Seven quality tools training is incomplete without learning of control charts. Control charts help to control the process with in the set control limits. Control charts are mainly two types; Mean Chart and Range Chart. Mean chart showcase the process data complied by the designated person and signal when the data go beyond the control limits. Every process has variation and due to this variation data get fluctuated. This fluctuation shown on the mean and range chart by data points. The causes of fluctuation in the data are assignable and common causes. Due to common causes data fluctuated around the average of the data but due to assignable cause data go beyond the control limits. When data go beyond the control limits control charts warn the operator that something is going wrong in the process and need to special attention. Mean chart is the spread of the mean values of the samples around the mean line. Range chart is spread of the range of samples around the mean line of range.

1. SEVEN QC TOOLS TRAINING
Control Charts
Mean Chart and Range Chart

2. SEVEN QC TOOLS TRAINING: CONTROL CHARTS
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Introduction
 Control charts are the tools which work to control the process variation and show an indication when the data go beyond the control limits.
 Variation in any process is inevitable.
 This variation comes in the process due to two types of causes namely Assignable and Common causes.
Causes of Variation
Assignable Causes
Common Causes

3. SEVEN QC TOOLS TRAINING: CONTROL CHARTS
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 Data go beyond the control limits for assignable causes which needs immediate corrective action to control the process within control limits.

4. SEVEN QC TOOLS TRAINING: CONTROL CHARTS
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Mean Chart
 Mean Chart is the graphical presentation of the data around the mean line, between the upper and lower control limits.
 Mean is mathematically shown as ̅ (X bar) therefore it is also called bar chart.

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Why Mean Chart?
 Mean chart maintain the accuracy of the data.
 Accuracy can be understood by closeness of mean value to its target value.
 Accuracy suffers as much as the mean value distant from its target value.

6. SEVEN QC TOOLS TRAINING: CONTROL CHARTS
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Calculation For Mean Chart
 First collect the data for different samples.
 Calculate the mean ( ̅ for different sample data.
 Now calculate the mean of means ( ̿ for given sample data this serve as the mean line or central line on control chart.
 Calculate the standard deviation.
 Calculate the upper and lower control limits.

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Upper and Lower Control Limits
 Upper and lower control limits are given below
̿ ̿
 Std. Dev. can be calculated as below
√Σ( ̅ ̿ )

8. SEVEN QC TOOLS TRAINING: CONTROL CHARTS
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Construction of Mean Chart
 Draw the X-Axis and Y-Axis on the graph paper.
 Take sample no. on X-Axis.
 Take Mean values of samples on Y-Axis.
 Draw the mean line parallel to X-Axis.
 Draw the lines at upper control limit and lower control limit parallel to X-Axis.
 Now make a graph between Mean values of respective sample no.
 Make a line graph and analyze it.

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Range Chart
 Range Chart is the graphical presentation of the data around the mean line of range of different sample data.
 Range is mathematically shown as
Hence, it is called Range chart.

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Why Range Chart?
 Range chart maintain the precision of the data.
 Precision can be understood by closeness of individual value of the data.
 Precision suffers as much as the individual value distant from each other.

11. SEVEN QC TOOLS TRAINING: CONTROL CHARTS
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Calculation For Range Chart
 First collect the data for different samples.
 Calculate the Range ( ) for different sample data.
 Now calculate the mean of Ranges ( ̅ ) for given sample data, this serves as the mean line or central line on Range chart.
 Calculate the standard deviation.
 Calculate the UCL.
 LCL for Range chart is insignificant.

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Control Limits for Range Chart
 Upper control limit is given below
̅
 Std. Dev. can be calculated as below
√ Σ( ̅

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Construction of Range Chart
 Draw the X-Axis and Y-Axis on the graph paper.
 Take sample no. on X-Axis.
 Take Range values of samples on Y-Axis.
 Draw the mean line parallel to X-Axis.
 Draw the line at upper control limit parallel to X-Axis.
 Now indicate Range values of respective sample no. on the graph.
 Connect all points with line graph and analyze it.

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Example Problem
In a Pen manufacturing company the height of Pens in 8 different samples are given as below
Sample No.
H1
H2
H3
H4
1
133
132
134
135
2
132
133
136
135
3
135
134
135
136
4
135
132
131
136
5
136
135
132
132
6
132
132
134
136
7
132
133
135
136
8
134
132
133
135
Construct a mean and range chart for the given data

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Solution
Sample No.
H1
H2
H3
H4
Sample Mean
Sample Range
1
133
132
134
135
133.50
3.00
2
132
133
136
135
134.00
4.00
3
135
134
135
136
135.00
2.00
4
135
132
131
136
133.50
5.00
5
136
135
132
132
133.75
4.00
6
132
132
134
136
133.50
4.00
7
132
133
135
136
134.00
4.00
8
134
132
133
135
133.50
3.00
Mean of Sample Mean and Sample Range
133.84
3.63

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Central Line and Control Limits for Mean Chart
 Central Line = 133.84
 UCL=135.29
 LCL=132.39

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Mean Chart for Pen Heights
130.50
131.00
131.50
132.00
132.50
133.00
133.50
134.00
134.50
135.00
135.50
136.00
1
2
3
4
5
6
7
8
Mean Values
Sample No.
Mean Chart for Pen Heights
Central Line
UCL
LCL
Mean Values

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Central Line and Control Limits for Range Chart
 Central Line = 3.63
 UCL= 6.20

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Range Chart for Pen Heights
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1
2
3
4
5
6
7
8
Range Values
Sample No.
Range Chart
Range
Central Line
UCL

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Contact
Narender Sharma
Mob: 08684861131, 09315132462
Website: www.shakehandwithlife.in | www.shakehandwithlife.puzl.com | www.shakehandwithlife.blogspot.in
Email: shakehandwithlife@gmail.com | narender@shakehandwithlife.in