An X Chart Based on Standard Deviations (Instead of Ranges)

question 19

Essay

An x chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline
at x and control limits at x + A3 s and x - A3 s where A3 is found in the Control Chart Constants table and s is
the mean of the sample standard deviations. Construct an x chart based on standard deviations for the data
below.
A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality
control. The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated.
The results for 12 consecutive days are shown in the table below. $$\begin{array} { c | c | c | c } \text { Day } & \bar { x } & \text { Range } & \mathrm { s } \\\hline 1 & 21.1 & 3.4 & 1.2 \\2 & 23.4 & 4.7 & 1.7 \\3 & 20.9 & 3.1 & 0.9 \\4 & 25.6 & 6.2 & 2.3 \\5 & 21.3 & 4.7 & 1.3 \\6 & 20.5 & 3.7 & 1.7 \\7 & 25.8 & 5.8 & 2.1 \\8 & 23.7 & 6.2 & 2.9 \\9 & 29.8 & 2.1 & 0.8 \\10 & 22.7 & 4.4 & 1.6 \\11 & 20.0 & 2.7 & 0.7 \\12 & 24.6 & 7.8 & 3.0\end{array}$$

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Definitions:

Period Cost

Costs that are expensed in the period in which they are incurred, not directly tied to production activities.

Fixed Selling Cost

Expenses that do not change with the level of goods or services sold, such as salaries of sales personnel and rent of the sales space.

EBITDA

An acronym for Earnings Before Interest, Taxes, Depreciation, and Amortization, indicating a company's financial performance.

Film Segment

In accounting and finance, this refers specifically to accounting for the income and expenses related to film production and distribution, acknowledging the unique aspects of the entertainment industry.