control charts - mba

8/13/2019 Control Charts - MBA

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Quality Control Charts


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Control Charts

Primary purpose of control charts is toindicate at a glance when productionprocesses might have changed sufficientlyto affect product quality.

If the indication is that product quality hasdeteriorated, or is likely to, then corrective istaken.

If the indication is that product quality isbetter than expected, then it is important tofind out why so that it can be maintained.

Use of control charts is often referred to as

statistical process control (SPC).


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Constructing Control Charts

Vertical axis provides the scale for the

sample information that is plotted on the

chart.

Horizontal axis is the time scale.

Horizontal center line is ideally determined

from observing the capability of theprocess.

Two additional horizontal lines, the lower

and upper control limits, typically are 3standard deviations below and above


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Constructing Control Charts

If the sample information falls within thelower and upper control limits, the qualityof the population is considered to be incontrol; otherwise quality is judged to beout of control and corrective actionshould be considered.

Two versions of control charts will be

examined Control charts for attributes

Control charts for variables


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Control Charts for Attributes

Inspection of the units in the sample is

performed on an attribute

(defective/non-defective) basis.

Information provided from inspecting a

sample of size n is the percent

defective in a sample, p, or the numberof units found to be defective in that

sample divided by n.


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Control Charts for Attributes

Although the distribution of sampleinformation follows a binomialdistribution, that distibution can beapproximated by a normal distribution

with a

mean of p

standard deviation of

The 3scontrol limits are

)/np(100p

)/np(100p3-/p

-


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Example: Attribute Control Chart

Every check cashed or deposited atState Bank of India must be encodedwith the amount of the check before it

can begin the clearing process. Theaccuracy of the check encodingprocess is of upmost importance. Ifthere is any discrepancy between theamount a check is made out for andthe encoded amount, the check isdefective.


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Twenty samples, each consisting of250 checks, were selected and

examined. The number of defective

checks found in each sample is shownbelow.

4 1 5 3 2 7 4 5 2 3

2 8 5 3 6 4 2 5 3 6


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The manager of the check encodingdepartment knows from past

experience that when the encoding

process is in control, an average of1.6% of the encoded checks are

defective.

She wants to construct a p chart with

3-standard deviation control limits.


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s

(1 ) .016(1 .016) .015744.007936

250 250p

p p

n

UCL = 3 =.016+3(.007936)= .039808 or 3.98%p

p s

LCL = 3 =.016-3(.007936)=-.007808= 0%p

p s


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0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0 5 10 15 20SampleProportion

p

Sam le Number

p Chart for State Bank of IndiaU


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Control Charts for Variables

Inspection of the units in the sample isperformed on a variable basis.

The information provided from inspecting

a sample of size n is:

Sample mean, x, or the sum of measurement

of each unit in the sample divided by n

Range, R, of measurements within the

sample, or the highest measurement in the

sample minus the lowest measurement in the

sample


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Control Charts for Variables

In this case two separate control chartsare used to monitor two different

aspects of the processsoutput:

Central tendency Variability

Central tendency of the output is

monitored using the x-chart. Variability of the output is monitored

using the R-chart.


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x-Chart

The central line is x, the sum of a

number of sample means collected

while the process was considered to bein control divided by the number of

samples.

The 3slower control limit is x - AR The 3supper control limit is x + AR

Factor A is based on sample size.

=

=


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R-Chart

The central line is R, the sum of a

number of sample ranges collected while

the process was considered to be in

control divided by the number ofsamples.

The 3slower control limit is D1

R.

The 3supper control limit is D2R.

Factors D1and D2 are based on sample

size.

3 C t l Ch t F t f


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3sControl Chart Factors for

Variables

Control Limit Factor Control Limit FactorSample for Sample Mean for Sample Range

Size n A D1 D2

2 1.880 0 3.267

3 1.023 0 2.575

4 0.729 0 2.282

5 0.577 0 2.116

0.308 0.223 1.777

15 0.223 0.348 1.65220 0.180 0.414 1.586

25 0.15310 0.459 1.541

Over 25 0.45+.001n 1.55-.0015n0.75(1/ )n


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Statistical Process Control


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Quality Control (QC)

Controlthe activity of ensuringconformance to requirements and

taking corrective action when

necessary to correct problems Importance

Daily management of processes

Prerequisite to longer-term improvements


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Designing the QC System

Quality Policy and Quality Manual Contract management, design control and

purchasing

Process control, inspection and testing

Corrective action and continual improvement

Controlling inspection, measuring and test

equipment (metrology, measurement system

analysis and calibration)

Records, documentation and audits


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Commonly Used Control

Charts

Variables data

x-bar and R-charts

x-bar and s-charts Charts for individuals (x-charts)

Attribute data

For defectives (p-chart, np-chart) For defects (c-chart, u-chart)


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Inspection/Testing Points

Receiving inspection

In-process inspection

Final inspection


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Receiving Inspection

Spot check procedures

100 percent inspection

Acceptance sampling


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Acceptance Sampling

Lot received for inspection

Sample selected and analyzed

Results compared with acceptance criteria

Accept the lot

Send to production

or to customer

Reject the lot

Decide on disposition


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In-Process Inspection

What to inspect? Key quality characteristics that are related

to cost or quality (customer requirements)

Where to inspect? Key processes, especially high-cost and

value-added

How much to inspect?All, nothing, or a sample

St ti ti l P C t l


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Statistical Process Control

(SPC)

A methodology for monitoring aprocess to identify special causes of

variation and signal the need to take

corrective action when appropriate SPC relies on control charts


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Common

Causes

Special Causes


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Histograms do

not take intoaccount changes

over time.

Control charts

can tell us

when aprocess

changes


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Control Chart Applications

Establish state of statisticalcontrol

Monitor a process and signalwhen it goes out of control

Determine process capability

C l U d C t l


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Commonly Used Control

Charts

Variables data

x-bar and R-charts

x-bar and s-charts Charts for individuals (x-charts)

Attribute data

For defectives (p-chart, np-chart)

For defects (c-chart, u-chart)


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SPC Implementation

Requirements

Top management commitment

Project champion

Initial workable projectEmployee education and training

Accurate measurement system

control charts - mba

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