8/14/2019 Doc 18 Control Charts

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Syntel CQA Forum Control Charts CQA Doc No 18

Control Charts

Control charts are powerful and simple tools that can help you determinewhether a process is in control or out-of-control.

An in-control process exhibits only random variation within the control

limits.

An out-of-control process demonstrates unusual variation that may be dueto the presence of special causes.

In other words, control charts can help you determine whether or not theprocess average (center) and process variability (spread) are operating atconstant levels. Control charts help you focus problem-solving efforts bydistinguishing between common and special cause variation.

A control chart consists of:Plotted points, which represent individual observations, moving

ranges, or moving averages and are typically summary statistics for the quality

characteristic of interest. The data points are plotted in time order.Center line, which is the expected value of the individual observations,

moving ranges, or moving averages.Control limits, which are set at a distance of 3 s above and below the

center line and provide a visual display for the expected amount of variationfor the individual observation.

Control limits predict how the process should behave. The control limitsare based on the actual behavior of the process, not the desired behavior they are not specification limits. A process can be in control and yet not becapable of meeting requirements.

Control charts evaluate the pattern of variation for stability through theuse of tests for special causes. If you detect special cause variation, you shouldseek out the factors that contribute to this variation so that you can implementcorrective measures.

UCL : Upper Control Limit, LCL: Lower Control Limit. They are derived usingprocess variation data for a extended period.UTL: Upper Tolerance limit, LTL: Lower Tolerance Limit. They are acceptedlimits of customer.

Types of Control Chart

Individual chart (X)

An Individuals (I) chart allows you to monitor a quality characteristicwhen your data are individual measurements. Each plotted point represents asingle sample measurement. Use an I chart to determine whether the processcenter is in control.An in-control process exhibits only random variation within the 3-s controllimits.An out-of-control process exhibits unusual variation, which may be due to thepresence of special causes.

The process variation should be in control before assessing the processcenter using an I chart. If the process variation is out-of-control, then thecontrol limits for the I chart will be inaccurate and may not adequatelydetermine the control ofyour process. Use a moving range (MR) chart or the10718244.doc Page 1of 2

8/14/2019 Doc 18 Control Charts

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Syntel CQA Forum Control Charts CQA Doc No 18

combined I-MR chart to assess whether or not the process variation is incontrol.

Formulas for calculating control limits :

UCL : X bar + 2.66 mr barLCL : X bar - 2.66 mr bar

Moving Range (MR) ChartThe Moving Range (MR) Chart is used to monitor and detect changes in

process variation when your data are individual measurements. Each plottedpoint, or moving range, is simply the absolute value of between twoconsecutive measurements. The MR chart helps you to determine whetherthere has been a sudden change in your process.

Formulas for calculating control limits :

UCL : 3.27 * mr bar

LCL : 0

Example :Sample Value Moving Range1 32 4 13 7 34 4 35 6 2Sum 24 9

Mean 4.8(Xbar) 2.25(mr bar)Formulas for calculating control limits :Individual chart:UCL = X bar + 2.66 mr bar = 4.8 + 2.66 * 2.25 = 10.795LCL = X bar - 2.66 mr bar = 4.8 - 2.66 * 2.25 = -1.185

Moving range chart:UCL = 3.27 * mr bar = 3.27*2.25 = 7.3575LCL = 0

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1Subgroup 2 3 4 5

0

5

10

IndividualValue

3 4 7 4 6C2

Mean=4.8

UCL=10.78

LCL=-1.184

0

1

2

3

4

5

6

7

8

MovingRa

nge

R=2.25

UCL=7.351

LCL=0

sample I MR