Question

Explain the steps on how to calculate each one thanks

AnderSet Laboratories produces rough lenses that will ultimately be ground into precision lenses for use in laboratory equipment. The company has developed the following thickness measures, based on 15 samples of four lenses that were taken when the process was under control E Click the icon to view the sample data More Info Click the icon to view the values of the A2, D3, and D4 constants a. X is 4.184. (Enter your response rounded to three decimal placos.) R is 0.665. (Enter your response rounded to three decimal places.) n (MicronS Minimum Maximum Upper Control Limit (UCL) 4.669e response rounded to three decimal pla Lower Control Limit (LCL)-3.699 . (Enter your response rounded to three decimal pla Upper Control Limit (UCLR)1.516. (Enter your response rounded to three decimal pl Lower Control Limit (LCLR)= 0.000. (Enter your response rounded to three decimal pla the needs of An 3.965 4.184 4.363 3.881 3.526 3.828 3.529 4.871 3.954 6.239 4.217 4.106 4.308 3.744 4.042 3.712 3.878 4.067 3.745 3.459 3.508 2.967 3.794 2.848 5.161 4.066 3.947 3.968 3.663 4.007 3.981 4.343 4.404 3.958 4.056 4.558 3.962 5.665 4.299 6.358 4.298 4.343 4.372 3.887 4.275 b. Ca More Info than scheduled derSet's custom ter than the pr Sample Size N 2 e size, yielding any o 3.27 2.57 2.28 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31 0.29 0.27 Print Done 4. Choo 2.00 0.08 8 1.86 1.82 0.22 0.26 0.28 Quest 1.74 1.72

Answer 1

The following question can be best explained through Excel.

In the above question, 15 total samples with each having 4 lenses are taken and their thickness is measured.

For each sample, the average of the thickness or the mean thickness ( X bar) of the sample is taken out which is given in the table in the question.

X double bar is the average value of the mean of all the 15 samples, i.e. mean of X bar values.

The range for each sample is the difference between the maximum thickness and the minimum thickness of lens from the sample.

R bar is the average value of the ranges of all the 15 samples. The following screenshot shows the formulas used.

The formulas for the Upper control limit (UCL) and the Lower control limit (LCL) for both the x bar and R charts have been included in the first screenshot.

For X bar chart

UCL = X double bar + A2 *R bar

LCL = X double bar - A2 *R bar

For R chart

UCL = D4* Rbar

LCL = D3* Rbar

The value of A2, D4 and D3 have been used from the table given in the question and the values for N = 4 are used in solving the question as the sample size was 4,i.e. 4 lenses were measured in each sample.

This final screenshot shows the application of the formulas for UCL and LCL for both the X bar and R chart.

In summary, the first step is to find the X double bar and R bar values from the table given in the question and then use these values in the formulas for the UCL and LCL for X bar and R chart.