# Question

A firm monitors the use of its email system. A sudden change in activity might indicate a virus spreading in the system, and a lull in activity might indicate problems on the network. When the system and office are operating normally, about 16.5 messages move through the system on average every minute, with a standard deviation near 8.

The data for this exercise count the number of messages sent every minute, with 60 values for each hour and eight hours of data for four days (1,920 rows). The data cover the period from 9 A.M. to 5 P.M. The number of users on the system is reasonably consistent during this time period.

Motivation

(a) Explain why the firm needs to allow for variation in the underlying volume. Why not simply send engineers in search of the problem whenever email use exceeds a rate of, say, 1,000 messages?

(b) Explain why it is important to monitor both the mean and the variance of volume of email on this system.

Method

(c) Because the computer support team is well-staffed, there is minimal cost (aggravation aside) in having someone check for a problem. On the other hand, failing to identify a problem could be serious because it would allow the problem to grow in magnitude. What value do you recommend for a, the chance of a Type I error?

(d) To form a control chart, accumulate the counts into blocks of 15 minutes rather than use the raw counts. What are the advantages and disadvantages of computing averages and SDs over a 15-minute period compared to using the data for 1-minute intervals?

Mechanics

(e) Build the X-bar and S-charts for these data with α = 0.0027 (i.e., using control limits at {3 SE). Do these charts indicate that the process is out of control?

(f) What is the probability that the control charts in part (e) signal a problem even if the system remains under control over these four days?

(g) Repeat part (e), but with the control limits set according to your choice of α.

Message

(h) Interpret the result from your control charts (using your choice of a) using nontechnical language. Does a value outside the control limits guarantee that there’s a problem?

The data for this exercise count the number of messages sent every minute, with 60 values for each hour and eight hours of data for four days (1,920 rows). The data cover the period from 9 A.M. to 5 P.M. The number of users on the system is reasonably consistent during this time period.

Motivation

(a) Explain why the firm needs to allow for variation in the underlying volume. Why not simply send engineers in search of the problem whenever email use exceeds a rate of, say, 1,000 messages?

(b) Explain why it is important to monitor both the mean and the variance of volume of email on this system.

Method

(c) Because the computer support team is well-staffed, there is minimal cost (aggravation aside) in having someone check for a problem. On the other hand, failing to identify a problem could be serious because it would allow the problem to grow in magnitude. What value do you recommend for a, the chance of a Type I error?

(d) To form a control chart, accumulate the counts into blocks of 15 minutes rather than use the raw counts. What are the advantages and disadvantages of computing averages and SDs over a 15-minute period compared to using the data for 1-minute intervals?

Mechanics

(e) Build the X-bar and S-charts for these data with α = 0.0027 (i.e., using control limits at {3 SE). Do these charts indicate that the process is out of control?

(f) What is the probability that the control charts in part (e) signal a problem even if the system remains under control over these four days?

(g) Repeat part (e), but with the control limits set according to your choice of α.

Message

(h) Interpret the result from your control charts (using your choice of a) using nontechnical language. Does a value outside the control limits guarantee that there’s a problem?

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