unidad 6- sem 16,17
TRANSCRIPT
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Slide 1
Copyright 2004 Pearson Education, Inc.
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Slide 2
Copyright 2004 Pearson Education, Inc.
13-1 Overview
13-2 Control Charts for Variation and Mean
13-3 Control Charts for Attributes
Chapter 13
Statistical Process Control
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Slide 3
SEMANA 16
Esther Flores Ugarte ESTADSTICA II
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Slide 4
Copyright 2004 Pearson Education, Inc.
Created by Erin Hodgess, Houston, Texas
Section 13-1 and 13-2
Overview and Control
Charts for Variation and
Mean
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Slide 5
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Overview
Chapter 2 Review Center: Measure of center
Variation: Measure of the amount
that scores vary among themselves Distribution: Nature or shape
of distribution of the data
Outliers: Sample values that are veryfar away from majority of other values
Time: Changing characteristics of
the data over time
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Slide 6
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Chapter 13The main objective is to address the
changing characteristics over time.
By monitoring this characteristic, we arebetter able to control the production of
goods and services, thereby ensuring
better quality.
Overview
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Slide 7
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Control Charts for
Variation and Mean
Definition
Process Data
These are data arranged according to
some time sequence.
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Slide 8
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Definition
Process Data
These are data arranged according to
some time sequence.
Important characteristics of process data
can change over time.
Control Charts for
Variation and Mean
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Slide 9
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Definition
Run Chart
A run chart is a sequential plot of
individual data values over time.
One axis (usually vertical) is used forthe data values, and the other axis
(usually the horizontal) is used for
the time sequence.
Control Charts for
Variation and Mean
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Slide 10
Copyright 2004 Pearson Education, Inc.
Example: MeasuringAircraft Altimeters
Treating the 80 altimeter errors in Table 13-1 as a string of
consecutive measurements, construct a run chart by
using a vertical axis for the errors and a horizontal axis to
identify the order of the sample data.
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Slide 11
Copyright 2004 Pearson Education, Inc.
Example: MeasuringAircraft Altimeters
Treating the 80 altimeter errors in Table 13-1 as a string of
consecutive measurements, construct a run chart by
using a vertical axis for the errors and a horizontal axis to
identify the order of the sample data.
We notice that the values on the right of the chart show
more fluctuations than those on the left of the chart. This
increased variation could mean that the altimeters are notmeeting FAA standards. The movement should be
investigated.
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Slide 12
Copyright 2004 Pearson Education, Inc.
Definition
A process is statistically stable (or withinstatistical control) if it has naturalvariation, with no patterns, cycles, or anyunusual points.
Only when a process is statistically stablecan its data be treated as if they came from
a population with a constant mean,standard deviation, distribution, and othercharacteristics.
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Slide 13
Copyright 2004 Pearson Education, Inc.
Figure 13-2 Process with Patterns
That Are Not Statistically Stable
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Slide 14
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Figure 13-2 Process with Patterns
That Are Not Statistically Stable
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Slide 15
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Figure 13-2 Process with Patterns
That Are Not Statistically Stable
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Slide 16
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Figure 13-2 Process with Patterns
That Are Not Statistically Stable
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Slide 17
Copyright 2004 Pearson Education, Inc.
A common goal of many differentmethods of quality control is this:
Reduce variation in aproduct or a service.
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Slide 18
Copyright 2004 Pearson Education, Inc.
Definition
Random variation
Random variation is due to chance; it is thetype of variation inherent in any process
that is not capable of producing every goodor service exactly the same way every time.
Assignable variation
Assignable variation results from causesthat can be identified.
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Slide 19
Copyright 2004 Pearson Education, Inc.
Definition
A control chart of a process characteristic (such
as mean or variation) consists of value plotted
sequentially over time, and it includes a center
line as well as a lower control limit (LCL) and an
upper control limit (UCL). The center line
represents a central value of the characteristicmeasurements, whereas the control limits are
boundaries used to separate and identify any
points considered to be unusual .
Control Chart for Monitoring
Variation: The RChart
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Slide 20
Copyright 2004 Pearson Education, Inc.
An Rchart is a plot of the sample ranges
instead of individual values and is used
to monitor the variation in a process.
Control Chart for Monitoring
Variation: The RChart
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Slide 21
Copyright 2004 Pearson Education, Inc.
