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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

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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.