7-selection of appropriate control charts & x mr charts-ok

Selection of Appropriate Control ChartType of Data

Variable or Attribute?

Variable Attribute?

n=1 of more? N=1 or more?

More 1 More 1x & R x & MR Is n constant? Unit or portion

Yes No Unit Portion

np p u c

Electronics Test & Development Centre, ChennaiMinistry of Communications & Information Technology

Control Charts For Variables & Attribute Data

• Most important tools for process control of variation

• The knowledge of distribution is used in control charts

• They are visual representations of variations in selected parameters over real time

• Their limits are based on data collected under control conditions. They are practical and achievable.


TYPES OF DATA & CONTROL CHARTSVariable and Attribute Data

Variable Data:

Relates what can be measured and Expressed Quantitatively in specific units of measurement.

Eg. Dimensions, Volumes, Temperature, Pressure, Time, Strength.

Attribute Data:

Expresses good or bad, Defective or defect free, Acceptable or unacceptable, It is qualitative.


CONTROL CHARTS FOR VARIABLES

X & R charts most commonly used.

In rare cases when one cannot have more items in a sample or where generation of data is very expensive; X & MR (moving range) chart of (i-chart) is used.


CONROL CHART FOR ATTRIBUTES

Attribute details converted into numerical data. Depending on the type of sample and the attribute.

np – chart is used in case sample size is big enough and constant.

P – chart is used if sample size is not a constant fraction or % of defective is charted.

U – chart is used to control if the sample is single.

C – chart is used to control no. of defects per square meter.

X & MR CHART (i-CHART) MOVING RANGE CHART

When it is not convenient to get multiple items in a sample. Eg. Chemical industry where test is too expensive to replicate an X & MR chart is used.

The control limits for MR chart and X chart are calculated as follows:

For MR Chart, Central line = MR


Upper control limit for MR-UCLMR = MR x D4

= MR x 3.27

Lower Control Limit for MR–LCRMR= MRxD2


For X Chart

Central line = X

Upper control limitx – UCLx = X + 3

(Action lines) = X + 3 MR

= X + (3 MR)

d2

1.13

Lower control limitx – LCLx

(Action lines) = X - 3

= X - (3 MR)

Warning Lines @ X ± 2 or X ± 2 MR

or = X ± 2 MR

1.13

d2

1.13


For x Chart:

Central line = x

Upper Control Limit for x–UCLx = x+3 (MR/1.13)

Lower Control Limit for x–LCLx = x-3 (MR/1.13)

The factors used for the control limits for the MR Chart are the same as for R chart with sample size of 2. In case of x chart the limits are often referred to a natural process limits. Let us see an example of x and MR chart.


In the manufacture of a chemical, the percentage yields of 25 consecutive items were:

1. 90.5 2. 93.0 3. 91.5 4. 92.5 5. 90.5

6. 88.5 7. 89.0 8. 93.0 9. 91.5 10. 93.0

11. 94.5 12. 92.0 13. 91.5 14. 91.5 15. 91.0

16. 92.0 17. 90.5 18. 87.5 19. 92.0 20. 92.5

21. 89.5 22. 91.0 23. 93.5 24. 91.5 25. 92.0


The first step is to calculate the moving range. It must be noted that with 25 values of x, we get only 24 values of MR as there is no MR corresponding to the first value of x. In this case, the 24 values of MR are:

1. - 2. 2.5 3. 1.5 4. 1.0 5. 2.0

6. 2.0 7. 0.5 8. 4.0 9. 1.5 10. 1.5

11. 1.5 12. 0.5 13. 0.5 14. 0.0 15. 0.5

16. 1.0 17. 1.5 18. 3.0 19. 4.5 20. 0.5

21. 3.0 22. 1.5 23. 2.5 24. 2.0 25. 0.5

The values of x and MR are calculated next. These are 91.42% and 9.73% respectively. Now let us calculate the control limits for MR.UCLMR = MR x 3.27

= 1.73 x 3.27= 5.6571 rounded to 5.66

LCLMR = MR x 0= 1.73 x 0= 0

Control limits for MR are 5.66 and 0. All MR values are in this range. So we can proceed to calculate the limits for x chart.


Upper limit = x + 3 (MR/1.13)= 91.42 + 3 (1.73/1.13)= 91.42+ 4.59= 96.01

Lower limit = x – 3 (MR/1.13)= 91.42 – 3 (1.73/1.13)= 91.42 – 4.59= 86.83

All the individual values of x are within these limits. Hence the process seems to be under control. We now have all the information to complete the x and MR control charts. These are shown in Diagram 6.8.


DRAW THE X & MR CHART FOR THE FOLLOWING EXAMPLES:

1 90.5 2 93.0 3 91.5 4 92.5 5 90.5 6 88.5 7 89.0 8 93.0 9 91.5 10 93.5


11 94.512 92.013 91.514 91.515 91.016 92.017 90.518 87.519 92.020 92.021 89.522 91.023 93.524 91.525 92.0


7-selection of appropriate control charts & x mr charts-ok

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