BakingtonTools Company

When Jim Walker was hired at the Bakington ToolsCompany (BTC), the company's managers considered him a top recruitment. After a short introduction period in each of the company's departments, Jim was assigned to the production control division. He reported directly to AnnettCarter, who had been in charge of production control for about 3 years. Annett was excited about having Jim in her department because the workload had been increasing very fast during the past few months. It was becoming difficult to maintain the type of control on incoming parts that Annett wanted with the increasing volume of orders.

Annett assigned Jim immediately to the task of reviewing the acceptance- sampling plan for a critical part. This part was singled out because of its high failure rate, and because its manufacturer AMG ran a production line known to be “inconsistent” when it came to quality. In particular, one of the part specifications required it was 12” long. It could be reworked if found it was too long, but scrapped if found to be shorter than 11” long. Therefore, BTC and AMG have agreed the production line should be calibrated to produce13” long items, while the acceptance-sampling plan consisted of a random sample of 25 parts from each shipment where the entire shipment is accepted if the sample mean per item was greater than 11.75”. Otherwise, the shipment would be returned claiming AMG did not stand behind its own obligation (namely the mean is less than 13”). The sampling plan was based on a normally distributed item length with a standard deviation of 3.5”.

Assignments:

  1. Annett’s first request was that Jimchecked the risk involved in running this quality control procedure, and suggest changes if needed. The manufacturer risk was the rejection of a good shipment. BTC’s risk was the acceptance of a bad shipment. To evaluate these risks, the corresponding probabilities needed to be determined: For the manufacturer risk evaluation – P(shipment is rejected when = 13”); For BTC’s risk evaluation – P(shipment is not rejected when  = 11”).The results of this analysis were not very encouraging. The manufacturer’s risk turned out to be much smaller than BTC’s risk! Annett wanted to see a written report of this analysis.
  2. Jim thought it was going to be easy to improve this plan. “Suppose”, he said to himself, “BTC and AMG share the risk evenly”. Talking to Annett about it she believed BTC can sell the idea to AMG in the name of fair business practice.Jim needed to find the new plan keeping the sample at 25 observations.
  3. Annettknew there was one other issue they had not discussed yet, the economies of the testing procedure. This is what Jim learnt from her: Each observation taken costs $5; each bad shipment (when  = 11”) kept,costs BTC an additional $1500 due to production stoppage; On the other hand each good shipment (when = 13”) sent back,costs BTC $2000 paid to AMG to cover the re-shipping and other expenses the manufacturer might have;It was important to remember that in the long run 70% of all the shipments are actually “good”. This information called for a testing plan based on cost considerations and not based on probability evaluation only. Jimneeded to provide a testing plan with not necessarily 25 observations, with same risk values for both parties, but minimum expected cost.
  4. As a footnote Annett was wondering, whether or not it was imperative to keep the principle of equal risk sharing in place. She wanted to know how much can be saved if the risk is shared such that the expected cost for BTCis minimized. Of course this means that the acceptance value of shipment meanlength should vary as well as the sample size. It would suffice to try a few acceptance values between 11” and 12” to demonstrate the effect on total expected cost. Jimwas a little bit rattled….

Appendix

Annett is trying to help Jim. To calculate the risk taken by AMG in the current plan find the probably P(Sample mean < 11.75 when = 13). Please follow this lead to calculate the other risk. As far as designing an equal shared risk plan you’ll need to find a new acceptance value (different than 11.75). Finally, to calculate the expected cost note that the risk is still assumed to be even between the two parties, but the sample size may change. Particularly, the expected cost for BTCis generally 5n + .7*P(Good shipment is rejected)*2000+.3*P(Bad shipment is accepted)*1500. This applies to both part C and D.

You’ll need to use Excel to calculate probabilities, andto construct a spreadsheet to calculate expected costs for different values of ‘n’.

Your report should show the probabilities calculated for each case and interpret the results. For case C and D you are advised to use Excel to calculate probabilities, andto construct a spreadsheet to calculate expected costs for different values of n.