If you’re in line for a coffee at the local Starbucks, analysis conducted by graduate students at Rutgers University suggests that the probability of waiting more than five minutes for your tall, hot, three-pump sugar-free vanilla, one-pump mocha, half soy, half non-fat latte with whip is very high.
Brandon Theiss and Matthew Brown used a reliability engineering project to combine their passions for Starbucks’ coffee and gathering and analyzing data with Minitab Statistical Software.
Theiss drew on his work experience in crafting the study. Currently a principal industrial engineer at Medtronic, he previously was a Master Black Belt at American Standard Brands, and a systems engineer at Johnson Scale Company. In 2010, the American Society for Quality named him one of their Top 40 Leaders in Quality Under 40.
“Virtually anything can be characterized as a process and measured,” Theiss says. “Once you have the data you can use a tool like Minitab to draw conclusions and hopefully improve the process. I personally love Minitab and use it daily—I think it is by far the best software in the industry.”
While many of their classmates simply analyzed existing data, Theiss had a personal motivation for collecting real data. “I selected Starbucks to study because I am quite an addict,” he admits. “However, going to Starbucks is a very common experience, so it’s something everyone can relate to.”
When customers visit a Starbucks, they expect a consistent experience in terms of both their beverage and the time required to receive it. The team defined meeting a customer’s expectations as receiving their beverage in under 5 minutes. Then, to see if the national Starbucks experience would be delivered at arbitrarily selected Starbucks locations, Theiss and Brown chose two Starbucks stores in New Jersey, one in Marlboro, the other in New Brunswick.
Brown collected data in the Marlboro store for three hours, while Theiss sat in the New Brunswick location for four. Each set up a laptop and used a simple stopwatch application to record customer arrival and wait times in Excel. Starbucks “public café” culture made it easy to gather data without attracting attention. “I spend so much of my time in the New Brunswick Starbucks that I am seen as furniture, so I went undetected,” Theiss says. “I believe Matt received a few awkward glances.”
After gathering their data, they used Minitab to analyze it. They subjected the frequencies of arrivals to a goodness-of-fit test for the Poisson distribution. In theory, Poisson-distributed arrivals typically experience Gamma-distributed wait times. The team then tested how well their wait-time data fit the Normal, Gamma, and Weibull distributions, both to validate the theoretical assumption and to account for potential confounding by the beverage-making process.
Once they confirmed the wait time distribution, the team performed a process capability analysis for each location, correcting for biased data due to small sample size. Finally, they used individuals and moving range (I-MR) control charts to evaluate whether the beverage delivery process was in statistical control.
The process capability analysis for the 94 wait-time measurements collected from the Marlboro data had a very low Ppk value, which implies a process that is not capable of meeting the 5 minute upper specification limit. Another interesting statistic in this analysis is the PPM value. Analysis of the Marlboro data implies that for every 1,000,000 customer entering, 127,306 will not receive their beverage in less than 5 minutes.
The analysis of the 198 wait time measurements collected from the New Brunswick location yielded a Ppk of 0.13 for the Gamma model, again implying a process that is not capable. The PPM value implies that more than 1 out of every 4 customers will wait longer than expected to receive their beverage.
Next the team assessed whether a statistically significant difference existed between the wait times at the two locations. Because they had sufficient evidence to believe that the underlying distributions were non-normal, Brown and Theiss used a Kruskal-Wallis comparison test, which does not assume that the data are normally distributed. The low p-value from the Kruskal-Wallis Test indicated that there was a significant difference between wait times at the two locations, with New Brunswick taking the longest. The data set supports the conclusion that the location a customer visits has a significant effect on the time they will wait for their beverage, with neither location meeting the expected 5-minute maximum wait time.
Of course, Theiss notes, this study had many limitations. “Our data set was small and far from comprehensive,” he says. “Both the New Brunswick and Marlboro data were collected for a rather short duration, on a single day. A more complete analysis would include a long data collection window, which would allow the model to include factors such as the time of day, day of the week, and even time of the year. In addition the data set did not include the number or type of drinks ordered, but this data would be difficult to collect without the assistance of Starbucks.”
While the mean time-to-beverage was less than five minutes for all scenarios analyzed, the probability of waiting more than five minutes is still very high. This implies that thirsty, caffeine-craving customers are willing to wait what would appear to be a long time to receive their beverage. And these findings certainly haven’t reduced the frequency of his own visits to Starbucks, Theiss says. “Unfortunately, I still go there several times a day, and I am on a first-name basis with the baristas at 3 different locations.”