThe 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 ExampleEvery room is briefly inspected each day by a
housekeeping supervisor. However, hotel management also conducts inspection for quality-control 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 ExampleAn 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 # Defects Sample # Defects1 12 11 122 8 12 103 16 13 144 14 14 175 10 15 156 117 98 149 13
10 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
.
0
3
6
9
12
15
18
21
24
0 2 4 6 8
10
12
14
Sample number
Nu
mb
er
of
de
fect
s
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 Slip Ring Diameter (cm)
Sample 1 2 3 4 5 X R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.08
2 5.01 5.03 5.07 4.95 4.96 5.00 0.12
3 4.99 5.00 4.93 4.92 4.99 4.97 0.08
4 5.03 4.91 5.01 4.98 4.89 4.96 0.14
5 4.95 4.92 5.03 5.05 5.01 4.99 0.13
6 4.97 5.06 5.06 4.96 5.03 5.01 0.10
7 5.05 5.01 5.10 4.96 4.99 5.02 0.14
8 5.09 5.10 5.00 4.99 5.08 5.05 0.11
9 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15
Constructing an Range Chart
UCLR = D4 R = (2.11) (.115) = 0.24
LCLR = D3 R = (0) (.115) = 0
where R = R / k = 1.15 / 10 = .115
k = number of samples = 10
R = range = (largest - smallest)
0
0.05
0.1
0.15
0.2
0.25
1 2 3 4 5 6 7 8 9 10
Sample number
Ra
ng
e
Example R-Chart
UCL
R
LCL
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 = X / n
= 50.09 / 10 = 5.01
R = average range = R / k = 1.15 / 10 = .115
4.92
4.94
4.96
4.98
5.00
5.02
5.04
5.06
5.08
5.101 2 3 4 5 6 7 8 9
10
Sample number
Sa
mp
le a
vera
ge
Example X-bar Chart
UCL
X
LCL
Variation Common Causes
Variation inherent in a process
Can be eliminated only through improvements in the system
Special CausesVariation due to identifiable factors
Can be modified through operator or management action
UCL
LCL LCL
UCL
Sample observationsconsistently below thecenter line
Sample observationsconsistently above thecenter line
Control Chart Patterns
Control Chart Patterns
LCL LCL
UCL UCL
Sample observationsconsistently increasing
Sample observationsconsistently decreasing
Sample Size Determination
Attribute control charts50 to 100 parts in a sample
Variable control charts2 to 10 parts in a sample