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Chapter 14Chapter 14Chapter 14Chapter 14
Statistical Statistical
ProcessProcess
ControlControl
Statistical Statistical Quality Quality ControlControl
Acceptance sampling
Process Control
Attributes Variables
Statistical Quality Control for Acceptance Sampling and for Process Control.
Attributes Variables
Statistical Statistical Process ControlProcess Control
Statistical process controlStatistical process control is the is the application of statistical techniques to application of statistical techniques to determine whether a process is determine whether a process is delivering what the customer wants.delivering what the customer wants.
Acceptance samplingAcceptance sampling is the is the application of statistical techniques to application of statistical techniques to determine whether a quantity of material determine whether a quantity of material should be accepted or rejected based on should be accepted or rejected based on the inspection or test of a sample.the inspection or test of a sample.
Types of VariationsTypes of Variations
Common CauseCommon Cause Random Random ChronicChronic SmallSmall System problemsSystem problems Mgt controllableMgt controllable Process Process
improvementimprovement Process capabilityProcess capability
Special CauseSpecial Cause SituationalSituational SporadicSporadic LargeLarge Local problemsLocal problems Locally controllableLocally controllable Process controlProcess control Process stabilityProcess stability
Variation from Common Variation from Common CausesCauses
Variation from Special Variation from Special CausesCauses
Causes of VariationCauses of Variation
Two basic categories of variation in output include Two basic categories of variation in output include common causescommon causes and and assignable causesassignable causes..
CommonCommon causescauses are the purely random, are the purely random, unidentifiable sources of variation that are unidentifiable sources of variation that are unavoidable with the current process.unavoidable with the current process.
– If If processprocess variabilityvariability results solely from common causes results solely from common causes of variation, a typical assumption is that the distribution is of variation, a typical assumption is that the distribution is symmetric, with most observations near the center.symmetric, with most observations near the center.
AssignableAssignable causescauses of variation are any variation- of variation are any variation-causing factors that can be identified and eliminated, causing factors that can be identified and eliminated, such as a machine needing repair.such as a machine needing repair.
Assignable CausesAssignable Causes
The red distribution line below indicates that the process produced a preponderance of the tests in less than average time. Such a distribution is skewed, or no longer symmetric to the average value.
A process is said to be in statistical control when the location, spread, or shape of its distribution does not change over time.
After the process is in statistical control, managers use SPC procedures to detect the onset of assignable causes so that they can be eliminated.
Location Spread Shape
© 2007 Pearson Education
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Statistical Process Control Statistical Process Control (SPC)(SPC)
A methodology for monitoring a A methodology for monitoring a process to identify special causes process to identify special causes of variation and signal the need of variation and signal the need to take corrective action when to take corrective action when appropriateappropriate
SPC relies on SPC relies on control chartscontrol charts
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Control Chart Control Chart ApplicationsApplications
Establish state of statistical Establish state of statistical controlcontrol
Monitor a process and signal Monitor a process and signal when it goes out of controlwhen it goes out of control
Determine process capabilityDetermine process capability
Key IdeaKey IdeaCapability and ControlCapability and Control
Process capability calculations make little sense if the process is not in statistical control because the data are confounded by special causes that do not represent the inherent capability of the process.
