Problem
Due to increasing competition among local banks, the top management has embarked a continuous improvement program of statistical process control and has decided to use variable control charts (Xbar-R chart) to study the queue time of customers during the peak noon to 1 p.m. lunch hour to monitor customer queue time and determine whether additional front line counter is required to minimize customer waiting time.
Four customers are selected during the one hour measurements make up a subgroup. The table below lists the waiting time (operationally defined as the time from when the customer enters the lines until he or she begins to be served by the teller) for 20 days (base on five working days in a week).
Data
Raw data in JMP 9 data table – queue time for customer at a bank
Interpretation of results
(Note : the result is generated by making use of Graph > Control Chart > Xbar)
Base on the charts below, the first panel is the Xbar chart and the second panel is the R chart. None of the points on the R-chart is outside the control limits, and there are no other signals indicating a lack of control. Thus there is no indication of special sources of variation on the R-chart.
For Xbar chart, it notices that on 16/11/2009, the data is below 2 standard deviation zone (2 out of 3 point or beyond rule). This indicates lack of control. Further investigation should be carried out to determine the sources of these special causes that may have caused a low queue time on this day. For this case, since shorter queue time is better, no corrective action is required.
Since the management defines the average queue time for a customer should not exceed 10 min, base on Xbar chart, there is no data exceed 10 minutes, therefore we can conclude that for the time being, no additional front line service counter is required.
XBar of Queue Time
Note: The sigma was calculated using the range.
R of Queue Time
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