Question

25. What is the seventh step in the construction of the X bar chart?

26. Explain how the centerline and control limits of the R chart are mathematically calculated.

28. What is the eighth step in the construction of the X bar chart?

35. What is the ninth step in the construction of the X bar chart?

36. What are the four steps taken to revise the charts?

Answer 1

Ans 25, 26, 28, 35:

X-bar chart is also known as average chart. Different books have given the different steps of plotting the X- bar chart. Some books have given the eighth steps and some books have given nine steps. For the convenience of study, I am mentioning herby all steps of constructing X-bar chart.

X-bar charts are made by taking the average of groups and sub-groups and then after plotting the averages on the graph chart.

Step 1: Take the samples of size n and their relative frequencies e.g. 200 samples taken.

Step 2: make the initial set of samples. It is grouping of samples in suitable ranges to make more meaningful conclusions. e.g. grouping of 200 samples in 20 sets to draw X-bar and R.

Step 3: Calculate X-bar i.e the samples of each sub group of samples. e.g. in above example 20 means of different subgroups will be drawn.

Step 4: Now calculate R. It is the range of given sets. It is difference between larger value and smallest value.

Step 5: Calculate X-double bar. It is average of averages. In above example, it is mean of 20 means. It is the centerline of the X-bar control chart.

Step 6: Calculate R-bar. It is average of R values calculated above. It is the centerline of the R-bar control chart.

Step 7: Find the control limits:

Firstly, find the R chart limits:

Upper Control Limits of R= Table constants (D₄) for given number of samples in subgroup * R-bar

Lower Control Limits of R= Table constants (D₃) for given number of samples in subgroup * R-bar

D₄ and D₃ are have the table values given as under:

Remember to plot the data on the R chart and if not in control, before proceeding with making the control chart, construct to make the variability of the process under control.

Secondly, find the X-bar limits:

Upper Control Limits of X-bar= X-double bar + A₂* R-bar

Lower Control Limits of X-bar = X-double bar - A₂* R-bar

A₂ has the table constants value for given number of samples.

Step 8: After getting the control limit, take the samples and proceed to plot the data.