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Capability Versus ControlCapability Versus Control
Control
Capability
Capable
Not Capable
In Control Out of Control
IDEAL
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Commonly Used Control Commonly Used Control ChartsCharts
Variables dataVariables data– x-bar and R-chartsx-bar and R-charts– x-bar and s-chartsx-bar and s-charts– Charts for individuals (x-charts)Charts for individuals (x-charts)
Attribute dataAttribute data– For “defectives” (p-chart, np-chart)For “defectives” (p-chart, np-chart)– For “defects” (c-chart, u-chart)For “defects” (c-chart, u-chart)
Developing Control Developing Control ChartsCharts
1.1. PreparePrepare– Choose measurementChoose measurement– Determine how to collect data, sample Determine how to collect data, sample
size, and frequency of samplingsize, and frequency of sampling– Set up an initial control chartSet up an initial control chart
2.2. Collect DataCollect Data– Record dataRecord data– Calculate appropriate statisticsCalculate appropriate statistics– Plot statistics on chartPlot statistics on chart
Next StepsNext Steps
3.3. Determine trial control limitsDetermine trial control limits– Center line (process average)Center line (process average)– Compute UCL, LCLCompute UCL, LCL
4.4. Analyze and interpret resultsAnalyze and interpret results– Determine if in controlDetermine if in control– Eliminate out-of-control pointsEliminate out-of-control points– Recompute control limits as Recompute control limits as
necessarynecessary
Key IdeaKey IdeaInterpreting Control ChartsInterpreting Control Charts
When a process is in statistical control, the points on a control chart fluctuate randomly between the control limits with no recognizable pattern.
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Typical Out-of-Control Typical Out-of-Control PatternsPatterns
Point outside control limitsPoint outside control limits Sudden shift in process averageSudden shift in process average CyclesCycles TrendsTrends Hugging the center lineHugging the center line Hugging the control limitsHugging the control limits InstabilityInstability
Shift in Process AverageShift in Process Average
Identifying Potential Identifying Potential ShiftsShifts
CyclesCycles
TrendTrend
Final StepsFinal Steps
5.5. Use as a problem-solving Use as a problem-solving tooltool
– Continue to collect and plot Continue to collect and plot datadata
– Take corrective action when Take corrective action when necessarynecessary
6.6. Compute process capabilityCompute process capability
Key IdeaKey IdeaProcess Monitoring and ControlProcess Monitoring and Control
Control charts indicate when to take action, and more importantly, when to leave a process alone.
Spreadsheet Template Spreadsheet Template
Special Variables Control Special Variables Control ChartsCharts
x-chart for individualsx-chart for individuals
Key IdeaKey IdeaCharts for IndividualsCharts for Individuals
Control charts for individuals offer the advantage of being able to draw specifications on the chart for direct comparison with the control limits.
Charts for AttributesCharts for Attributes
Fraction nonconforming (p-chart)Fraction nonconforming (p-chart)– Fixed sample sizeFixed sample size– Variable sample sizeVariable sample size
np-chart for number nonconformingnp-chart for number nonconforming
Charts for defectsCharts for defects– c-chartc-chart– u-chartu-chart
Key IdeaKey IdeaChoosing between C- & U-chartsChoosing between C- & U-charts
Confusion often exists over which chart is appropriate for a specific application, because the c- and u-charts apply to situations in which the quality characteristics inspected do not necessarily come from discrete units.
Control Chart FormulasControl Chart Formulas
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Control Chart SelectionControl Chart Selection
Quality Characteristicvariable attribute
n>1?
n>=10 or computer?
x and MRno
yes
x and s
x and Rno
yes
defective defect
constant sample size?
p-chart withvariable samplesize
no
p ornp
yes constantsampling unit?
c u
yes no
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Control Chart Design Control Chart Design IssuesIssues
Basis for samplingBasis for sampling Sample sizeSample size Frequency of samplingFrequency of sampling Location of control limitsLocation of control limits
Key IdeaKey Idea
In determining the method of sampling, samples should be chosen to be as homogeneous as possible so that each sample reflects the system of common causes or assignable causes that may be present at that point in time.
Key IdeaKey Idea
In practice, samples of about five have been found to work well in detecting process shifts of two standard deviations or larger. To detect smaller shifts in the process mean, larger sample sizes of 15 to 25 must be used.
Economic TradeoffsEconomic Tradeoffs
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Pre-ControlPre-Control
nominal value
Green Zone
Yellow Zones
RedZone
RedZone
LTL UTL
Key IdeaKey Idea
Pre-control is not an adequate substitute for control charts and should only be used when process capability is no greater than 88 percent of the tolerance, or equivalently, when Cp is at least 1.14. If the process mean tends to drift, then Cp should be higher.