Question

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For 107 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 10 bottles. The average across all 1070 bottles (107 days, 10 bottles per day) was 43 degrees Fahrenheit. The standard deviation across all bottles was 1.1 degrees Fahrenheit When constructing an X-bar chart, what would be the center line? degrees Fahrenheit

Answer 1

1) To be calculated:

Center line of X-bar chart

Given values:

Number of days = 107 days

Sample size, n = 10 bottles

Average temperature, $\mu$ = 43 degrees Fahrenheit

Standard deviation, $\sigma$ = 1.1 degrees Fahrenheit

Solution:

When constructing an X-bar chart, the centerline is represented by the mean of the given process. In the given scenario;

Mean of the process = 43 degrees Fahrenheit

Centerline = 43 degrees Fahrenheit

2) To be calculated:

Upper control limit (UCLx)

Given values:

Number of days = 127 days

Sample size, n = 5 bottles

Average temperature, $\mu$ = 43 degrees Fahrenheit

Standard deviation, $\sigma$ = 1 degree

Solution:

When constructing an X-bar chart, the upper control limit (UCLx) is calculated as;

UCLx = $\mu$ + 3 ( $\sigma$ / √n)

where;

$\mu$ = mean temperature

$\sigma$ = standard deviation of given process

n = sample size

Putting the given values in the above formula, we get;

UCLx = 43 + [3 x (1 / √5)]

UCLx = 43 + 1.3416

UCLx = 44.3416

Upper control limit of X-bar chart = 44.3416 degrees Fahrenheit.