Control charts

Control Charts

1. Introduction

Introduction

Quality control charts, are graphs on which the quality of the product is plotted as the manufacturing is actually proceeding.

By enabling corrective actions to be taken at the earliest possible moment and avoiding unnecessary corrections, the charts help to ensure the manufacture of uniform products.

History of Control Chart

Mr. Shewart, an American, has been credited with the invention of control charts for variable and attribute data in the 1920s, at the Bell Telephone Industries.

The term ‘Shewart Control Charts’ is in common use.

Dynamic Picture of Process

Plotting graph, charting and presenting the data as a picture is common to process control method, used throughout the manufacturing and service industries.

Converting data into a picture is a vital step towards greater and quicker understanding of the process.

Confidence While Control Charting

Control charting enables everyone to make

decision and to know the degree of

confidence with which the decisions are

made. There may be some margin of error.

No technique, even 100% automated

inspection, can guarantee the validity of the

result; there is always some room to doubt.

Control Charts

Statistically based control chart is a device intended to be used

- at the point of operation- by the operator of that process- to asses the current situation- by taking sample and plotting

sample result

To enable the operator to decide about the process.

What Control Chart Does?

It graphically, represents the output of

the process.

And

Uses statistical limits and patterns of

plot, for decision making

Analogy to Traffic Signal

A control chart is like a traffic signal, the operation of which is based on evidence from samples taken at random intervals.

A control chart is like a traffic signal, the operation of which is based on evidence from samples taken at random intervals.

Analogy to Traffic Signal

GoNo action on Process

Wait and Watch

StopInvestigate/Adjust

Decision About The Process

Go

To let the process continue to run without any adjustment.

This means only common causes are present.

Decision About the Process

Wait and watch

Be careful and seek for more information

This is the case where presence of trouble is possible

Decision About the Process

Stop

Take action ( Investigate/Adjust )

This means that there is practically no doubt a special cause has crept in the system. Process has wandered and corrective actions must be taken, otherwise defective items will be produced.

2. Why control charts

Why Control Chart?

To ensure that the output of the process is ‘Normal’

Whether Output is Normal?

Both histogram and control chart can tell us whether

the output is normal? However,

Histogram views the process as history ,

as the entire output together.

Control chart views the process in real time,

at different time intervals as the process

progresses.

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6Fre

quen

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Histogram: a History of Process Output

Control Chart Views Process in Real Time

UCLx

Target

UCLr

Time Intervals

Ran

ge

Mea

n

LCLx

Target

Output of the process in real time

Why Control Chart?

It helps in finding

Is there any change in location of process

mean in real time?

Change in Location of Process Mean

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Process with mean at Target

Process with mean at more

than target

Process with mean at less than target

Why Control Chart?

It helps in finding

Is there any change in the

spread of the process in real

time?

Change in Spread of Process

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Larger spread dueto special causes

Spread dueto common causes

Why Control Chart?

To keep the cost of production minimum

Since the control chart is maintained in real time, and gives us a signal that some special cause has crept into the system, we can take timely action. Timely action enables us to prevent manufacturing of defective. Manufacturing defective items is non value added activity; it adds to the cost of manufacturing, therefore must be avoided.

By maintaining control chart we avoid 100% inspection, and thus save cost of verification.

Why Control Chart?

Pre-requisite for process capability studies

Process capability studies, are based on premises that the process during the study was stable i.e. only common causes were present. This ensures that output has normal distribution. The stability of the process can only be demonstrated by maintaining control chart during the study.

Why Control Chart?

Decision in regards to production process

Control chart helps in determining whether we should :

- let the process to continue without adjustment

- seek more information

- stop the process for investigation/adjustment.

3. Basic steps for control charting

Basic Steps for Control Charts

Step No. 1

Identify quality characteristics of product or process that affects “fitness for use”.

Maintaining control chart is an expensive activity. Control charts should be maintained only for critical quality characteristics. Design of Experiments is one of the good source to find the critical quality characteristics of the process.


Step No . 2

Design the sampling plan and decide method of its measurement.

At this step we decide, how many units will be in a sample and how frequently the samples will be taken by the operator.


Step No. 3

Take samples at different intervals and plot statistics of the sample measurements on control chart.

