A Design Engineer Wants to Construct a Sample Mean Chart

question 138

Multiple Choice

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $$\begin{array} { r } { \text { Service Life (hours) } }\\\begin{array} { l l l l l } \text { Sample } & \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}\end{array}$$ If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error) ?

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Definitions:

Automated Machine

A machine operated with minimal human intervention, typically using computer-controlled systems.

Margin of Safety

The difference between actual or projected sales and the break-even point, indicating the extent to which sales can drop before a business incurs a loss.

Variable Expenses

Costs that fluctuate in direct proportion to changes in the level of business activity or output.

Fixed Expenses

Outlays that stay the same no matter the amount of goods produced or sold, encompassing rent, payroll, and insurance costs.