“Trial by Computer”—A Case Study of the Use of Simple Statistical Techniques in the Detection of a Fraud

Abstract

This case study describes an investigation which was undertaken for a local shopkeeper after one of his shop assistants had been convicted of theft. The person concerned had admitted stealing a few pounds on just one occasion, but a series of worsening year-end results over a period of three or four years caused the shopkeeper to suspect that stealing had been taking place on a very large scale over a long period of time. Could this be ‘proved’ by examining in detail the records of the shop's business for the years in question?

The analysis undertaken involved principally the number of customers each week and the revenue per customer. The most usual form of theft involves ‘understriking’ (ringing into the till less than the value of the sale and subsequently taking out the difference). This practice will be expected to reduce the revenue per customer and increase the number of customers (because the incorrect entry is usually disguised by immediately ringing in a no-sale or a zero amount). Clear evidence was found of stealing on a much larger scale than had been admitted.

Keywords:

• cusum
• change-point analysis
• intervention analysis
• autoregressive-moving average processes