SDA 3E Chapter 8

8/4/2019 SDA 3E Chapter 8

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2007 Pearson Education

Chapter 8: Statistical QualityControl


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Variation Common causes variation

resulting from process factors suchas people, materials, methods, andmeasurement systems

Special causes

variation thatoccurs sporadically and can beidentified or explained


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Statistical Process Control When only common causes of variation

are present, a process is in control.

If special causes of variation occur, theprocess is out of control.

SPC is focused on identifying when

special causes are present, or if aprocess is in control.


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SPC Methodology1. Select a sample of observations from a

process

2. Measure a quality characteristic3. Record data

4. Calculate key statistics

5. Plot statistics on a control chart

6. Examine the chart for out-of-controlconditions

7. Determine the cause and take correctiveaction


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Run Charts and Control Charts Run chart a line chart where the

independent variable is time and the

dependent variables is the value of asample statistic

Control chart a run chart with control

limits that describe limits of commoncause variation


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Control Chart Structure


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x- and R-charts

Thex-chart monitors the centering of aprocess over time as measured by the

mean of each sample

The R-chart monitors the variability indata as measured by the range of each

sample


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Example


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Run Chart of Sample Means


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Run Chart of Sample Ranges


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PHStat Tool: Control Charts PHStat menu > Control Charts > R &

Xbar Charts

Enter sample size andspecify data range forranges

Select type of chart; for

R and Xbar, specify datarange for means

Note: You must firstcompute ranges and

means in your worksheet


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Example: R-Chart


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Example:x-Chart


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In-Control Indicators No points outside control limits

Number of points above and below

center line about the same Points fall randomly above and below

center line

No steady upward or downward trends Most points, but not all are near the

center line; only a few are close tocontrol limits


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Out-of-Control Indicator: Shift


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Out-of-Control Indicator:

Cycles


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Trend


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Hugging the Center Line


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Hugging the Control Limits


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Illustration of Mixture


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p-Chart p-Chart monitors the fraction

nonconforming (fraction defective) for

attribute data Control limits

n

pps

)1(

UCLp = p + 3s LCLp = p - 3s


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PHStatTool: p-Chart PHStat menu > Control Charts >

p-Chart

Enter data range

Specify sample size;if variable, enterrange of data


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Example: Room Inspection.xls


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PHStatp-Chart Output


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p-Charts With Variable Sample

Sizes One approach: compute the average

sample size and use this for calculating

the standard deviation

Acceptable as long as the sample sizesfall within 25 percent of the average.


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Statistical Issues in Control

Chart Design Selection of sample data

Rational subgroups

Sample size

Size influences the ability to detectdifferent size shifts in processes

Frequency of sampling

Economic trade-offs


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Process Capability Analysis Compare the distribution of process

output to design specifications when

only common causes are present. Process capability is measured by the

proportion of output that can be

produced within design specifications.


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Capable Process


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Marginally Capable Process


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Incapable Process


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Process Capability Index

s

LSLUSLCp

6

Cp is the ratio of the specification range to thenatural variability of the process as measured bythe standard deviation


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Example: Syringe Data.xls Specifications of syringe lengths are 4.950

0.030 inches

Cp= (4.98 - 4.92)/(0.039) = 1.54

SDA 3E Chapter 8

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