© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

KR: Chapter 7

Statistical Process Control

Chapter OutlineIntroduction

Process control vs. acceptance sampling

Statistical Quality Control

Acceptance sampling

Process Control

Attributes Variables

Statistical Quality Control for Acceptance Sampling and for Process Control.

Attributes Variables

Ch 4 - 2© 2000 by Prentice-Hall Inc

Russell/Taylor Oper Mgt 3/e

Quality Control Approaches

Statistical process control (SPC) Monitors production process to

prevent poor quality

Acceptance samplingInspects random sample of product

to determine if a lot is acceptable

Chapter OutlineIntroduction

Process control vs. acceptance sampling

Sources of process variations

Types of Variations

Common CauseRandom ChronicSmallSystem problemsMgt controllableProcess improvementProcess capability

Special CauseSituationalSporadicLargeLocal problemsLocally controllableProcess controlProcess stability

Variation from Common Causes

Variation from Special Causes

Chapter OutlineIntroduction

Process control vs. acceptance sampling

Sources of process variationThe inspection process

Quality measures

Ch 4 - 5© 2000 by Prentice-Hall Inc

Russell/Taylor Oper Mgt 3/e

Types Of Data

Attribute dataProduct characteristic evaluated with a discrete choice

Good/bad, yes/no

Variable dataProduct characteristic that can be measured

Length, size, weight, height, time, velocity

Chapter OutlineIntroduction

Process control vs. acceptance sampling

Sources of process variationThe inspection process

Quality measuresSampling vs. screening

Sampling vs. ScreeningSampling

When you inspect a subset of the population

ScreeningWhen you inspect the whole population

The costs consideration

Chapter OutlineIntroduction

Process control vs. acceptance sampling

Sources of process variationThe inspection process

Quality measuresSampling vs. screening

Control charts

Ch 4 - 3© 2000 by Prentice-Hall Inc

Russell/Taylor Oper Mgt 3/e

Statistical Process Control

Take periodic samples from processPlot sample points on control chartDetermine if process is within limitsPrevent quality problems

Control ChartsFunction of control chartsTheoretical foundation of control chartsControl charts for variables:

Mean (x-bar) chartRange (R) chart

Control charts for attributep-chartc-chart

Common CausesCommon Causes

Grams(a) Location

Average

Figure 7.2

Assignable CausesAssignable Causes

(a) LocationGrams

Average

Figure 7.2

Assignable CausesAssignable Causes

(b) SpreadGrams

Average

Figure 7.2

The NormalThe NormalDistributionDistribution

Mean

= Standard deviation

Figure 7.5

The NormalThe NormalDistributionDistribution

Mean

68.26%

-1 +1

= Standard deviation

Figure 7.5

The NormalThe NormalDistributionDistribution

-2 -1 +1 +2 Mean

68.26%95.44%

= Standard deviation

Figure 7.5

The NormalThe NormalDistributionDistribution

-3 -2 -1 +1 +2 +3Mean

68.26%95.44%99.74%

= Standard deviation

Figure 7.5

Control ChartsControl Charts

UCL

Nominal

LCL

1 2 3SamplesFigure 7.6

Control ChartsControl Charts

UCL

Nominal

LCL

1 2 3SamplesFigure 7.6

Control ChartsControl Charts

UCL

Nominal

LCL

Assignable causes likely

1 2 3SamplesFigure 7.6

X-R CHART INTERPRETATION“Out-of-Control” X

I. OUTSIDE THE CONTROL LIMITS

Rule: The process is “out-of-control” anytime an X is outside the control limits.

UCL

LCL

x

UCL

x

LCL

Process “in-control” for averages

Process “out-of-control” for averages

(a point beyond the control limits)

X-R CHART INTERPRETATION“Out-of-Control” X

II. RUNS

Rule: The existence of seven or more consecutive averages (X’s) above the process average (X), or seven or more consecutive averages (X’s) below the process average (X), represents an “out-of-control” condition.

UCL

LCL

x

Process not in control for averages

(long runs both above and below the average)

X-R CHART INTERPRETATION“Out-of-Control” X

II. RUNS

Rule: Seven or more averages (X’s) constantly moving either up or down indicate an “out-of control” situation

UCL

LCL

x

Process “out-of-control” for averages

(long runs up)

X-R CHART INTERPRETATION“Out-of-Control” X

III. PATTERNS

Rule: The pattern of X’s between the control limits should follow a normal distribution

If we look at the middle third between our control limits, we should expect to find two-thirds of our X’s to be within this area.

UCL

LCL

x

Process “out-of-control” for averages

(points too close to the control limits))

Middle third

X-R CHART INTERPRETATION“Out-of-Control” X

III. PATTERNS

Rule: The pattern of X’s between the control limits should follow a normal distribution

If we look at the middle third between our control limits, we should expect to find two-thirds of our X’s to be within this area.

UCL

LCL

x

Process “out-of-control” for averages

(points too close to the process average)

Middle third

Chapter OutlineIntroduction

Process control vs. acceptance sampling

Sources of process variationThe inspection process

Quality measuresSampling vs. screening

Control chartsProcess capability

Process Control

Process Capability

Ch 4 - 43© 2000 by Prentice-Hall Inc

Russell/Taylor Oper Mgt 3/e

Process Capability

Process cannot meet specifications Process can meet specifications

Process capability exceeds specifications

PR

OC

ES

S

PR

OC

ES

S

PR

OC

ES

S

Naturalvariation

limits

Naturalvariation

limits

Naturalvariation

limits

Des

ign

spec

ifica

tions

Des

ign

spec

ifica

tions

Designspecifications

Process CapabilityProcess Capability

Nominalvalue

800 1000 1200 Hours

Upperspecification

Lowerspecification

Process distribution

(a) Process is capableFigure 7.13

Process CapabilityProcess Capability

Lowerspecification

Mean

Upperspecification

Two sigma

Nominal value

Figure 7.14

Process CapabilityProcess Capability

Lowerspecification

Mean

Upperspecification

Four sigma

Two sigma

Nominal value

Figure 7.14

Process CapabilityProcess Capability

Lowerspecification

Mean

Upperspecification

Six sigma

Four sigma

Two sigma

Nominal value

Figure 7.14

Sample Means and theSample Means and theProcess DistributionProcess Distribution

425 Grams

Mean

Processdistribution

Distribution ofsample means

Figure 7.4