Six Sigma Process and Performance Capability Measurement

You're examining a nickel plating process for a furniture manufacturer. The specification range is 8 to 10 microns. The long-term process standard deviation is 0.33 and the mean is 8.9. What's the Ppk?

0.909 or 0.91 Ppk = (USL - X) / (3 long-term sigma), ( X - LSL) / (3 long-term sigma) USL = 10 LSL = 8 Long-term sigma = 0.33 Mean = 8.9 (10-8.9) / 3(0.33), (8.9 - 8) / 3(0.33) = (1.1 / 0.99), (0.9 / 0.99) = 1.11 and 0.909 The lowest number is 0.909, and that is your Ppk.

A process capability study measures the extent to which processes can create end products that meet customers' requirements. Put the steps for performing a capability study in the correct order.

1. Identifying measurable characteristics. 2. Developing sampling plans and collecting data. 3. Verifying normality and stability of the process. 4. Calculating capability indices and determining the sigma level. 5. Making recommendations for process improvement.

Specification limits, process limits, and process spread help determine process capability. How do you use these elements to measure process capability?

Compare the actual process spread to the allowable process spread to determine if a process is in control. Check that the process spread is within the specification limits.

What is the formula to calculate Cp?

Cp = (USL - LSL) / 6sigma USL = Upper specification limit LSL = Lower specification limit sigma = standard deviation

Process capability analysis is used to evaluate and understand current processes. Which capability values indicate a process needs improvement? Cp = 1.17; Cpk = 0.67 Cp = 2.0.; Cpk = 2.0 Cp = 1.0; Cpk = 0.50 Cp = 2.43; Cpk = 2.01

Cp = 1.17; Cpk = 0.67 Cp = 1.0; Cpk = 0.50

In order to have a six sigma process, what does the Cp value have to equal?

Cp = 2

What is the formula to calculate Cpk?

Cpk = min (LSL - X / 3sigma), (X - USL / 3sigma) USL = Upper specification limit LSL = Lower specification limit X = Mean sigma = standard deviation

You're testing a client's manufacturing process. Cp = 3.205; Cpk = 3.14; Cpm = 2.1; Pp = 3.1; Ppk = 2.98; sigma level = >6. The client won't change specifications or accept losses. What should you do?

Do nothing.

What does a Cpk value of 1 mean?

It means the system is capable.

Example of calculating Cpk:

Mean = 1.255 USL = 1.15 LSL = 1.35 Sigma = 0.025 (1.35 - 1.255 / 3(0.025)), (1.255 - 1.15 / 3(0.025)) = 0.95 / 3(0.025), 0.105 / 3(0.025) = 0.95 / 0.075, 0.105 / 0.075 = 1.267 & 1.40 The lower number is your Cpk value = 1.267.

Process performance can be measured by counting defects or measuring variability. Match each performance metric to the method for which it provides data. Methods may have more than one match. Measuring Variability Counting Defects

Measuring Variability - Capability indices. Cost of poor quality. 5. Counting Defects - Parts per million. Rolled throughput yield. Defects per unit.

What is the formula to calculate the Pp?

Pp = (USL - LSL) / 6 long-term sigma USL = Upper specification limit LSL = Lower specification limit sigma = standard deviation

What is the formula to calculate the Ppk?

Ppk = (USL - X) / (3 long-term sigma), ( X - LSL) / (3 long-term sigma)

Which methods can help to verify the normality of a process?

Probability plot. Comparison of descriptive statistics to the normal distribution characteristics. Histogram. A goodness-of-fit test for normality of population data. The Anderson-Darling test.

Process and specification limits are required to measure performance. Match each description to the appropriate type of limit. Limit types may have more than one match. Process Specification

Process Represents the natural variation that occurs in a process. In a call center context, may be based on the average number of calls a customer service rep can answer in an hour. Specification In a call center context, may be based on how many calls customers expect reps to answer per hour. Comes from the voice of the customer.

A Six Sigma team at a manufacturing plant is measuring the performance of its process for creating cast iron parts. How are process and specification limits used in measuring the performance?

Process limits are based on readings of the average tensile strength of a cast iron part. Specification limits may be based on the tensile strength that customers require.

As Cpk increases, what happens to process variation?

Process variation decreases.

You're testing the performance of a new product. Cp = 0.97; Cpk = 0.91; Pp = 0.82, Ppk = 0.93; sigma level = 2.9. The customer doesn't want to change specifications or accept losses. What should you do?

