1. Process Yield

1a. For 2 process steps, each with 5% fraction defective, what is our final Process Yield?

Hint: Process Yield for a process with n steps and fraction defective, p, at each step = (1-p)^n

1b. For 4 process steps, each with a yield of 25%, what is our final Process Yield?

Hint: here 1-p = 0.25

1c. A process has 3 steps. Assuming each step has the same fraction defective and given that the overall process yield is 85.7%, what is the fraction defective, p, at each step?

Hint: for n=3, overall process yield = (1 p)^3

2. Process Capability

From the lecture we learned that natural process variability is the variability that we expect to face in our normal production environment. This natural variability is defined as +/-3 from the mean, which is equivalent to 99.73% of the production (property of a normally distributed variable).Comparing this natural process variability (represented by +/-3 to the specification limits gives us a measure for our Process Capability.

2a. A cable manufacturer produces micro USB cables.

The size of the connector is allowed to vary between 4.998 mm and 5.002 mm.

The process is currently centered and running with a standard deviation () of 0.001mm.

What is the value of CPK for this process?

Cpk = MinUSL - 3 , -LSL3

2b. A food producer is bottling vinegar.

The amount of acid in this vinegar is allowed to be between 12 mg 1mg.

Currently the process is running with a mean () of 12.7 mg and a standard deviation () of 2 mg.

What is the value of CPK for this process?

Cpk = MinUSL - 3 , -LSL3

2c. The LSL is given by 15mm for a process, the USL is 20 mm.

The standard deviation () is 1 mm.

The process is centered () at 17 mm.

What is the CPK?

Cpk = MinUSL - 3 , -LSL3

2d. For a given process, the distance between the upper and lower specification limits equals 6, and the CPK value is 0.5

What do we know about this process?

Select one:

1. The process is in control.
2. The natural process variability is larger than the distance between the upper and lower specification limits.
3. The process is not centered.
4. There is an error because the CPK value cannot be less than 1.00.

3. Process Control

Process Capability is a measure of how capable a process is of producing product within specifications, USL and LSL. We learned two of the most common capability metrics, CP and CPK.

Process control is another important topic, part of Statistical Process Control (SPC), which we only touch on in this course, but we should understand the importance of process control (see async lecture 5.7):

• Data is taken from samples at different times and a sample statistic (e.g., mean or range of the sample) is plotted.
• The data is assumed to be normally distributed with a mean (process centering) and standard deviation (process variability).
• Common sample sizes are between 2 and 10.
• Control limits (UCL and LCL) are constructed for each control chart.

Control charts are constructed from data for a critical-to-quality parameter and used to monitor the process.

• Center line: average of the statistic over a representative set of samples from stable process
• Upper and lower control limits (UCL and LCL): the UCL (LCL) is usually set at 3 standard deviations* above (below) the average*

*of the sample statistic in a representative sample set

3a. According to Dr. Shewart (Bell Labs), there are two types of variation:

Select one:

a) Normal variation and Random variation.

b) Normal variation and Assignable cause variation.

c) Common cause variation and Assignable cause variation.

d) Common cause variation and Random variation.

3b. A process is in control, if

Select one:

a) All the data points for a critical-to-quality parameter are within the specification limits (LSL, USL).

b) All the data points for a critical-to-quality parameter are within the control limits (LCL, UCL).

c) Calculated sample statistics from samples taken from production of a critical-to-quality parameter are within the specification limits (LSL, USL).

d) Calculated sample statistics from samples taken from production of a critical-to-quality parameter are within the control limits (LCL, UCL).

Extra Practice Problem: Control Charts

If there is an effect that results in changes to the parameters of the underlying statistical distribution of the process this is an example of

Select one:

a) Normal variation

b) Random variation

c) Common cause variation

d) Assignable cause variation