Quality and statistical process control ppt @ bec doms
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Transcript of Quality and statistical process control ppt @ bec doms
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Introduction to Quality and Statistical Process Control
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Chapter Goals
After completing this chapter, you should be able to:
Use the seven basic tools of quality
Construct and interpret x-bar and R-charts
Construct and interpret p-charts
Construct and interpret c-charts
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Chapter OverviewQuality Management and
Tools for Improvement
Deming’s 14 Points
Juran’s 10 Steps to Quality
Improvement
The Basic 7 Tools
Philosophy of Quality
Tools for Quality Improvement
Control Charts
X-bar/R-charts
p-charts
c-charts
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Themes of Quality Management Primary focus is on process improvement Most variations in process are due to systems Teamwork is integral to quality management Customer satisfaction is a primary goal Organization transformation is necessary It is important to remove fear Higher quality costs less
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1. Create a constancy of purpose toward improvement become more competitive, stay in business, and provide jobs
2. Adopt the new philosophy Better to improve now than to react to problems later
3. Stop depending on inspection to achieve quality -- build in quality from the start Inspection to find defects at the end of production is too late
4. Stop awarding contracts on the basis of low bids Better to build long-run purchaser/supplier relationships
Deming’s 14 Points
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5. Improve the system continuously to improve quality and thus constantly reduce costs
6. Institute training on the job Workers and managers must know the difference between common cause and
special cause variation
7. Institute leadership Know the difference between leadership and supervision
8. Drive out fear so that everyone may work effectively.
9. Break down barriers between departments so that people can work as a team.
(continued)Deming’s 14 Points
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10. Eliminate slogans and targets for the workforce They can create adversarial relationships
11. Eliminate quotas and management by objectives
12. Remove barriers to pride of workmanship 13. Institute a vigorous program of education
and self-improvement 14. Make the transformation everyone’s job
(continued)Deming’s 14 Points
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Juran’s 10 Steps to Quality Improvement
1. Build awareness of both the need for improvement and the opportunity for improvement
2. Set goals for improvement 3. Organize to meet the goals that have been set 4. Provide training 5. Implement projects aimed at solving
problems
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Juran’s 10 Steps to Quality Improvement
6. Report progress 7. Give recognition 8. Communicate the results 9. Keep score 10. Maintain momentum by building
improvement into the company’s regular systems
(continued)
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The Deming Cycle
The Deming
CycleThe key is a continuous cycle of improvement
Act
Plan
Do
Study
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The Basic 7 Tools
1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
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The Basic 7 Tools1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
Map out the process to better visualize and understand opportunities for improvement
(continued)
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The Basic 7 Tools1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
Cause 4Cause 3
Cause 2Cause 1
Problem
Fishbone (cause-and-effect) diagram:
Sub-causes
Sub-causes
Show patterns of variation
(continued)
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The Basic 7 Tools1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
time
y
x
y
Identify trend
Examine relationships
(continued)
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The Basic 7 Tools1. Process Flowcharts
2. Brainstorming
3. Fishbone Diagram
4. Histogram
5. Trend Charts
6. Scatter Plots
7. Statistical Process Control Charts
X
Examine the performance of a process over time
time
(continued)
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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
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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
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Sources of Variation
Total Process Variation
Common Cause Variation
Special Cause Variation= +
People
Machines
Materials
Methods
Measurement
Environment
Variation is often due to differences in:
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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
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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
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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
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Process Average
Control Chart Basics
UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations
UCL
LCL
+3σ
- 3σ
Common Cause Variation: range of expected variability
Special Cause Variation: Range of unexpected variability
time
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Process Average
Process Variability
UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations
UCL
LCL
±3σ → 99.7% of process values should be in this range
time
Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present
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Statistical Process Control ChartsStatistical
Process Control Charts
X-bar charts and R-charts
c-charts
Used for measured
numeric data
Used for proportions
(attribute data)
Used for number of
attributes per sampling unit
p-charts
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x-bar 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
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Steps to create an x-chart and an R-chart
Calculate subgroup means and ranges
Compute the average of the subgroup means and the average range value
Prepare graphs of the subgroup means and ranges as a line chart
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Steps to create an x-chart and an R-chart