Mean, range, standard deviation etc are the statistics of measurements of a sample. On a mean control chart, we plot the mean of sample and on a range control chart, we plot the range of the sample.


Step No. 4

Take corrective action - when a signal for significant change in process characteristic is received.

Here we use OCAP (Out of Control Action Plan) to investigate, as why a significant change in the process has occurred and then take corrective action as suggested in OCAP, to bring the process under control.

Summary of Control Chart Techniques

Quality characteristics

Sampling procedure

Plotting of statistics

Corrective action

In ‘Control Chart Technique’ we have:

4. Typical control charts

Elements of Typical Control Chart

1. Horizontal axis for sample number

2. Vertical axis for sample statistics e.g.

mean, range, standard deviation of sample.

3. Target Line

4. Upper control line

5. Upper warning line

6. Lower control line

7. Lower warning line

8. Plotting of sample statistics

9. Line connecting the plotted statistics

Elements of Typical Control Chart

1 2 3 4 5Sample Number

Upper control line

Target

Lower control line

Upper warning line

Lower warning line

Sam

ple

Sta

tistic

s

5. Types of control chart

Types of Control Chart

We have two main types of control charts. One for variable data and the other for attribute data.

Since now world-wide, the current operating level is ‘number of parts defective per million parts produced’, aptly described as ‘PPM’; control charts for ‘attribute data’ has no meaning. The reason being that the sample size for maintaining control chart at the ‘PPM’ level, is very large, perhaps equal to lot size, that means 100% inspection.

Most Commonly Used Variable Control Charts

Following are the most commonly used variable control charts:

To track the accuracy of the process- Mean control chart or x-bar chart

To track the precision of the process- Range control chart

Most Common Type of Control Chart for Variable Data

VariableControlChart

VariableControlChart

For tracking Accuracy

For tracking Accuracy

For tracking Precision

For tracking Precision

Mean control chart

Mean control chart

Rangecontrol chart

Rangecontrol chart

6. Concepts behind control charts

Understanding effect of shift of process mean

Case When Process Mean is at Target

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Target ProcessMean

Chances of getting a reading beyond U & L is almost nil

42

UL

- 3 s +3 s

U - L = 6 s

Case - Small Shift of the Process Mean

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Target

ProcessMean

Chances of getting a reading outside U is small

Small shift in process

42

Shaded area shows the

probability of getting

a reading beyond U

UL

U-L = 6 s

ProcessMean

Case - Large Shift of the Process Mean

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Target

Chances of getting a reading outside U is large

Large shift in process

42

Shaded area shows the

probability of getting

a reading beyond U

UL

U-L = 6 s

Summary of Effect of Process Shift

When there is no shift in the process nearly all the

observations fall within -3 s and + 3 s.

When there is small shift in the mean of process some

observations fall outside original -3 s and +3 s zone.

Chances of an observation falling outside original -3 s and +

3 s zone increases with the increase in the shift of process

mean.

Conclusion from Normal Distribution

When an observation falls within original +3 s and -3 s zone of mean of a process, we conclude that there is no shift in the mean of process. This is so because falling of an observation between these limits is a chance.

When an observation falls beyond original +3 s and -3 s zone of process mean, we conclude that there is shift in location of the process

7. Distribution of population vs

Distribution of mean

Distribution of Mean of Samples

Since on the control charts for accuracy we plot and watch

the trend of the means and ranges of the samples, it is

necessary that we should understand the behaviour of

distribution of mean of samples.

Distribution of Averages of Samples

Suppose we have a lot of 1000 tablets, and let us say, weight of the tablets follows a normal distribution having a standard deviation, s.

Let us take a sample of n tablets. Calculate mean of the sample and record it. Continue this exercise of taking samples, calculating the mean of samples and recording, 1000 times.

The mean of samples shall have normal distribution with standard deviation, Sm = (s÷ n). Distribution of population and ‘means of sample’ shall have same means.

