Quality Control Pertemuan 12

Mata kuliah : J0444 - Manajemen OperasionalTahun : 2010

Learning Objectives

• List and briefly explain the elements of the control process.

• Explain how control charts are used to monitor a process, and the concepts that underlie their use.

• Use and interpret control charts. • Use run tests to check for nonrandomness in

process output. • Assess process capability.

Phases of Quality Assurance

Acceptancesampling

Processcontrol

Continuousimprovement

Inspection of lotsbefore/afterproduction

Inspection andcorrective

action duringproduction

Quality builtinto theprocess

The leastprogressive

The mostprogressive

Inspection

• How Much/How Often• Where/When • Centralized vs. On-site

Inputs Transformation Outputs

Acceptancesampling

Processcontrol

Acceptancesampling

Where to Inspect in the Process

• Raw materials and purchased parts

• Finished products

• Before a costly operation

• Before an irreversible process

• Before a covering process

Examples of Inspection Points

Type ofbusiness

Inspectionpoints

Characteristics

Fast Food CashierCounter areaEating areaBuildingKitchen

AccuracyAppearance, productivityCleanlinessAppearanceHealth regulations

Hotel/motel Parking lotAccountingBuildingMain desk

Safe, well lightedAccuracy, timelinessAppearance, safetyWaiting times

Supermarket CashiersDeliveries

Accuracy, courtesyQuality, quantity

•Statistical Process Control: Statistical evaluation of the output of a process during production

•Quality of Conformance:A product or service conforms to specifications

Statistical Control

Control Chart

• Control Chart– Purpose: to monitor process output to see

if it is random

– A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means)

– Upper and lower control limits define the range of acceptable variation

Control Chart

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

UCL

LCL

Sample number

Mean

Out ofcontrol

Normal variationdue to chance

Abnormal variationdue to assignable sources

Abnormal variationdue to assignable sources

Statistical Process Control

• The essence of statistical process control is to assure that the output of a process is random so that future output will be random.

Produce GoodProvide Service

Stop Process

Yes

NoAssign.

Causes?Take Sample

Inspect Sample

Find Out WhyCreate

Control Chart

Start

Statistical Process Control Steps

Statistical Process Control

• Variations and Control– Random variation: Natural variations in the

output of a process, created by countless minor factors

– Assignable variation: A variation whose source can be identified

Sampling Distribution

Samplingdistribution

Processdistribution

Mean

Normal Distribution

Mean

95.44%

99.74%

Standard deviation

Control Limits

Samplingdistribution

Processdistribution

Mean

Lowercontrol

limit

Uppercontrol

limit

SPC Errors

• Type I error– Concluding a process is not in control

when it actually is.

• Type II error– Concluding a process is in control when it

is not.

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Type I and Type II Errors

In control Out of control

In control No Error Type I error

(producers risk)

Out of control

Type II Error

(consumers risk)

No error

Type I Error

Mean

LCL UCL

/2 /2

Probabilityof Type I error

Observations from Sample Distribution

Sample number

UCL

LCL

1 2 3 4

Control Charts for Variables

• Mean control charts

– Used to monitor the central tendency of a process.

– X bar charts

• Range control charts

– Used to monitor the process dispersion

– R charts

Variables generate data that are Variables generate data that are measuredmeasured..

Mean and Range Charts

UCL

LCL

UCL

LCL

R-chart

x-Chart Detects shift

Does notdetect shift

(process mean is shifting upward)

SamplingDistribution

x-Chart

UCL

Does notreveal increase

Mean and Range Charts

UCL

LCL

LCL

R-chart Reveals increase

(process variability is increasing)

SamplingDistribution

Control Chart for Attributes

• p-Chart - Control chart used to monitor the proportion of defectives in a process

• c-Chart - Control chart used to monitor the number of defects per unit

Attributes generate data that are Attributes generate data that are countedcounted..

Use of p-Charts

• When observations can be placed into two categories.– Good or bad– Pass or fail– Operate or don’t operate

• When the data consists of multiple samples of several observations each

Use of c-Charts

• Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted.– Scratches, chips, dents, or errors per item– Cracks or faults per unit of distance– Breaks or Tears per unit of area– Bacteria or pollutants per unit of volume– Calls, complaints, failures per unit of time

Use of Control Charts

• At what point in the process to use control charts

• What size samples to take

• What type of control chart to use

– Variables

– Attributes

Run Tests

• Run test – a test for randomness

• Any sort of pattern in the data would suggest a non-random process

• All points are within the control limits - the process may not be random

Nonrandom Patterns in Control charts

• Trend• Cycles• Bias• Mean shift• Too much dispersion

Counting Above/Below Median Runs (7 runs)

Counting Up/Down Runs (8 runs)

U U D U D U D U U D

B A A B A B B B A A B

Counting RunsCounting Runs

NonRandom Variation

• Managers should have response plans to investigate cause

• May be false alarm (Type I error)• May be assignable variation

• Tolerances or specifications

– Range of acceptable values established by engineering design or customer requirements

• Process variability

– Natural variability in a process

• Process capability

– Process variability relative to specification

Process Capability

Process Capability

LowerSpecification

UpperSpecification

A. Process variability matches specifications

LowerSpecification

UpperSpecification

B. Process variability well within specifications

LowerSpecification

UpperSpecification

C. Process variability exceeds specifications

Process Capability Ratio

Process capability ratio, Cp = specification widthprocess width

Upper specification – lower specification6

Cp =

3

X-UTLor

3

LTLXmin=C pk

If the process is centered use Cp

If the process is not centered use Cpk

Limitations of Capability Indexes

1. Process may not be stable

2. Process output may not be normally distributed

3. Process not centered but Cp is used

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Example

MachineStandard Deviation

Machine Capability Cp

A 0.13 0.78 0.80/0.78 = 1.03

B 0.08 0.48 0.80/0.48 = 1.67

C 0.16 0.96 0.80/0.96 = 0.83

Cp > 1.33 is desirableCp = 1.00 process is barely capableCp < 1.00 process is not capable

The End