The center line would be located at R,which denotes the mean of all sampleranges as well as another line for thelower control limit and a third line forthe upper control limit.
An Rchart is a Plot of the sample ranges
instead of individual values and is used
to monitor the variation in a process.
Control Chart for Monitoring
Variation: The RChart
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Slide 22
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Notation
n= size of each sample, or subgroup
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Slide 23
Copyright 2004 Pearson Education, Inc.
n= size of each sample, or subgroup
x= mean of the sample means, which isequivalent to the mean of all sample
values combined
Notation
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Slide 24
Copyright 2004 Pearson Education, Inc.
n= size of each sample, or subgroup
x= mean of the sample means, which isequivalent to the mean of all sample
values combined
R= mean of the sample ranges (that is,the
sum of the sample ranges divided bythe number of samples)
Notation
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Slide 25
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Point plotted: Sample ranges
Monitoring Process
Variation: Control Chart for R
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Slide 26
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Point plotted: Sample ranges
Center line: R
Monitoring Process
Variation: Control Chart for R
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Slide 27
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Point plotted: Sample ranges
Center line: R
Upper Control Limit (UCL): D4R
Monitoring Process
Variation: Control Chart for R
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Slide 28
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Point plotted: Sample ranges
Center line: R
Upper Control Limit (UCL): D4R
Lower Control Limit (LCL): D3R
Monitoring Process
Variation: Control Chart for R
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Slide 29
Copyright 2004 Pearson Education, Inc.
Point plotted: Sample ranges
Center line: R
Upper Control Limit (UCL): D4R
Lower Control Limit (LCL): D3
R
where the values of D4 and D3 are found inTable 13-2
Monitoring Process
Variation: Control Chart for R
T bl 13 2
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Slide 30
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Table 13-2
Control Chart
Constants
E l M i
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Slide 31
Copyright 2004 Pearson Education, Inc.
Example: MeasuringAircraft Altimeters
Refer to the altimeter errors in Table 13-1. Using thesamples of size n= 4 collected each day of manufacturing,
construct a control chart for R.
R= 19 + 13 + ...+ 63 = 21.220
E l M i
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Slide 32
Copyright 2004 Pearson Education, Inc.
Example: MeasuringAircraft Altimeters
Refer to the altimeter errors in Table 13-1. Using thesamples of size n= 4 collected each day of manufacturing,
construct a control chart for R.
R= 19 + 13 + ...+ 63 = 21.220
D3 = 0.000
D4 = 2.282 from Table 13-2
E l M i
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Slide 33
Copyright 2004 Pearson Education, Inc.
Example: MeasuringAircraft Altimeters
D4R= (2.282)(21.2) = 48.4
D3R= (0.000)(21.2) = 0.0
Refer to the altimeter errors in Table 13-1. Using thesamples of size n= 4 collected each day of manufacturing,
construct a control chart for R.
R= 19 + 13 + ...+ 63 = 21.220
D3 = 0.000
D4 = 2.282 from Table 13-2
MINITAB Di l
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Slide 34
Copyright 2004 Pearson Education, Inc.
MINITAB Display
RChart for Errors
I t ti
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Slide 35
Copyright 2004 Pearson Education, Inc.
Interpreting
Control Charts
Upper and lower control limits of
a control chart are based on the
actual behavior of the process,not the desired behavior.
Criteria for Determining When a
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Slide 36
Copyright 2004 Pearson Education, Inc.
Criteria for Determining When a
Process Is Not Statistically Stable
(Out of Statistical Control)
1. There is a pattern, trend, or cycle that is obviously
not random (such as those depicted in Figure 13-2).
2. There is a point lying beyond the upper or lower
control limits.
3. Run of 8 Rule: There are eight consecutive points all
above or all below the center line. (With a
statistically stable process, there is a 0.5 probabilitythat a point will be above or below the center line, so
it is very unlikely that eight consecutive points will
all be above the center line or below it.)
W ill l th th t f t l
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Slide 37
Copyright 2004 Pearson Education, Inc.
We will use only the three out-of-control
criteria listed previously, but some
businesses use additional criteria such as these:
There are 6 consecutive points all increasing or all
decreasing.
There are 14 consecutive point alternating between up
and down (such as up, down, up, down, and so on).
Two out of 3 consecutive points are beyond control
limits that are 2 standard deviation away from
centerline.
Four out of 5 consecutive points are beyond control
limits that are 1 standard deviations away from the
centerline.
