Chapter 18 Introduction to Quality and Statistical Process Control

1
Chapter 18Introduction to Quality and
Statistical Process Control
2
Quality

• Quality is the totality of features and
  characteristics of a product or service that
  bears on its ability to satisfy given needs.

• Organizations recognize that they
  must strive for high levels of quality.

• They have increased the emphasis on
  methods for monitoring and maintaining quality.

3
Quality Terminology
QA
refers to the entire system of
policies, procedures, and
guide- lines established by an organization to
achieve and maintain quality.
Quality Assurance
Its
objective is to include quality
in the design of products
and processes and to identify potential
quality problems prior to production.
Quality Engineering
QC
consists of making a series
of inspections and measure-
ments to determine whether quality standards
are being met.
Quality Control
4
The Basic 7 Tools of Quality Assurance

• Process Flowcharts
• Brainstorming
• Fishbone Diagram
• Histogram
• Trend Charts
• Scatter Plots
• Statistical Process Control Charts

Pg. 860 - 861
5
Statistical Process Control (SPC)

• Output of the production process is sampled and
  inspected.

• Using SPC methods, it can be determined whether
  variations in output are due to common causes or
  assignable causes.

• The goal is decide whether the process can be
  continued or should be adjusted to achieve a
  desired quality level.

6
Introduction to Control Charts

• Control Charts are used to monitor variation in a
  measured value from a process
• Exhibits trend
• Can make correction before process is out of
  control
• A process is a repeatable series of steps leading
  to a specific goal
• Inherent variation refers to process variation
  that exists naturally. This variation can be
  reduced but not eliminated

7
Process Variation
Total Process Variation
Common Cause Variation
Special Cause Variation

• Variation is natural inherent in the world
  around us
• No two products or service experiences are
  exactly the same
• With a fine enough gauge, all things can be seen
  to differ

8
Sources of Variation
Total Process Variation
Common Cause Variation
Special Cause Variation


Variation is often due to differences in

• People
• Machines
• Materials
• Methods
• Measurement
• Environment

9
Common Cause Variation
Total Process Variation
Common Cause Variation
Special Cause Variation

• Common cause variation
• naturally occurring and expected
• the result of normal variation in materials,
  tools, machines, operators, and the environment

10
Special Cause Variation
Total Process Variation
Common Cause Variation
Special Cause Variation

• Special cause variation
• abnormal or unexpected variation
• has an assignable cause
• variation beyond what is considered inherent to
  the process

11
Control Charts

• SPC uses graphical displays known as control
  charts to monitor a production process.

• Control charts provide a basis for deciding
  whether the variation in the output is due to
  common causes (in control) or special causes (out
  of control).

12
Control Charts

• Two important lines on a control chart are the
  upper control limit (UCL) and lower control limit
  (LCL).

• These lines are chosen so that when the process
  is in control, there will be a high probability
  that the sample finding will be between the two
  lines.

• Values outside of the control limits provide
  strong evidence that the process is out of
  control.

13
Statistical Process Control Charts

• Show when changes in data are due to
• Special or assignable causes
• Fluctuations not inherent to a process
• Represents problems to be corrected
• Data outside control limits or trend
• Common causes or chance
• Inherent random variations
• Consist of numerous small causes of random
  variability

14
Process Control Chart Format
Special Cause Variation
UCL
UCL Average 3 standard deviations
Common Cause Variation
Process average
99.7
LCL Average ? 3 standard deviations
LCL
Special Cause Variation
15
Process Control Chart Format
Special Cause Variation
UCL
Common Cause Variation
Process average
99.7
LCL
Special Cause Variation
16
Statistical Process Control Charts
x Chart
R Chart
This chart is used to monitor the range of
the measurements in the sample.
17
Attributes Control Charts
p Chart
This chart is used to monitor the proportion
of a sample with a specific attribute (defective,
for example)
c Chart
This chart is used to monitor the number of
defective items in the sample.
18
x Chart Structure
Upper Control Limit
UCL
Center Line
Process Mean When in Control
LCL
Time
Lower Control Limit
19
x-chart and R-chart

• Used for measured numeric data from a process.
• Start with at least 20 subgroups of observed
  values.
• Subgroups usually contain 3 to 6 observations
  each.

20
x-chart and R-chart

• Example
• The Haines Lumber Company makes
  plywood for residential and
  commercial construction. One
  of the key quality measures
  is plywood thickness. Every
  hour, five pieces of plywood are selected and the
  thicknesses are measured. A partial list of the
  data (in inches) for the first 20 subgroups are
  on the next slide.

21
Example x-chart
Note Subgroups 6 20 are not visible
22
Steps to create an x-chart and an R-chart

• Calculate subgroup means x, and ranges R

23
Example x-chart
Note Subgroups 6 20 are not visible
24
Steps to create an x-chart and an R-chart

• Calculate subgroup means x, and ranges R
• Compute the average of the subgroup means x, and
  the average range value R

25
Example x-chart
Note Subgroups 6 20 are not visible
26
Average of Subgroup Means and Ranges
Average of subgroup means
Average of subgroup ranges
where xi ith subgroup average k number of
subgroups
where Ri ith subgroup range k number of
subgroups
27
Example x-chart
Note Subgroups 6 20 are not visible
28
Steps to create an x-chart and an R-chart

• Calculate subgroup means x, and ranges R
• Compute the average of the subgroup means x, and
  the average range value R
• Prepare graphs of the subgroup means and ranges
  as a line chart

29
Example x-chart
30
Example R-chart
31
Steps to create an x-chart and an R-chart

• Compute the upper and lower control limits for
  the x-chart and use lines to indicate the limits
  and process mean x.