Reduce variability. The process is new, but for a new process you should typically have high capability, high performance indices, and a high sigma value. All these indications are pointing to the fact that the process needs to be thoroughly analyzed to determine the causes of excess variability, and the variability must be reduced to make the process more capable.

What is the formula to calculate the long-term sigma?

Short term Sigma - 1.5

You're examining the capability of a casting for a stove part. The Cp = 1.95; Cpk = 0.835; Cpm = 0.332; Pp = 1.7; Ppk = 0.86; short-term sigma level = 5.5. What statements are correct about the process?

The amount of process variation is within allowable limits. With a Pp of 1.7, process variation is within limits of allowable variation. The higher the Pp over 1, the less variation in the process. The process is capable. A Cp of 1.95 and a short-term sigma level of 5.5 indicates that the process is capable.

What does higher Pp and Ppk values mean?

The higher the Pp and Ppk values, the more stable and capable the process.

You're examining gas mileage for a new hybrid car.The Cp is 1.01, Cpk is 0.998, Cpm is 1.0, Pp is 0.980, Ppk is 0.979, and sigma level is approximately 3. Which statements are true?

The process is almost centered. The process needs improvement.

You're examining a nickel plating process for a furniture manufacturer. The specification range is 8 to 10 microns. The long-term process standard deviation is 0.33 and the mean is 8.9. What is the Pp?

1.01 Pp = (USL - LSL) / 6 long-term sigma USL = 10 LSL = 8 long-term sigma = 0.033 Mean = 8.9 (10 - 8) / 0.198 = 2 / 0.198 = 10.10 ... = 1.01?

Wait times at a health care center range from 5 (LSL) to 33 (USL) minutes. The mean of the wait time is 23.8 minutes, and the estimated standard deviation is 2.4 minutes.What is the Cp?

1.94 Cp = (USL - LSL) / 6sigma USL = Upper specification limit LSL = Lower specification limit sigma = standard deviation 33 - 5 / 6 (2.4) 28 / 14.4 = 1.94

A coffee machine's temperature specifications range from 150 (LSL) to 170 (USL) degrees, with 160 degrees being the mean. The standard deviation of the sample population is 1.67. What is the Cpk?

1.99 or 2 Cpk = min (LSL - X / 3sigma), (X - USL / 3sigma) USL = Upper specification limit LSL = Lower specification limit X = Mean sigma = standard deviation 150 - 160 / 3 (1.67), 160 - 170 / 3(1.67) -10 / 5.01, -10 / 5.01 = 1.99, 1.99 or 2.

Your delivery company is tracking on-time deliveries. You find the process has a DPMO of 3,677, giving a short-term sigma level of 4.2. What is the approximation of the long-term process sigma level?

2.7 The formula for approximating long-term sigma is short-term process sigma minus 1.5 sigma, which in this case is 4.2 - 1.5 = 2.7.

You're examining an order-taking process. Out of a sample of 1,351 orders, 75 were incorrect. The DPMO is 60, and the short-term sigma value is 5.45. What's the long-term process sigma level?

5.45 - 1.5 = 3.95

If Cp = 1.33, what is the parts per million?

64 part per million, or 0.0064%

Another way to express process capability is with the capability index, or Cpm. Which statements describe Cpm?

A Cpm of more than 1 is preferred. The Cpm will be less than Cpk if the process average drifts from the target value. It's used to determine variation between the process average and a target value. A capability ratio of less than 0.75 signifies the process is capable. Lower values of the capability ratio, rather than the Cpm, are better. The capability ratio, or Cr, is the reciprocal of the capability index Cp. The capability ratio offers the same information as Cp, just from a different perspective. It's used when you want to have data clustered more closely around a target specification rather than around the process average. It measures the amount of loss resulting from variation when processes are within specification but not centered adequately around the target. It's also called the Taguchi loss function.

Label the control chart descriptions as either in control or out of control. Each label may be used more than once. In Control Out of Control

In Control A control chart with data points that are just inside the lower control limit. A control chart in which there are no nonrandom sequences of data points. Out of Control A control chart with data points leading upward in sequence. A control chart with a data point above the UCL.

What does it mean if the Cp and Cpk values are less than one?

Indicates that the process is not in control. Therefore, a Six Sigma team should focus on eliminating variation from the process.