Distribution - Population Vs Sample Means

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Quality Characteristics

Distribution of population(standard deviation = s

Distribution of means of samples

[standard deviation = (s÷ n)]

Control and Warning Limits for Mean Control Chart

If we know the standard deviation of the population, say sand the number of units in a sample, say n; then the control and warning limits are calculated as follows:

If desired target of the process is T, then

Upper control limit, UCL = T + 3 (s÷ n)

Upper warning limit. UWL = T + 2 (s÷ n)

Lower control limit, LCL = T - 3 (s÷ n)

Lower warning limit, LWL = T - 2 (s÷ n)

Control Limits for Mean Control Chart

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Sample Number

UCL

Target

LCL

Distribution of mean of samples

3 (s ÷ n)UWL

LWL

2 (s ÷ n)

2 (s ÷ n)3 (s÷ n)

8. Flow Chart for Establishing Control Chart

Decide subgroup size

Record observations

Find mean and range of each subgroup

Calculate mean range, R

Start

Flow Chart for Establishing Control Chart

Is any sub-group mean or range

out side the controllimit ?

Drop thatGroup

UCLx = T + A2 x RLCLx = T - A2 x R

UCLr = D4 x RLCLr = D3 x R

Yes

No

Flow Chart for Control Chart

Select suitable scale formean control chart and

range control chart

Draw Lines forTarget, UCL, UWL, LCL & LWL for mean

Mean range, UCL , UWL, LCL & LWL for range

Stop

9. Interpreting control charts

Interpreting Control Chart

The control chart gets divided in three zones.

Zone - 1 If the plotted point falls in this zone, do not make any adjustment, continue with the process.

Zone - 2 If the plotted point falls in this zone then special cause may be present. Be careful watch for plotting of another sample(s).

Zone - 3 If the plotted point falls in this zone then special cause has crept into the system, and corrective action is required.

Zones for Mean Control Chart

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Sample Number

UCL

Target

LCL

UWL

LWL

Zone - 3

Sa

mp

le M

ean

Zone - 2

Zone - 3

Zone - 2

Zone - 1

Action

Action

Warning

Warning

Continue

ContinueZone - 1

Interpreting Control Charts

Since the basis for control chart theory follows the normal distribution, the same rules that governs the normal distribution are used to interpret the control charts. These rules include:

- Randomness.- Symmetry about the centre of the distribution.- 99.73% of the population lies between - 3 s of and + 3 s the centre line.- 95.4% population lies between -2 s and + 2 s of the centre line.


If the process output follows these rules, the process is

said to be stable or in control with only common causes of

variation present. If it fails to follow these rules, it may be

out of control with special causes of variation present.

These special causes must be found and corrected.


A single point above or below the control limits.

Probability of a point falling outside the control limit is less than 0.14%. This pattern may indicate:

- a special cause of variation from a material, equipment, method, operator etc.- mismeasurement of a part or parts.- miscalculated or misplotted data point.


UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tis

tic

s

UWL

LCL

Target

LWL

One point outsidecontrol limit


Seven consecutive points are falling on one side of the centre line.

Probability of a point falling above or below the centre line is 50-50. The probability of seven consecutive points falling on one side of the centre line is 0.78% ( 1 in 128)

This pattern indicates a shift in the process output from changes in the equipment, methods, or material or shift in the measurement system.


UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tis

tic

s

UWL

LCL

Target

LWL

Seven consecutive points on one side of the centre line


Two consecutive points fall between warning limit and corresponding control limit.

In a normal distribution, the probability of two consecutive points falling between warning limit and corresponding control limit is 0.05% (1 in 2000).

This could be due to large shift in the process, equipment, material, method or measurement system.


UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tis

tic

s

UWL

LCL

Target

LWL

Two consecutive points between warning limit and corresponding control limit


Two points out of three consecutive points fall between warning limit and corresponding control limit.

This could be due to large shift in the process, equipment, material, method or measurement system.


UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tis

tic

s

UWL

LCL

Target

LWL

Two points out of three consecutive points between warning limit and corresponding control limit


A trend of seven points in a row upward or downward demonstrates non-randomness.

This happens in the following cases:

- Gradual deterioration or wear in equipment.- Improvement or deterioration in technique.- Operator fatigue.


UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tis

tic

s

UWL

LCL

Target

LWL

Seven consecutive points having upward trend


UCL

1 2 3 4 5 6 7 8

Sample Number

Sta

tis

tic

s

UWL

LCLLCL

Target

LWL

Seven consecutive points having downward trend

Control charts

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