Question

A small chemical company uses process control charts for the container filling processes within its operations. One of the products is a weed killer, Lawn Order. The company wants to setup process control charts for this product and has the following data.

                                     Observations

Sample            1          2          3          4          X-Bar R

     1                 50        90        40        80        65.0     50

     2                 50        60        80        60        62.5     30

     3                 40        70        40        90        60.0     50

     4                 50        60        100      90        75.0     50

     5                 90        60        50        30        57.5     60

     6                 70        60        90        40        65.0     50

     7                 100      30        80        70        70.0     70

     8                 50        100      60        90        75.0     50

A. What are the center line, lower control limit, and upper control limit equal to for the X-Bar chart? (Use the sample range to calculate the upper and lower control limits)

Answer 1

Answer:

Step 1: First, we will find X=X=(Average of X-Bar) and R-R- (Average of Samples Ranges)

Average of X-Bar (X=X=) = Sum of X-Bar Column / No. of Samples = (65 + 62.5 + 60 + 75 + 57.5 + 65 + 70 + 75) / 8 = 66.25

Average of all Sample Ranges = R-bar = Sum of Ranges / No. of Samples = (50 + 30 + 50 + 50 + 60 + 50 + 70 + 50 ) / 8 = 51.25

Step 2: Now, we will apply the following formulas to find the Upper Control Limit (UCL), Lower Control Limit (LCL), and Central Limit (CL):

Upper Control Limit = UCLx = X=X= + (A2* R-) = 66.25 + (0.729 * 51.25) = 103.61 (Rounded to 2 decimal places)

Where, A2 =  Control chart constant for the subgroup size of 4 = 0.729 (Derived from the Table of Control Charts)

Lower Control Limit = LCLx = X=X= - (A2* R-) = 66.25 - (0.729 * 51.25) = 28.89 (Rounded to 2 decimal places)

Center line (X=X=))= (UCL + LCL) / 2 = (103.61 + 28.89) / 2 = 66.25 (Rounded to 2 decimal places)