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Control chart signifies the process variation, when data goes beyond control limits, and inspires the process owner to identify the assignable causes of the variation in the process to take immediate corrective action to control the process.

- Defects are the result of process variation, and variation
comes in the process because of assignable and common
causes
- When data goes beyond control limits, it is because of
assignable or special causes, and it requires immediate corrective
action to maintain the process with in control limits
- Hence to maintain the process variation within control limits,
process owner requires a control chart

There are two major types of Control Charts;

**Control Charts for variables such as:** length,
weight, volume etc. further subdivided into two categories

- Mean Chart for accuracy; (Accuracy is the closeness of average value to the target value)
- Range Chart for precision; (Precision is the closeness of individual values)

**Control Charts for attributes such as:** (Go,
NoGo), (Ok, Not Ok), (Good, Bad) etc. further subdivided into two
types

- P-Chart for proportion defective
- C-Chart for defect count

- The Target value for the volume of an item to be manufactured given by the client is 750ml along with tolerance of plus/minus 7
- Data collected for the measurement of volume of the items in 16 samples are shown in table 1. Each sample has 4 items
- Calculate the mean value of each sample and then calculate the average of sample mean values
- Now calculate the population standard deviation of sample mean values by taking the square root of squared deviation of sample mean values from their average value and it comes as 1.28
- Now Calculate the Upper and lower control limits by adding and subtracting three population standard deviation to average of sample mean values.
- Now to daw the control chart for sample mean values; take sample no. on X-Axis and Sample mean values on Y-Axis
- Draw the straight lines from Y-Axis parallel to X-Axis at 750, the target line, from 752.10, the process average, and from 755.95 and 748.25 the Upper and lower control limits. Now draw the dot plot for sample mean values against each sample no.
- For better accuracy the process average should be close to the target line. But the difference between Orange and Blue line shows the accuracy suffers by 2.10
- The dot plot shows the random variation between the control limits but only sample no. 6, 10, 11, 12, and 13 have mean values close to the target line.
- Try to find the causes of variation in the sample mean values that are responsible for difference between process average and target line and try to reduce the gap by eliminating the concerned causes

- Now calculate the range instead of mean for each sample shown in table 2, by subtracting min. value from max. value and then calculate the average of sample range values
- Calculate the population standard deviation of sample range values
- Calculate the Upper control limit, there is no need to calculate the lower control limit because the minimum range value can be zero.
- Now to daw the range chart for sample range values; take sample no. on X-Axis and Sample range values on Y-Axis
- Draw the straight lines parallel to X-Axis, from 7.69, the process average, and 17.25 the upper control limit, set lower control limit at zero. Now draw the dot plot of sample range values against each sample
- For better results the orange line should be as low as possible and the dot plot of sample values have minimum variation
- The range of Sample no. 9 and 14 are very high, find the causes of variation and take corrective action to reduce the difference between maximum and minimum values of each sample so that the orange line comes down at lower value

- Table 3 shows the twenty days data of no. of parts inspected
and no. of parts found defective during attribute
inspection.
- Calculate the Proportion defective by dividing the no. of
defective parts found in each sample of inspected parts.
- Now calculate the average sample size, average proportion
defective, and upper control limit
- To draw the p-chart, take days on X-Axis and proportion
defective on Y-Axis,
- Draw the straight lines parallel to X-Axis from 0.0732, the
process average, and 0.1019 the upper control limit. Set lower
control limit at zero. Now draw the dot plot for proportion
defective against each sample
- It is seen that sample number 2 and 4 cross the control limit,
other samples showcase a random trend. Since the sample after
fourth day appear at random and are well within control limit,
there is no need to anxiety, the two points might have gone astray
due to unforeseen reasons.

- Table 4 shows the data collected for 30 samples for defect
count for a defect named blister.
- Calculate average defect count and Upper control
limit
- To draw the C-chart, take lot no. on X-Axis and defect count on
Y-Axis,
- Draw the straight lines parallel to X-Axis from 33.53, the
process average, and 50.91 the upper control limit. Set lower
control limit at zero. Now draw the dot plot for defect count
against each lot, the dot plot shows random variation of the defect
count with in the limit.

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**Last updated
on: 04 July, 2017**

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