1. 50-Step Assembly Line

Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps has a defect probability of 1%. The final product produced on the assembly line is defective if any one of the 50 steps made a defect.

At the end of the assembly line there are two operators independently inspecting the product. Each of them is recognizing a defective product with a 90% probability. Assuming that the product is not defective, it is moved to the shipping department. Otherwise, the product is scrapped.

Probability that a defective product is produced (independent of the defect being found or not) (in decimal form):

What is the probability that a defective product is moved to the shipping department?

2 Lean Burgers

The management of a large fast food chain evaluates the supplier of their deep-frozen beef patties. The supplier delivers frozen beef patties that according to the specifications have to weigh between 94.5 grams and 95.5 grams. All other beef patties are rejected.

A random sample of 30 patties that were inspected over the course of the last week revealed that the average weight was 95.0 grams. The standard deviation was 0.25 grams.

What percentage of the deliveries is likely to be outside the specification limits (outside the interval of [94.5, 95.5])?

3 Lean Burgers

The management of a large fast food chain evaluates the supplier of their deep-frozen beef patties. The supplier delivers frozen beef patties that according to the specifications have to weigh between 94.5 grams and 95.5 grams. All other beef patties are rejected.

A random sample of 30 patties that were inspected over the course of the last week revealed that the average weight was 95.0 grams. The standard deviation was 0.25 grams.

To what level would the supplier have to reduce the standard deviation of the operation if his goal were to obtain a capability score of 1 (i.e., get less than or equal to 0.27 percent defective)?

(Note: Please enter your answer as a decimal. Fractions are not accepted by the software)