1. Control Charts For Variable
Normal Curve

2. Control Charts For Variable
Variations
Variations due to Assignable causes
- Greater magnitude
- because of difference among M/cs, workers, material etc.
Variations due to chance causes
- Random
- example – little play between nut and screw of table

3. Control Charts For Variable
If many random samples of any given size are taken from universe, the averages of the samples will themselves form a F.D. having its own central tendency and dispersion or spread.
If the universe is normal, statistical theory tells that expected F.D. of the average values will also be normal.
In long run
1. Average of samples = Average of the universe
2. S. D. of the expected F.D. of the average
= S. D. Of the universe / √ sample size

4. Control chart : Procedure
Making and recording measurement
Calculate the average characteristic value and Range for each subgroup
Calculate the grand average and average range
Calculation of control limits on control chart for X-chart
Calculation of control limits on R-chart
Plot the X and R chart
Draw conclusions from control chart

5. Some control chart patterns
Chance pattern

6. Some control chart patterns
Chance pattern characteristics
1. Most of the points will lie near the central line
2. Very few points will be near the control limits
3. None of the points (except 3 in 1000) fall outside the control limits

7. Some control chart patterns
Extreme variations

8. Some control chart patterns
Extreme variations Causes
Error in measurement and calculations.
Sample chosen at peak position of pressure, temp. etc.
Wrong setting of machine, tool etc.
Sample chosen at the commencement or end of an operation

9. Some control chart patterns
Trend

10. Some control chart patterns
Causes of Trend
Tool wear
Wear of threads on clamping device
Effects of temperature and humidity
Accumulation of dirt and clogging of fixtures and holes
On R chart
Increasing trend – gradual wearing of operating machine part
Decreasing trend – Improvement in operations, better maintenance, improved control on back process

11. Some control chart patterns
Shift

12. Some control chart patterns
Causes of Shift
Change in material
Change in operator, inspector, inspection equipment
Change in machine setting
New operator carelessness of operator
Loose fixture etc.

13. Some control chart patterns
Erratic fluctuations

14. Some control chart patterns
Causes of Erratic fluctuations
Frequent adjustment of machine
Different types of material being processed
Change in operator. Machine, test equipment etc.

15. Process capability
Minimum spread of a specific measurement variation which will include 99.7% of the measurements from the given process.
Measure of a process spread (6σ) – Natural tolerance
Process capability analysis consists of
Finding whether the process is inherently capable of meeting the specified tolerance limit.
Discovering why a process capable is failing to meet specification

16. Specifications and process capability
Case I: 6σ < ( Xmax - Xmin ) or (USL – LSL)

17. Conclusion
In a, b, c practically all the products manufactured will meet specification as long as the process stays in control
X¯ may be permitted to go out of control or the distribution may be allowed to move between b and c. cost of frequent machine setup and cost and time of hunting causes will reduce.
If ( Xmax - Xmin )/6σ is considerably large, frequency of control chart may be reduced.
For economical advantages the specification limits may be tightened.

18. Case II: 6σ > ( Xmax - Xmin ) or (USL – LSL)

19. Conclusion Defective parts will always be there. The remedy will be
Increase the tolerance
Reduce the dispersion
Suffer and sort out the defectives
Important to maintain the centering of the process.

20. Case III: 6σ = ( Xmax - Xmin ) or (USL – LSL)

21. Conclusion
A little change in centering will cause defective parts. Calls for continuous use of control charts.
To increase tolerance if they are tighter than necessary.
Reduce dispersion if economical

22. Control Charts for Attributes
Practical limitations of the control charts for Variables:
Can be used for quality characteristics that can be measured and expressed in numbers. However many quality characteristics can be observed only as attributes.
Can be used only for one measurable quality characteristic at a time.
For the reason of economy even in some cases , where the direct measurement of variable quality characteristics is possible, it is common practice to classify them as good or bad on the basis of inspection by GO-No-GO gauges.

23. P-Chart (control chart for fraction defectives)
The day’s production or other lot of any manufactured article can be thought of as a sample from a larger quantity with some unknown fraction defective. This unknown universe fraction defective depends upon a complex set of causes influencing the production and inspection operations. Fraction defective in the sample may vary considerably. But as long as the universe fraction defective remains unchanged, relative frequencies of various sample fraction defectives may be expected to follow the binomial law.

24. Inspection results of magnets for nineteen observations
Week No.
No. of magnets inspected
No. of defective magnets
Fraction defectives 1
724 48
0.066 2
763 83
0.109 3
748 70
0.094 4 85
0.114 5 45
0.062 6
727 56
0.077 7
726 8
719 67
0.093 9
759 37
0.049 10
745 52
0.07 11
736 47
0.064 12
739 50
0.068 13
723
0.065 14 57
0.076 15
770 51 16
756 71 17 53
0.074 18
757 34
0.045 19
760 29
0.038
Total
14091
1030

25. Calculate the average fraction defective and 3 sigma control limits, construct the control chart and state whether the process is in statistical control.
The avg. sample size = 14091/19 = n = 742 (say) Total defectives in all samples The avg. Fraction defectives = Total inspected in all samples 1030 = =

26. Calculation of 3 sigma limits
UCLp =
0.1018
LCLp =
0.0444

27. P-Chart

28. Conclusion
From the resulting control chart Sample numbers 2nd and 4th go above the upper control limit and the sample number 19th goes below the lower control limit. Therefore the process does not exhibit statistical control.

29. Problem : A certain product is given 100% inspection as it is manufactured and resultant data are summarized by the hour. In the following table, 16 hours of data are recorded. Calculate the 3 sigma limits, construct the control chart.
Hour
No. of units inspected
No. of defective units
Fraction defective 1 48 5
0.104 2 36
0.139 3 50 4 47
0.106 6 54
0.056 7 8 42
0.024 9 32
0.156 10 40
0.05 11
0.043 12
0.085 13 46
0.022 14 15
0.063 16 39
Total
720

30. C-Chart (Control chart for Number of defects)
Control limits on C chart based on Poisson distribution.
Two conditions:
The area of opportunity for occurrence of defects should be fairly constant from period to period.
Opportunities for defects should be large, while the chances of a defect occurring in any one spot should be small.

31. C-Chart (Control chart for Number of defects)
Area of application:
Number of surface defects in a roll of coated paper
Number of defective rivets in an aircraft wing
Number of small air holes in glass bottle
Number of imperfections observed in a cloth of unit area
Number of defects such as blow holes, cracks, undercuts etc in a casting or welded piece.

32. Problem : The following table gives the numbers of missing rivets noted at aircraft final inspection. Find C¯ compute trial control limits, and plot control chart for C’ would you suggest for the subsequent period?
Air plane no.
no. of missing rivets 1 8 10 12 19 11 2 16 23 20 9 3 14 21 4 13 22 5 25 7 6 15 24 28 17 18

33. C-Chart

34. Comparison between Attribute charts and variable charts
Attirbute charts
Example
X¯, R, σ charts
P, np, C, u charts
2. Data required
Variable data ( Measured values
of characteristics)
Attribute data ( Using Go-No-Go gauges)
3. Field of applications
Control of individual characteristics
Control of proportion of defectives or number of defects
4. Advantage
provides detailed information on
process average and variation
Provides overall picture of quality history
5. Disadvantage
Not easily understood
Do not recognize different degree of defectiveness