The supervisor of a refining department has just received a Performance Evaluation Report for the departments automated processing machine. The Performance Evaluation Report shows an above normal rejection rate which could indicate that malfunction has occurred in the processing machine. The supervisor must decide whether or not to order an investigation of the automated processing machine. Past experience has shown that the cost of an investigation would be TZS 45,000 and the cost to repair the processing machine if malfunction has occurred would be TZS 245,000. If the processing machine is malfunctioning and repairs are made, it will lead to cash savings of TZS 150,000 per month in the future. The supervisor is unsure of the ultimate value of the cash savings because they are affected by the number of months until the machine malfunctions again. The following table provides the estimate of the time until the next malfunction will occur. Time until next malfunction Probability 2 months 3 months 4 months 5 months 0.15 0.30 0.45 0.10 Based on past experience and evaluation of operating results, there is a probability of 0.20 that the processing machine is malfunctioning.

Required: a) Should the supervisor order an investigation? Show supporting calculations.

b) At what level of critical probability that the process is out of control would the expected savings from investigating equal the expected costs?