Vigilance Inc. provides secret shopping services to assist other companies in quality control. Vigilance has just been awarded a contract by Freshway Supermarkets to monitor the customer service experience at all its stores. To gather baseline data, Vigilance sent secret shoppers to pose as custom- ers in 50 Freshway stores during an intensive 2-week period that the store managers were warned about, on the assumption that extra precautions would be taken to assure each store worked normally. Vigilance Inc. uses this data to create control charts for monitoring feedback from future ran- dom visits of secret shoppers. The data concerns a variety of customer ser- vice issues, but one measure that Freshway is particularly concerned about is the chain-wide number of misdirects. A misdirect occurs when the secret shopper asks an employee for help locating a particular item but is not personally escorted to that item, as per the store's service standards. Across the entire chain, Vigilance secret shoppers recorded the following number of misdirects during the baseline evaluation period: 

On each day, each of the 50 Freshway stores was visited twice, and on each visit, the secret shopper asked one employee for help with locating an item. Questions 1. From the baseline data, what are the mean and the standard deviation of the natural variation in the daily proportion of misdirects that resulted from asking for help to locate an item? 2. Assume that in the future Vigilance intends to repeat this procedure on random days, sending two secret shoppers to 50 stores, where each asks for directions once. Calcu- late the control limits for a p-chart to monitor the number of misdirects reported on those days, assuming that Vigilance always draws control charts with z = 3.0. Draw this chart and plot the existing baseline data on it. 3. Now assume that Vigilance would prefer to use a c-chart, because it may not always visit exactly 50 stores with two secret shoppers each during future sampling of the work for FAST lanes. Every time we draw up a chart from the data of a flawlessly func- tioning lane, it just indicates that lane is out of control. We're stuck before we even start using the chart." The manager at exit 53 volunteered its FAST lane as the site for yet another pilot proj- ect to develop a relevant tool to monitor FAST lane violations, one that would correctly signal any unusual changes, to be acted on quickly by closing the lane. Exit 53's FAST lane equipment was upgraded less than a year ago, and preventative maintenance was conducted in late May, so the following 30 days of past data from exit 53 represents the behavior of a system that is in complete control:

Questions 

1. Use this data to create a c-chart for daily FAST lane violations issued, assuming z = 3.0. This is the method that WMA attempted to use earlier. Mark the past data on the chart. Does your c-chart indicate that the FAST lane system was in control over these past 30 days?

2. One employee at exit 53 remembers the previous pilot project and says, "That wasn't ever going to work. You can't just watch the number of violations, because that varies with the number of cars each day." This employee is referring to the choice of a c-chart versus a p-chart, but WMA management assumed that a p-chart couldn't be used because there is no fixed sample size n. Propose a logical adaptation of the p-chart methodology and create a chart to track the proportion of vehicles in the FAST lane that are issued violations each day. Does this chart indicate the current system is in control?

3. Now create a charting system that solves WMA's monitoring problem. The secret to this lies in the employee's previous statement and in an additional remark about the earlier unsuccessful pilot project: "Why did they think that we'd be able to use the same chart all week?"

Transcribed Image Text:

Number of Number of Day Misdirects Day Misdirects Day Number of Misdirects 1 0 6 1 11 1 2 6 7 5 12 3 3 1 8 0 13 0 4 3 9 5 14 3 5 0 10 3