Researchers at Miami University in Oxford, Ohio, investigated the use of p charts to monitor the market share of a product and to document the effectiveness of marketing promotions. ­Market share is defined as the company’s proportion of the total number of products sold in a category. If a p chart based on a company’s market share indicates an in control process, then the company’s share in the marketplace is deemed to be stable and consistent over time. In the example given in the article, the RudyBird Disk ­Company collected daily sales data from a nationwide retail audit service. The first 30 days of data in the accompanying table (stored in RudyBird) indicate the total number of cases of computer disks sold and the number of RudyBird disks sold. The final 7 days of data were taken after RudyBird launched a major in store promotion. A control chart was used to see if the in store promotion would result in special cause variation in the marketplace.

a. Construct a p chart, using data from the first 30 days (prior to the promotion) to monitor the market share for RudyBird disks.

b. Is the market share for RudyBird in control before the start of the in store promotion?

c. On your control chart, extend the control limits generated in (b) and plot the proportions for days 31 through 37. What effect, if any, did the in store promotion have on RudyBird’s market share?

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Cases Sold Before the Promotion Day Ttal RudyBirdDay Ttal RudyBird 154 153 16 177 143 18 200 19 134 20 192 155 22 135 23 189 24 184 170 26 178 167 204 29 183 169 35 43 69 17 197 194 172 190 47 45 38 21 173 53 39 10 47 173 168 184 211 179 37 45 58 35 12 13 27 28 42 71 15 43 Day 31 32 Cases Sold After the Promotion Total 201 RudvBird 76 85 90 199 187 168 198 36 37 79 97