Statistical Quality Control: The Payoff Calculations

When making business decisions, a key need is quality control and risk assessment in order to predict the success of changes and minimize the potential damage to the company. A tool for such control can be statistical analysis, which is based on the use of data, so it prevents problems of human error and bias. Such analyses can be performed based on inferential tests and sample distributions in order to extrapolate data to the whole population (Statistical quality control, 2022). Keep in mind, however, that statistical quality control is not an exact assessment tool and has some limitations, including its reliance on assumptions. Any statistical test is subject to error, and it is possible that an error could occur during the implementation of a business solution, although companies strive to significantly reduce such probabilities.

A Payoff Table

The table above shows the three payoff strategies. Consistently, the four strategies were applied to the data in order to select the best one for each case.

1. For the Maximax strategy, we must choose the maximum payoff value of all cells. The maximum value is 150 (in $000) for the third strategy, so S3 must be chosen for this criterion.
2. For the Minimax regret strategy, the current table had to be further expanded:

Max (N1) is the maximum value for the second column, and Max (N2) for the third. From these values subtract the individual values in each row, which gives the coefficients A and B. Thus, for the first strategy, the maximum regret is 90 (in $000), for the second, is 170 (in $000), and for the third, is 80 (in $000). The maximum regret should be kept to a minimum, so the optimal strategy is the third strategy.

1. For Maximin, each of the strategies should be considered from the position of the smallest payoff. Thus, for the first strategy the smallest payoff is 40 (in $000), for the second -20 (in $000), and for the third -40 (in $000). Maximin implies choosing the maximum value of the minimum payoff, that is, 40 (in $000) and hence the first strategy is optimal.
2. Finally, to calculate the Minimum risk, assuming equiprobable states for each of the strategies, we need to calculate the average value. For the first strategy, it is 50 (in $000), for the second, it is -5 (in $000), and for the third, it is 55 (in $000). The maximum value corresponds to the optimal strategy, that is, the third one should be chosen.

Reference

Statistical quality control | SQC. (2022). Web.