Question 1:

An airline was interested in measuring the length of time customers have to wait in the queue prior to check-in for seat allocation. There are four separate lines for customers to queue.

Lines 1 and 2 are for Economy Class passengers and Lines 3 and 4 are for Business Class passengers. The number of passengers waiting in the Economy Class queue for Lines 1 and 2 tends to be about the same since passengers tend to join whichever queue appears shorter and a balancing effect occurs. There is no statistically discernible difference in the competency levels of check-in staff between Lines 1 and 2.

The number of passengers waiting in the Business Class queue for Lines 3 and 4 tends to be about the same since passengers tend to join whichever queue appears shorter and a balancing effect occurs. There is no statistically discernible difference in the competency levels of check-in staff between Lines 3 and 4.

Queuing times (minutes) have been collected for all four lines for the same flight number over 20 consecutive days. Times were averaged over the amount of time each passenger spent in the queue that had formed thirty minutes after the flight was open. See the data file. The flight is always a popular one and there are very few vacant seats on any given day.

(a) Display the appropriate control chart(s) for all Lines combined.

(b) Interpret and identify any unusual features in the control chart(s).

(c) Based on your analysis in parts (a) and (b), perform the next steps (if any).

(d) Write a brief Conclusion discussing and quantifying the current state for queuing times and how they should be monitored.

Question 2:

A courier company conducted a brainstorming session amongst drivers to ascertain the reasons why it was unable to deliver items to households, always right first time. One major reason suggested by the drivers was "customer not at home" when the driver arrived. If there were no specific instructions from the customer, for example "leave on door step" or "leave behind garbage bins", drivers were generally reluctant to leave the item unattended. In such cases, items were returned to the company's warehouse, the customer contacted and an alternative time arranged. For some customers, it took several attempts before an item was delivered successfully.

The result was a poor customer experience and significant rework costs incurred by the company.

The company decided to measure the size of the issue, which it classified as the defect "customer not at home". It examined Monday to Friday data from 3rd August 2009 to 1st October 2009 with an intention of developing a baseline from which to consider improvement. It sampled its Monday to Friday deliveries, each day taking 500 random delivery attempts and recording whether the driver was unable to deliver due to "customer not at home". See the data file. There was no reason to believe that Monday was systematically better or worse than Tuesday or Tuesday was systematically better or worse than Wednesday etc.

(a) Summarise the baseline performance of deliveries with respect to the defect "customer not at home". Do not remove any data.

Having established the baseline, the company set about asking the courier drivers for improvement suggestions. It was agreed that a solution called "Double SMS" be trialled.

The customer would be sent an SMS advising on possible delivery time windows soon after the item was received in the company's warehouse. The customer would then select a preferred delivery window. A few hours before the scheduled delivery, a second SMS would be sent, asking the customer for a confirmation that he/she would be at home during the agreed delivery time window. If the customer advised he/she would not be at home, the customer would be offered an alternative delivery window. Trials with the "Double SMS" solution began on 2nd October and continued until 11th November when enough data points had been gathered to consider the solution successful and sustainable.

(a) Summarise the performance of the new process. Do not remove any data.

(b) Discuss and demonstrate using a single control chart the extent of the improvement that has occurred from the old process to the new process. Do not remove any data.

(c) Recommend what next steps you would take with the new process.

Question 3:

Your employer, Quick Hit Agency (QHA), is a debt collections agency. The company specializes in collecting small accounts. QHA does not deal in large accounts and does not take on risky collections, such as those in which the debtor tends to be chronically late in payments or is known to be hostile.

To distinguish itself from competing collection agencies, the company wants to establish a reputation for collecting delinquent accounts fast. The marketing department has just suggested that QHA adopt the slogan:

"Under 60 days or your money back!" At the last staff meeting in which this slogan was proposed, the marketing department was asked how they arrived at the number 60. You found the reply unsatisfactory at best: "Well, 60 sounded like a nice round number."

Since you work as an accountant at QHA, you have access to account balances. You suspect that the number of days to collect the payment is related to the size of the bill. If this is the case, you may be able to estimate how quickly certain accounts are likely to be collected, which, in turn, may assist the marketing department in determining an appropriate level for the money-back guarantee.

To test this theory, you've taken a sample of accounts closed out during the months of January through June. The data set includes the initial size of the account and the total number of days to collect payment in full. QHA deals in both residential and commercial accounts and you've collected data from both groups. The first 48 observations in the data set are residential accounts and the second 48 are commercial accounts. QHA has approximately equal numbers of residential and commercial accounts so the samples are of the right size.