Where’s the Thief?

The solution

Published: Tuesday, June 19, 2007 - 22:00

The manager of a local grocery store is having dinner with his statistician friend. The store manager tells his friend about a certain cashier who is stealing from the company.

The manager is frustrated because he thinks he knows who the thief is, but can’t fire the miscreant because the employee has been with the company for years and is well-liked by customers, and neither the manager nor corporate accounting has ever actually caught this employee stealing.

At the end of each shift, each register is reconciled. The corporate rule is that any underage greater than $15 or overage greater than $10 causes an investigation. It’s common for a register to exceed these limits, but these triggers have never raised suspicion around the suspected thief. The manager’s hands are tied.

The store has eight cash registers and 12 cashiers. No more than eight cashiers work on a given day.

The statistician says that if the manager will provide 10 days worth of reconciliation records, the thief can be found. The data below are what the manager provides.

Which employee is the thief? The answer can be found using a single time-ordered chart and solidified with a little added deduction.

You must correctly identify the thief and describe your method or provide the chart with the employee identified.

Answer
Employee 8 is the thief.

Justification
This store employs 12 cashiers, and only eight work on any given day. Assuming the money-changing habits of all the cashiers are random, the probability of any cashier having the lowest reconciliation on any given day is 1/8 = 0.125. Looking at the group chart; on days 1, 2, and 3 cashier 8 had the lowest reconciliation. The probability that this would happen randomly is 0.00195. This is rare indeed. With just three days of data, the case against cashier 8 is probably strong enough to hold up in court—and there’s even more evidence. Of the 10 days that were part of the study, cashier 8 came up lowest six days (rare). Cashier 8 came up lowest every day he worked (rare). This employee was able to get away with his crime day after day because the dollars stolen never triggered the corporate alarm of –$15.

About The Author

Steve Wise

Steve Wise is the vice president of statistical methods for InfinityQS, helping companies from all industries implement real-time production for statistical process control and advanced statistical tools. He co-authored  an  industry standard, “D1-9000 Advanced Quality System” in 1991 for Boeing suppliers. Wise is co-author of the book Innovative Control Charting: Practical SPC Solutions for Today's Manufacturing Environment (ASQ Quality Press, 1997).