Question

Basin Ridge Manufacturing

Jim Davies is the night shift production lead at Basin Ridge Manufacturing. Basin Ridge produces climbing gear including ropes, harnessess, pitons, and carabiners. Jim has noticed that mean rate of defective units per hour for the A38 Locking Carabiner has increased from 0.5% up to 0.7%. That is, for every 1000 units produced, 7 are now defective instead of 5.

Overall, this defect rate is still below the target rate of 1%, but Jim is concerned that he may need to overhaul one of the production machines which has been notoriously finicky over the past year. Jim is trying to decide if he should shut down the machine for the overhaul. The overhaul would take two hours.

Jim has asked you to set a control limit for the next 1000 units. If the number of defective units exceeds the control limit, Jim will shut down the production and overhaul the machine. Answer the following questions and report back to Jim.

1) Based on the mean rate of 5 or 7 defective units per hour, what probability distribution should be used?

2) How many defective units should Jim set as his control limit? Explain your reasoning for choosing that control limit.

3) If the mean rate continues to be 0.7%, what is the likelihood that Jim will need to shut down production using the control limit you recommended? What if the mean rate rises to 1%? What if the mean rate falls back to 0.5%?

Answer 1

Weibull probability distribution best suits for this problem. It sets a bar and helps in controlling the defects. I would refer jim to set a control limit of 8 defective units and will ask him to decrease it by 1 after a specific period of time, so that jim can work on the problem. If the mean rate is 0.7% , then the likelihood jim shut down is low. If the number of defects increase, then the likelihood for shutting down the machine increases. If the control rate rise to 0.1%, then jim should definitely overhaul the machine.