Compute the upper and lower control limits for the x-bar chart
Compute the upper and lower control limits for the R-chart
Use lines to show the control limits on the x-bar and R-charts
(continued)
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Example: x-chart Process measurements:
Subgroup measuresSubgroup number
Individual measurements Mean, x Range, R
1
2
3
…
15
12
17
…
17
16
21
…
15
9
18
…
11
15
20
…
14.5
13.0
19.0
…
6
7
4
…Average
subgroup mean
= x
Average subgroup range = R
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Average of Subgroup Means and Ranges
k
xx i
k
RR i
Average of subgroup means:
where:xi = ith subgroup average
k = number of subgroups
Average of subgroup ranges:
where:Ri = ith subgroup range
k = number of subgroups
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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
3
3
xLCL
xUCL
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Computing Control Limits Since control charts were developed before it
was easy to calculate σ, the interval was formed using R instead
The value A2R is used to estimate 3σ , where A2 is from Appendix Q
The upper and lower control limits are
)R(AxLCL
)R(AxUCL
2
2
(continued)
where A2 = Shewhart factor for subgroup size n from appendix Q
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Example: R-chart
The upper and lower control limits for an R-chart are
)R(DLCL
)R(DUCL
3
4
where:D4 and D3 are taken from the Shewhart table(appendix Q) for subgroup size = n
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x-chart and R-chart
UCL
LCL
time
x
UCL
LCL
time
RR-chart
x-chart
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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
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Process In Control Process in control: points are randomly
distributed around the center line and all points are within the control limits
UCL
LCL
x
x
time
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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
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Process Not in Control One or more points outside control limits
UCL
LCL
x
Nine or more points in a row on one side of the center line
UCL
LCL
x
Six or more points moving in the same direction
UCL
LCL
x
14 or more points alternating above and below the center line
UCL
LCL
x
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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 increases quality, assignable causes must be incorporated into the process design
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p-Chart Control chart for proportions
Is an attribute chart
Shows proportion of nonconforming items Example -- Computer chips: Count the number of
defective chips and divide by total chips inspected Chip is either defective or not defective
Finding a defective chip can be classified a “success”
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p-Chart Used with equal or unequal sample sizes
(subgroups) over time Unequal sizes should not differ by more than
±25% from average sample sizes
Easier to develop with equal sample sizes
Should have np > 5 and n(1-p) > 5
(continued)
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Creating a p-Chart Calculate subgroup proportions
Compute the average of the subgroup proportions
Prepare graphs of the subgroup proportions as a line chart
Compute the upper and lower control limits
Use lines to show the control limits on the p-chart
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p-Chart Example
Subgroup number
Sample size
Number of successes Proportion, p
1
2
3
…
150
150
150
15
12
17
…
10.00
8.00
11.33
…Average subgroup
proportion = p
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Average of Subgroup Proportions
The average of subgroup proportions = p
where: pi = sample proportion for subgroup i k = number of subgroups of size n
where: ni = number of items in sample i ni = total number of items
sampled in k samples
If equal sample sizes: If unequal sample sizes:
k
pp i
i
ii
n
pnp
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Computing Control Limits The upper and lower control limits for an p-
chart are
or
UCL = Average Proportion + 3 Standard Deviations LCL = Average Proportion – 3 Standard Deviations
3
3
pLCL
pUCL
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Standard Deviation of Subgroup Proportions
The estimate of the standard deviation for the subgroup proportions is
n
)p)(1p(s
p
If equal sample sizes: If unequal sample sizes:
where: = mean subgroup proportion
n = common sample sizep
Generally, is computed separately for each different sample size
ps
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Computing Control Limits The upper and lower control limits for the p-
chart are
(continued)
n
)p)(1p(pLCL
n
)p)(1p(pUCL
3
3
)s(pLCL
)s(pUCL
p
p
3
3
If sample sizes are equal, this becomes
Proportions are never negative, so if the calculated lower control limit is negative, set LCL = 0
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p-Chart Examples For equal sample sizes For unequal
sample sizes
UCL
LCL
UCL
LCL
p p
ps is constant since
n is the same for all subgroups
ps varies for each
subgroup since ni varies
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c-Chart Control chart for number of nonconformities
(occurrences) per sampling unit (an area of opportunity) Also a type of attribute chart
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
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Mean and Standard Deviationfor a c-Chart
The mean for a c-chart is
k
xc i
The standard deviation for a c-chart is
cs
where: xi = number of successes per sampling unit k = number of sampling units
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c-Chart Control Limits
ccLCL
ccUCL
3
3
The control limits for a c-chart are
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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
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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
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Constructing the c-Chart The mean and standard deviation are:
1.71437
0150312
k
xc i
1.30931.7143cs
2.2143(1.3093)1.7143c3cLCL
5.6423(1.3093)1.7143c3cUCL
The control limits are:
Note: LCL < 0 so set LCL = 0
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The completed c-ChartThe 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
UCL = 5.642
LCL = 0
Sample number1 2 3 4 5 6 7
c = 1.714
6
5
4
3
2
1
0