The following data were collected on non-conformances
for a period of 10 days.
Day Sample Size Non-conformances
1 100 12
2 100 14
3 100 10
4 100 18
5 100 22
6 100 14
7 100 15
8 100 13
9 100 14
10 100 16
On what day is the proportion of non-conformances largest? smallest?
What are the LCL and UCL?
Are there any special causes of variation?
Largest = day 5
Smallest = day 3
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To determine the day with the largest and smallest proportion of non-conformances, we need to calculate the proportion for each day. The proportion can be found by dividing the number of non-conformances by the sample size and multiplying by 100 to express it as a percentage.
Let's calculate the proportions for each day:
Day 1: 12 non-conformances / 100 sample size * 100 = 12%
Day 2: 14 non-conformances / 100 sample size * 100 = 14%
Day 3: 10 non-conformances / 100 sample size * 100 = 10%
Day 4: 18 non-conformances / 100 sample size * 100 = 18%
Day 5: 22 non-conformances / 100 sample size * 100 = 22%
Day 6: 14 non-conformances / 100 sample size * 100 = 14%
Day 7: 15 non-conformances / 100 sample size * 100 = 15%
Day 8: 13 non-conformances / 100 sample size * 100 = 13%
Day 9: 14 non-conformances / 100 sample size * 100 = 14%
Day 10: 16 non-conformances / 100 sample size * 100 = 16%
To find the day with the largest proportion, we need to look for the maximum value among these proportions, which is 22% on Day 5. Therefore, the largest proportion of non-conformances occurs on Day 5.
Similarly, to find the day with the smallest proportion, we need to look for the minimum value among these proportions, which is 10% on Day 3. Therefore, the smallest proportion of non-conformances occurs on Day 3.
To find the Lower Control Limit (LCL) and Upper Control Limit (UCL) for this data, we need to calculate the control limits based on statistical process control.
The control limits are typically calculated using various statistical formulas, such as using the mean and standard deviation. However, since the data provided only includes the sample size and non-conformances, we cannot directly calculate the LCL and UCL without additional information.
To determine if there are any special causes of variation, we need to employ statistical analysis techniques. These techniques involve identifying patterns, trends, or points outside the control limits in the data.
Without the control limits, it is not possible to determine if there are any special causes of variation in this particular scenario. Additional information or analysis is required to make a conclusive determination about the presence of special causes.