E l St ti ti l
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Slide 38
Copyright 2004 Pearson Education, Inc.
Example: StatisticalProcess Control
Examine the Rchart shown in the Minitab display for the
preceding example and determine whether the process
variation is within statistical control.
E l St ti ti l
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Slide 39
Copyright 2004 Pearson Education, Inc.
Example: StatisticalProcess Control
Examine the Rchart shown in the Minitab display for the
preceding example and determine whether the process
variation is within statistical control.
1. There is a pattern, trend, or cycle that is obviously notrandom: Going from left to right, there is a pattern of
upward trend.
2. There is a point (the rightmost point) that lies above
the upper control limit.
E l St ti ti l
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Slide 40
Copyright 2004 Pearson Education, Inc.
Example: StatisticalProcess Control
Examine the Rchart shown in the Minitab display for the
preceding example and determine whether the process
variation is within statistical control.
We conclude that the variation (not necessarily the mean)of the process is out of statistical control. Because the
variation appears to be increasing with time, immediate
corrective action must be taken to fix the variat ion among
the altimeter errors.
Monitoring Process
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Slide 41
Copyright 2004 Pearson Education, Inc.
Point plotted: Sample means
Monitoring Process
Mean: Control Chart for x
Monitoring Process
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Slide 42
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Point plotted: Sample means
Center line: x
Monitoring Process
Mean: Control Chart for x
Monitoring Process
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Slide 43
Copyright 2004 Pearson Education, Inc.
Point plotted: Sample means
Center line: x
Upper Control Limit (UCL): x+ A2R
Monitoring Process
Mean: Control Chart for x
Monitoring Process
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Slide 44
Copyright 2004 Pearson Education, Inc.
Point plotted: Sample means
Center line: x
Upper Control Limit (UCL): x + A2R
Lower Control Limit (LCL): xA2R
Monitoring Process
Mean: Control Chart for x
Monitoring Process
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Slide 45
Copyright 2004 Pearson Education, Inc.
Point plotted: Sample means
Center line: x
Upper Control Limit (UCL): x+ A2R
Lower Control Limit (LCL): xA2R
where the values of A2 found in Table 13-2.
Monitoring Process
Mean: Control Chart for x
Example: Manufacturing
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Slide 46
Copyright 2004 Pearson Education, Inc.
Example: ManufacturingAircraft Altimeters
Refer to the altimeter errors in Table 13-1. Using thesamples of size n= 4 collected each day of manufacturing,
construct a control chart for x. Based on the control chart
for xonly, determine whether the process is within
statistical control.
Example: Manufacturing
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Slide 47
Copyright 2004 Pearson Education, Inc.
x = 2.50 + 2.75 + ...+ 9.75 = 6.45
20
Example: ManufacturingAircraft Altimeters
Example: Manufacturing
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Slide 48
Copyright 2004 Pearson Education, Inc.
x = 2.50 + 2.75 + ...+ 9.75 = 6.45
20
A2 = 0.729
Example: ManufacturingAircraft Altimeters
Example: Manufacturing
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Slide 49
Copyright 2004 Pearson Education, Inc.
x = 2.50 + 2.75 + ...+ 9.75 = 6.45
20
A2 = 0.729
UCL: x+ A2R= 6.45 + (0.729)(21.2) = 21.9
LCL: xA2R= 6.45
(0.729)(21.2) =
9.0
Example: ManufacturingAircraft Altimeters
Example: Manufacturing
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Slide 50
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Example: ManufacturingAircraft Altimeters
Example: Manufacturing
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Slide 51
Copyright 2004 Pearson Education, Inc.
Examination of the control chart shows that the process
mean is out of statistical control because at least one of
the three out-of-control criteria is not satisfied.
Specifically, the third criterion is not satisfied becausethere are 8 (or more) consecutive points all below the
center line. Also, there does appear to be a pattern of an
upward trend. Again, immediate corrective action is
required to fix the production process.
Example: ManufacturingAircraft Altimeters
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Slide 52
SEMANA 17
Esther Flores Ugarte ESTADSTICA II
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Slide 53
Copyright 2004 Pearson Education, Inc.
Created by Erin Hodgess, Houston, Texas
Section 13-3
Control Charts forAttributes
Control Charts
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Slide 54
Copyright 2004 Pearson Education, Inc.
