copyright © 2010, 2007, 2004 pearson education, inc. 14.1 - 1 lecture slides elementary statistics...

Copyright © 2010, 2007, 2004 Pearson Education, Inc. 14.1 - 1

Lecture Slides

Elementary Statistics Eleventh Edition

and the Triola Statistics Series

by Mario F. Triola


14-1 Review and Preview

14-2 Control Charts for Variation and Mean

14-3 Control Charts for Attributes

Chapter 14Statistical Process Control


Section 14-3 Control Charts for

Attributes


Key Concept

This section presents a method for constructing a control chart to monitor the proportion p for some attribute, such as whether a service or manufactured item is defective or nonconforming.

The control chart is interpreted by using the same three criteria from Section 14-2 to determine whether the process is statistically stable.


Control Charts for Attributes

These charts monitor the qualitative attributes of whether an item has some particular characteristic.

In the previous section, the charts monitored the quantitative characteristics.

The control chart for p (or p chart) is used to monitor the proportion p for some attribute.


Definition

A control chart for p (or p chart) is a graph of proportions of some attribute (such as whether products are defective) plotted sequentially over time, and it includes a centerline, a lower control limit (LCL), and an upper control limit (UCL).


Construct a control chart for

(or a “p chart”) that can be used to determine whether the proportion of some attribute (such as whether products are defective) from process data is within statistical control.

Monitoring a Process Attribute: Control Chart for p:

Objectivep


1. The data are process data consisting of a sequence of samples all of the same size n.

2. Each sample item belongs to one of two categories.

3. The individual sample data values are independent.

Requirements


= pooled estimate of proportion of defective items in the process

= total number of defects found among all items sampledtotal number of items sampled

= pooled estimate of the proportion of process items that are not defective

=

n = size of each sample or subgroup

Notation

p

q

1 p


Center line:

Upper control limit:

Lower control limit:

Graph

(If the 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.)

p

3pq

pn

3pq

pn


Upper and lower control limits of a control chart for a proportion p are based on the actual behavior of the process, not the desired behavior. Upper and lower control limits are totally unrelated to any process specifications that may have been decreed by the manufacturer.

Caution


The Guidant Corporation manufactures implantable heart defibrillators. Families of people who have died using these devices are suing the company. According to USA Today, “Guidant did not alert doctors when it knew 150 of every 100,000 Prizm 2DR defibrillators might malfunction each year.” Because lives could be lost, it is important to monitor the manufacturing process of implantable heart defibrillators.

Example: Defective Heart Defibrillators


Consider a manufacturing process that includes careful testing of each defibrillator. Listed below are the numbers of defective defibrillators in successive batches of 10,000. Construct a control chart for the proportion p of defective defibrillators and determine whether the process is within statistical control. If not, identify which of the three out-of-control criteria apply.

Defects:15 12 14 14 11 16 17 11 167 8 5 7 6 6 8 5 7 8 7



Defects:

15 12 14 14 11 16 17 11 16

7 8 5 7 6 6 8 5 7 8 7


total number of defects from all samples combinedtotal number of defibrillators sampled

p

15 12 14 ... 7 2000.001

20 10,000 200,000p



Upper control limit:

Lower control limit:

The Minitab control chart for p is on the next slide.

1 1 0.001 0.999q p

(0.001)(0.999)3 0.001 3 0.001948

10,000

pqp

n

(0.001)(0.999)3 0.001 3 0.000052

100

pqp

n



We can interpret the control chart for p by considering the three out-of-control criteria listed in Section 14-2. Using those criteria, we conclude that this process is out of statistical control for this reason: There appears to be a downward trend. Also, there are 8 consecutive points lying above the centerline, and there are also 8 consecutive points lying below the centerline. Although the process is out of statistical control, it appears to have been somehow improved, because the proportion of defects has dropped. The company would be wise to investigate the process so that the cause of the lowered rate of defects can be understood and continued in the future.


Recap

In this section we have discussed:

A control chart for attributes is a graph of proportions plotted sequentially over time.

It includes a centerline, a lower control limit, and an upper control limit.

The same three out-of-control criteria listed in Section 14-2 can be used.

copyright © 2010, 2007, 2004 pearson education, inc. 14.1 - 1 lecture slides elementary statistics...

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