Chapter 17 Statistical Quality Control Mr.Mosab I. Tabash. Learning Objectives. Students will be able to: Define the quality of a product or service. Develop four types of control charts
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Students will be able to:
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17.1 Introduction
17.2 Defining Quality and TQM
17.3 Statistical Process Control
17.4 Control Charts for Variables
17.5 Control Charts for Attributes
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Quality is a major issue in today’s organizations.
Quality control (QC), or quality management, tactics are used throughout the organization to assure deliverance of quality products or services.
Statistical process control (SPC) uses statistical and probability tools to help control processes and produce consistent goods and services.
Total quality management(TQM) refers to a quality emphasis that encompasses the entire organization.
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Thus, SPC involves taking samples of the process output and plotting the averages on a control chart.
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All processes are subject to variability.
The objective of control charts is to identify
assignable causes and prevent them from
reoccurring.
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No
Produce Good
Start
Provide Service
Assign.
Take Sample
Causes?
Yes
Inspect Sample
Stop Process
Create
Find Out Why
Control Chart
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Upper control
chart limit
Target
Normal behavior.
One point out above.
Investigate for
cause.
One point out below.
Investigate for
cause.
Lower control
chart limit
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Upper control
chart limit
Target
Two points near upper control. Investigate
for cause.
Two points near lower
control. Investigate
for cause.
Run of 5 points above central line.
Investigate for cause.
Lower control chart limit
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Upper control
limit
Target
Erratic behavior.
Investigate.
Run of 5 points below
central line.
Investigate for cause.
Trends in either
Direction.
Investigate for cause of progressive change.
Lower
control limit
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Continuous Numerical Data
Categorical or Discrete Numerical Data
Control
Charts
Variables
Attributes
Charts
Charts
R
P
C
X
Chart
Chart
Chart
Chart
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The central limit theorem
(CLT) says that the distribution
of sample means will follow a
normal distribution as the sample
size grows large.
µ = µ and δ = δ
n


x
x
x
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99.7% of all x
fall within ± 3 x
95.5% of all x fall within ± 2 x
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_
X charts measure the central tendency of a process and indicate whether changes have occurred.
R charts values indicate that a gain or loss in uniformity has occurred.
X charts and R charts are used together to monitor variables.

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__
1. Collect 20  25 samples of n = 4, or n = 5 from a stable process. Compute the mean and range of each sample.
2. Compute the overall means. Set appropriate control limits  usually at 99.7 level. Calculate upper and lower control limits. If process not stable, use desired mean instead of sample mean.
3. Graph the sample means and ranges on their respective control charts. Look to see if any fall outside acceptable limits.
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__
4. Investigate points or patterns that indicate the process is out of control. Try to assign causes for the variation, then resume the process.
5. Collect additional samples. If necessary, revalidate the control limits using the new data.
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Control Limits
From Table
Sample Range at Time i
Sample Mean at Time i
# of Samples
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Super Cola bottles soft drinks labeled “net weight 16 ounces.” Several batches of 5 bottles each revealed the following:
Each batch has 5 bottles of cola
_
Construct a X and R chart for the data
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Super Cola Example: x and R Chart
Step 1: Collected 20 samples with 5 bottles in each. Compute the mean and range of each batch.
The data are given on the previous slide.
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Super Cola Example: x and R Chart
Step 2: Compute the overall means and range (x , R), calculate the upper and lower control limits at the 99.7%:
Mean = 16.01 ounces
Range = 0.25 ounces
For X chart
UCL = 16.01 + (0.577)(0.25) = 16.154
LCL = 16.01 – (0.577)(0.25) = 15.866
For R Chart
UCL = (2.114)(0.25) = .5285
LCL = (0)(0.25) = 0
_
_
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Super Cola Example: x and R Chart
Step 3: Graph the sample means and determine if they fall outside the acceptable limits.
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Super Cola Example: x and R Chart
Step 4: Investigate points or patterns that indicate the process is out of control.
Are there any points we should investigate??
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Super Cola Example: x and R Chart
Step 5: Collect additional data and revalidate the control limits using the new data.This is particularly important for Super Cola because the original control limits were obtained from ‘unstable’ data.
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p chartsmeasure the percent defective in a sample and are used to control attributes that typically follow the binomial distribution.
c chartsmeasure the count of the number defective and are used to control the number of defects per unit. The Poisson distribution is its basis.For example:
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p
(
1
p
)
=
+
UCL
p
z
P
n

p
(
1
p
)
=

UCL
p
z
P
n
z = 2 for 95.5% limits; z = 3 for 99.7% limits
# Defective items in sample i
Size of sample i
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Data entry clerks at ARCO key in thousands of insurance records each day. One hundred records were obtained from 20 clerks and checked for accuracy.
p = 0.04
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p
(
1
p
)
=
+
= 0.04 – 3 (.04)(.96)
= 0.04 + 3 (.04)(.96)
UCL
p
z
P
n
100
100

p
(
1
p
)
=

UCL
p
z
P
n
So,
UCL = 0.10
LCL = 0… cannot have a negative percent defective
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UCLp = 0.10
pChart
.12
.11
.10
.09
Fraction Defective
.08
.07
.06
.05
.04
.03
.02
.01
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
.00
LCLp = 0.00
Sample Number
What can you say about the accuracy of ARCO’s clerks???
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UCL = c + z cLCL = c – z c
z = 2 for 95.5% limits; z = 3 for 99.7% limits
Where c = average of all of the samples
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Red Top Cab Company is interested in studying the number of complaints it receives about the poor cab driver behavior. For nine days the manager recorded the total number of calls he received.
c = 6 complaints per day
UCL = 6 + 3 ( 6 ) = 13.35
LCL = 6 – 3 ( 6 ) = 0… cannot have negative mistakes.
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After the control chart was posted prominently, the number of complaints dropped to an average of 3 per day. Can you explain why this may have occurred???
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