32
Computing Control Limits

• The upper and lower control limits for an x-chart
  are generally defined as
• or

UCL Process Average 3 Standard Deviations
LCL Process Average 3 Standard Deviations
33
Computing Control Limits

• Since the population standard deviation s cannot
  be determined, the interval is formed using R
  instead
• The value A2R is used to estimate 3s, where A2 is
  from Appendix Q
• The upper and lower control limits are

Where A2 Shewhart
factor for subgroup size n from appendix Q
34
Control Chart Factors
35
Haines Lumber Company
36
0.820
UCL 0.796
LCL 0.710
0.680
0.00
37
Steps to create an x-chart and an R-chart

• Compute the upper and lower control limits for
  the x-chart and use lines to indicate the limits
  and process mean x.
• Compute the upper and lower control limits for
  the R-chart and use lines to indicate the limits
  and process range R.

38
Example R-chart

• The upper and lower control limits for an
• R-chart are

where D4 and D3 are taken from the Shewhart
table (appendix Q) for subgroup size n
39
Control Chart Factors
40
Haines Lumber Company
41
UCL 0.156
LCL 0.00
42
Using Control Charts

• Control Charts are used to check for process
  control.
• H0 The process is in control
• i.e., variation is only due to common causes
• Ha The process is out of control
• i.e., special cause variation exists
• If the process is found to be out of control,
  steps should be taken to find and eliminate the
  special causes of variation

43
Process In Control

• Process in control points are randomly
  distributed around the center line and all points
  are within the control limits

UCL
LCL
time
44
Process Not in Control
Out of control conditions

• One or more points outside control limits
• Nine or more points in a row on one side of the
  center line
• Six or more points moving in the same direction
• 14 or more points alternating above and below the
  center line

45
Process Not in Control

• One or more points outside control limits

• Nine or more points in a row on one side of the
  center line

UCL
UCL
LCL
LCL

• Six or more points moving in the same direction

• 14 or more points alternating above and below the
  center line

UCL
UCL
LCL
LCL
46
Out-of-control Processes

• When the control chart indicates an
  out-of-control condition (a point outside the
  control limits or exhibiting trend, for example)
• Contains both common causes of variation and
  assignable causes of variation
• The assignable causes of variation must be
  identified
• If detrimental to the quality, assignable causes
  of variation must be removed
• If quality increases, assignable causes must be
  incorporated into the process design

47
UCL
LCL
UCL
LCL
48
R Chart
49
Now You Try pg. 882, 18-16
50
p-Charts

• This chart is used to monitor the proportion of a
  sample with a specific attribute.
• An attribute is a quality characteristic that is
  either present pr not present.
• Example Good (meets specifications) or defective
• p-charts are commonly used to monitor the
  proportion of defects.

51
Control Limits for a p Chart
where
assuming np gt 5 n(1-p) gt 5
Note If computed LCL is negative, set LCL 0
52
Control Limits for a p Chart

• Example Norwest Bank

• Every check cashed or deposited at
• Norwest Bank must be encoded with
• the amount of the check before it can
• begin the Federal Reserve clearing
• process. The accuracy of the check
• encoding process is of utmost
• importance. If there is any discrepancy
• between the amount a check is made
• out for and the encoded amount, the check is
• defective.

53
Control Limits for a p Chart

• Twenty samples, each consisting of 100
  checks, were selected and examined for errors.
  The number of defective checks found in the 20
  samples are listed below.

54
Control Limits for a p Chart

• Twenty samples, each consisting of 100
  checks, were selected and examined for errors.
  The number of defective checks found in the 20
  samples are listed below.

Expressed as proportions
55
Control Limits for a p Chart
Note that the computed LCL is negative.
56
Control Limits for a p Chart
UCL 0.10
LCL 0
57
Now You Try

• An automotive industry supplier produces pistons
  for several models of automobiles. Twenty
  samples, each consisting of 200 pistons, were
  selected and inspected for defects. The
  proportions of defective pistons found in the
  samples follow.

Construct a p-chart for the manufacturing process.
58
Now You Try
UCL
LCL

• What conclusion would be made if a sample of 200
  has 20 defective pistons?

59
c-Chart

• Control chart for number of nonconformities
  (occurrences) per sampling unit.
• Shows total number of nonconforming items per
  unit
• examples number of flaws per pane of glass
• number of errors per page of code
• Assume that the size of each sampling unit
  remains constant

60
Mean and Standard Deviationfor a c-Chart

• The standard deviation for a c-chart is

• The mean for a c-chart is

where xi number of occurrences per sampling
unit k number of sampling units
61
c-Chart Control Limits
The control limits for a c-chart are
62
Process Control

• Determine process control for p-chars and
  c-charts using the same rules as for x-bar and
  R-charts
• Out of control conditions
• One or more points outside control limits
• Nine or more points in a row on one side of the
  center line
• Six or more points moving in the same direction
• 14 or more points alternating above and below the
  center line

63
c-Chart Example

• A weaving machine makes cloth in a standard
  width. Random samples of 10 meters of cloth are
  examined for flaws. Is the process in control?

Sample number 1 2 3 4 5 6 7 Flaws
found 2 1 3 0 5 1 0
64
Constructing the c-Chart

• The mean and standard deviation are

• The control limits are

Note LCL lt 0 so set LCL 0
65
The completed c-Chart
6 5 4 3 2 1 0
UCL 5.642
c 1.714
LCL 0
1 2 3 4 5 6 7
Sample number

• The process is in control. Individual points are
  distributed around the center line without any
  pattern. Any improvement in the process must
  come from reduction in common-cause variation

66
End of Chapter 18