A Design Engineer Wants to Construct a Sample Mean Chart

question 48

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: $$\begin{array} { c c c c c } \text { Sample } &&{ \text { Service Life (hours) } } \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}$$
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) ?

• A) 0.0026
• B) 0.0456
• C) 0.3174
• D) 0.6826
• E) 0.9544

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Definitions:

Lag Indicator

A metric that indicates the performance of a business or system after an event or activity has occurred, often financial in nature.

Market Share

The proportion of total industry revenue attributed to a specific company during a certain time frame.

Financial Perspective

One of the four perspectives of the Balanced Scorecard framework, focusing on how well a company is performing financially, including measures such as revenue growth, profitability, and return on investment.

Customer Perspective

Reflects the viewpoint of customers regarding the value, quality, and benefits of products or services offered by a business.