Class 10 - Control Charts for Variables1 (2 of 2)

8/11/2019 Class 10 - Control Charts for Variables1 (2 of 2)

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X-Bar and R Control Charts

X-Bar and RControlCharts

Industrial Engineering

MR and s

ControlCharts

Examples

Control ChartIn Statistical Control

Out of Control

Assignable Cause

Types the control charts

Process Flowchart

PFMEA


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MR and s

ControlCharts

Examples

Guidelines for the Design of the Control Chart

Specify sample size, control limit width, and frequency of samplingIf the main purpose of the x-bar chart is to detect moderate to large processshifts, then small sample sizes are sufficient (n = 4, 5, or 6)

If the main purpose of the x-bar chart is to detect small process shifts, largersample sizes are needed (as much as 15 to 25)

If increasing the sample size is not an option, then sensitizing procedures canbe used to detect small shiftsbut this can result in increased false alarms.

R chart is insensitive to shifts in process standard deviation. Try S or S 2 chart.

The OC curve can be helpful in determining an appropriate sample size.

In general, small frequent samples are more desirable.


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MR and s

ControlCharts

Examples

Interpreting patterns in X-Bar and R Control Charts

General rules to determine whether a process is in control:No points outside the control limits.

The number of points above and below the center line are about the same.

Points seem to fall randomly above and below the center line.

Most points are near center line, and only a few are close to control limits.

One point outside control limits:

measurement or calculation error, power surge, a broken tool, incompleteoperation.

Sudden shift in process average:new operator or inspector, new machine setting.


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MR and s

ControlCharts

Examples

Cycles:

Operator rotation or fatigue at the end of shift, different gauges, seasonaleffects such as temperature and humidity.

Trends:

x-bar-chart learning effect, dirt or chip buildup, tool wear, aging of equipment;R-chart (increasing trend) gradual decline in material quality; R-chart(decreasing trend) improved skills, better materials.

Hugging the center line:

sample taken over various machines canceling out the variation within thesample.

Instability:

difficult to identify causes. Typically, over-adjustment of machine.

Always, R-chart analysis before the x-bar-chart analysis.


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MR and s

ControlCharts

Examples

Estimating the Process Standard Deviation

The process standard deviation can be estimated using a function of the sampleaverage range.

This is an unbiased estimator of

2

d

R


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X-Bar and s Control Charts



MR and s

ControlCharts

Examples

s-Control Chart

For the x- bar control chart in this case

5

4

6

B LCL

C CL

BUCL

m

ii sm

s1

1

s B LCL

sCL

s BUCL

3

4

1

)(1

2

n

x x s

n

jij

i

s A X LCL

X CL

s A X UCL

3

3


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MR and s

ControlCharts

Examples

What if you could not get a sample size greater than 1 (n =1), such in

Automated inspection and measurement technology is used, and every unitmanufactured is analyzed.

The production rate is very slow, and it is inconvenient to allow samples sizesof N > 1 to accumulate before analysis

The X and MR charts are useful for samples of sizes n = 1.

Moving Range Chart

The moving range (MR) is defined as the absolute difference between twosuccessive observations:

MR i = | x i - x i-1 |

which will indicate possible shifts or changes in the process from oneobservation to the next.


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MR and s

ControlCharts

Examples

X and Moving Range Charts

The X chart is the plot of the individual observations. The control limits are

Where

The control limits on the moving range chart are:

2

2

3

3

d MR

x LCL

xCL

d MR

xUCL

11

m

MR MR

m

ii

0

4

LCL

MRCL

M DUCL


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MR and s

ControlCharts

Examples

Interpretation of the X and MR Charts

X Charts can be interpreted similar to x-bar charts. MR charts cannot beinterpreted the same as x-bar or R charts.

Since the MR chart plots data that are correlated with one another, thenlooking for patterns on the chart does not make sense.

MR chart cannot really supply useful information about process variability.

More emphasis should be placed on interpretation of the X chart. The X chart isthe plot of the individual observations. The control limits are


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MR and s

ControlCharts

Examples

Control vs. SpecificationLimits

Control limits are derived fromnatural process variability, or thenatural tolerance limits of a process

Specification limits are determined

externally, for example bycustomers or designers

There is no mathematical orstatistical relationship between thecontrol limits and the specification

limits


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Examples



MR and s

ControlCharts

Examples

Packages of corn oil bottle are filled by a machine and weighed. Theweights (in ounces) for 15 successive bottles have been collected and are

displayed in following table . The engineer wishes to determine whether thefilling process is in control.

MR i = | x i - x i-1 |


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Examples



MR and s

ControlCharts

Examples

The x-bar control chart limit in this case are

Based on n=1 where is approximated in the constant table from the first rowas n=2 (d 2= 1.128 , D 4= 3.267)

The moving range control limits are


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Examples



MR and s

ControlCharts

Examples

Documents

Class 10 - Control Charts for Variables1 (2 of 2)