(a) State whether the following statements are True or False. Give reason in support of your answer:
(i) The R\mathrm{R} – chart is suitable when subgroup size is greater than 10 .
Answer:
The statement “The RR – chart is suitable when subgroup size is greater than 10″ is generally considered to be False.
Justification:
The RR – chart, or range chart, is used in statistical process control to help evaluate the stability of a process in terms of the variation among the values within a sample (subgroup). However, there are some considerations regarding subgroup size:
Small Subgroup Sizes: The RR – chart is most effective and commonly used when the subgroup size (nn) is small, typically between 2 and 10. This is because the range is a simpler and more efficient calculation when dealing with smaller subgroup sizes.
Large Subgroup Sizes: When subgroup sizes are larger than 10, the RR – chart may not be the most appropriate choice for evaluating within-group variability due to the following reasons:
Sensitivity: The range is less sensitive to the spread of data as the subgroup size increases. It only considers the largest and smallest values and ignores the distribution of all the values in between.
Normality Assumption: The distribution of the range is highly dependent on the underlying distribution of the process data, and this dependency increases with subgroup size. For larger subgroups, if the data is not normally distributed, the control limits calculated for the RR – chart may not be accurate or reliable.
Alternative Charts: The SS – chart (standard deviation chart) is often recommended for larger subgroup sizes because it considers all data points in the subgroup, providing a more accurate and reliable measure of dispersion, especially when n > 10n > 10.
Example:
Consider a subgroup of size 15 with the following values:
The range (RR) would be calculated as the difference between the largest and smallest values: R=13-5=8R = 13 – 5 = 8.
However, this doesn’t give any insight into the variability of all the other values in the subgroup.
If there were outliers or shifts within the subgroup, the RR – chart might not detect them effectively due to its insensitivity to the distribution of internal values.
Conclusion:
While the RR – chart is a valuable tool in statistical process control, its suitability is generally constrained to scenarios with smaller subgroup sizes. For larger subgroup sizes, alternative charts, such as the SS – chart, are typically recommended to provide a more accurate and reliable analysis of process variability.