The Department of Motor Vehicles wanted to understand and better control the wai

Question

The Department of Motor Vehicles wanted to understand and better control the waiting time of customers of the drivers license office. To do this, they constructed X-bar and R-charts by sampling the waiting times of the first five customers at the beginning of each shift (7 a.m., 12 p.m., and 3 p.m.). How might the sampling process be improved, and what would you recommend?

2. Suppose that you were monitoring the time it takes to complete order transactions at a call center. Discuss what might cause such out-of-control conditions as a trend, shift in the mean, or cycles in an x-bar chart in this situation.

Remember to show all work and to answer all parts of the questions. The work must be submitted in a Word or Excel document

Explanation / Answer

Answer1

As per my understanding sampling of first five customers at the begining of each shift may not be the correct approach rather samples should be representative of steady state. Beginning and ending of the queues are generally transient states and may not represent the true values of parameters like wiating times mentioned in the question. Sample size should be kept in proportion to the total populations (how many customers are served in each shift) and random sampling is preferred to sampling at fixed times (in the beginning only as mentioned in the question). It is quite possible that all five customers may be present before the start of the shift and or show higher values of waiting time which is very much dependent on the processing times as well as number of service providers, both in series and in parallel. Further it is also important to know the batch size, if any for providing any service and the discipline for the queue in terms of first in first out or to have some minimum batch size etc.

Answer 2

In case the x-bar chart shows the values (actual sample observations) falling beyond the limits (Upper Control Limit and Lower Control Limit) then it may be required to shift the mean values for different time intervals and or adjust the number of service providers. Out-of-control conditions may be at the times of change of persons at the beginning and or closing of shifts. It may be on account of varying skills of the persons providing services. There could be external factors responsible for increase or decrease in the number of calls received and or types of queries/ services asked for per call.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.