Control Charts
for Attributes
These charts monitor the qualitativeattributes of whether an item has some
particular characteristic.
In the previous section, the charts
monitored the quantitative characteristics.
The control chart for p(or pchart) isused to monitor the proportion pforsome attribute.
Notation
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p= pooled estimate of proportion ofdefective items in the process
Notation
Notation
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p= pooled estimate of proportion ofdefective items in the process
=
Notation
total number of defects found among all items sampled
total number of items sampled
Notation
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Slide 57
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p= pooled estimate of proportion of
defective items in the process
=
q= pooled estimate of the proportion ofprocess items that are not defective
Notation
total number of defects found among all items sampled
total number of items sampled
Notation
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Slide 58
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p= pooled estimate of proportion ofdefective items in the process
=
q= pooled estimate of the proportion ofprocess items that are not defective
= 1p
Notation
total number of defects found among all items sampled
total number of items sampled
Notation
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Slide 59
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p= pooled estimate of proportion ofdefective items in the process
=
q= pooled estimate of the proportion ofprocess items that are not defective
= 1p
n= size of each sample (not the number of
samples)
Notation
total number of defects found among all items sampled
total number of items sampled
Control Chart for p
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Control Chart for p
Control Chart for p
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Center line: p
Control Chart for p
Control Chart for p
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Slide 62
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p q
Center line: p
Upper control limit: p+ 3
Control Chart for p
n
Control Chart for p
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Slide 63
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p q
Center line: p
Upper control limit: p+ 3
Lower control limit: p 3
Control Chart for p
n
p q
n
Control Chart for p
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Slide 64
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p q
p q
Center line: p
Upper control limit: p+ 3
Lower control limit: p 3
Control Chart for p
n
n
(If calculation for the lower control limit results in a
negative value, use 0 instead. If the calculation for the
upper control limit exceeds 1, use 1 instead.)
Example: In 13 consecutive years 100,000 were
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Slide 65
Copyright 2004 Pearson Education, Inc.
randomly selected and the number who died from
respiratory tract infections is reported below. Construct a
control chart for pand determine whether the process is
within statistical control.
Number of deaths:
25 24 22 25 27 30 31 30 33 32 33 32 31
Example: In 13 consecutive years 100,000 were
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Slide 66
Copyright 2004 Pearson Education, Inc.
randomly selected and the number who died from
respiratory tract infections is reported below. Construct a
control chart for pand determine whether the process is
within statistical control.
Number of deaths:
25 24 22 25 27 30 31 30 33 32 33 32 31
p= 25 + 24 + 22 + ...+ 31 = 375 = 0.000288
(13)(100,000) 1,300,000
Example: In 13 consecutive years 100,000 were
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Slide 67
Copyright 2004 Pearson Education, Inc.
randomly selected and the number who died from
respiratory tract infections is reported below. Construct a
control chart for pand determine whether the process is
within statistical control.
Number of deaths:
25 24 22 25 27 30 31 30 33 32 33 32 31
p= 25 + 24 + 22 + ...+ 31 = 375 = 0.000288
(13)(100,000) 1,300,000
q= 1
p= 0.999712
Example: In 13 consecutive years 100,000 were
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Slide 68
Copyright 2004 Pearson Education, Inc.
randomly selected and the number who died from
respiratory tract infections is reported below. Construct a
control chart for pand determine whether the process is
within statistical control.
Number of deaths:
25 24 22 25 27 30 31 30 33 32 33 32 31
p= 25 + 24 + 22 + ...+ 31 = 375 = 0.000288
(13)(100,000) 1,300,000
q= 1
p= 0.999712
n
p qp+ 3 = 0.000449
n
p qp 3 = 0.000127
P Chart for Death from
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Slide 69
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Respiratory Tract Infections
Example: In 13 consecutive years 100,000 were
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Slide 70randomly selected and the number who died from
respiratory tract infections is reported below. Construct a
control chart for pand determine whether the process is
within statistical control.
Number of deaths:
25 24 22 25 27 30 31 30 33 32 33 32 31
Interpretation: Using the three out-of-control criteria listed
in Section 13-2, we conclude that this process is out of
statistical control since from the p-chart there appears to be
an upward trend, and there are eight consecutive points all
lying above the centerline (Run of 8 Rule). Based on thesedata, public health policies affecting respiratory tract
infections should be modified to cause a decrease in the
death rate.