Taken over a long enough period of time, a policy of not carrying out an inspection would lead to a saving in cost of 7 per sub-assembly. On a purely quantitative analysis, therefore, this is the correct policy to adopt. However, in the real world such a high level of failures is incompatible with a requirement for a ‘quality product’, and the concept of continuous improvement.
It would be more useful to ask the supplier some basic questions regarding his quality management, in order to bring about a fundamental shift towards outcome (iii), rather than simply implementing a policy on the basis of such an uncritical analysis of the situation. Exercise An individual is considering backing the production of a new musical in the West End.
It would cost 100,000 to stage for the first month. If it is well received by the critics, it will be kept on at the end of the first month for a further six months, in which case a profit of 350,000 would be made. If the critics dislike it, it will close at the end of the first month. There is a 50:50 chance of a favourable review. As this provides a positive return it would be accepted as the alternative yields zero. However, the expected value can be misleading here as it is a one-off situation and the expected profit of 75,000 is not a feasible outcome.
The only feasible outcomes of this project are a profit of 250,000 or a loss of 100,000. Whilst almost everybody would welcome a profit of 250,000, not many individuals could afford to sustain a loss of 100,000 and they would place a high utility on such a loss. Many investors would be risk averse in such a situation because they would not consider that a 50 per cent chance of making 250,000 was worth an equal 50 per cent risk of losing 100,000; the loss might bankrupt them. On the other hand, if the individual were a millionaire the return of 250 per cent would be very appealing and the loss of a mere 100,000 would have a low utility attached to it.
The two examples have only had single-point outcomes, that is conformity or otherwise with a pre-set quality standard and a successful show or a flop. It is obvious that the two outcomes of the former represent the only possible alternatives and so quantification of the related pay-offs along the lines of the example appears reasonable. It is also obvious that the profit of i?? 250,000 predicted for a successful show in the case of the latter is far too precise a figure. It would be more realistic to assume a range of possible successful pay-offs, as they will vary, according to the number of seats sold and the price of the seats.
If probabilities are attached to each estimate, the expected value of a successful outcome will take account of the range of possible outcomes, by weighting each of them by its associated probability, as in the following table. The statement of a range of possible outcomes and their associated probabilities is known as a probability distribution. Presenting the distribution to management allows two further useful inferences to be drawn: The most likely successful outcome. That is the outcome with the highest probability (a profit of 250,000 in Table 2. 3).
The probability of an outcome being above or below a particular figure. The particular figure will either be the EV or a figure of consequence, such as zero profit, where a lesser outcome might have dire consequences. By summing the probabilities for pay-offs of 150,000, 200,000 and 250,000, it can be concluded that there is a 37. 5 per cent probability that profits will be 250,000 or less if the musical is successful. By summing those for 300,000 and 350,000 it can be determined that the probability of a profit of 300,000 or more in the event of success is only 12. 5 per cent.
So far only a very small number of alternatives have been considered in the examples. In practice a greater number of alternative courses of action may exist, uncertainty may be associated with more than one variable and the values of variables may be interdependent, giving rise to many different outcomes. Example A company is assessing the desirability of producing a souvenir to celebrate a royal jubilee. The marketing life of the souvenir will be six months only. Uncertainty surrounds the likely sales volume and contribution, as well as the fixed costs of the venture. Estimated outcomes and probabilities are shown in the following table.