# 50-Step Assembly Line

# 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?*

1 punto

3.

Pregunta 3

**Process with Scrap**

Consider the following four-step assembly operation with quality problems:

- The first resource has a processing time of 5 minutes per unit and one employee doing the operation.
- The second resource has a processing time of 4 minutes per unit. It also has one employee doing the operation. However, this is a very delicate task and 80% of all products have to be scrapped after this step.
- Two workers are staffed for the third resource. No quality problems occur at this resource and the processing time is 20 minutes per unit.
- At the fourth and final resource, one operator handles the product. No quality problems exist at this step and the processing time is 12 minutes per unit.

*For every unit of demand, how many units have to flow through the second step in the process?*

1 punto

4.

Pregunta 4

**Process with Scrap**

Consider the following four-step assembly operation with quality problems:

- The first resource has a processing time of 5 minutes per unit and one employee doing the operation.
- The second resource has a processing time of 4 minutes per unit. It also has one employee doing the operation. However, this is a very delicate task and 80% of all products have to be scrapped after this step.
- Two workers are staffed for the third resource. No quality problems occur at this resource and the processing time is 20 minutes per unit.
- At the fourth and final resource, one operator handles the product. No quality problems exist at this step and the processing time is 12 minutes per unit.

*Where in the process is the bottleneck?*

1 punto

5.

Pregunta 5

**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 is the capability score of the supplier?*

1 punto

6.

Pregunta 6

**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])?*

1 punto

7.

Pregunta 7

**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)*

1 punto