Chapter 23

1. Chapter 23 Process Capability

2. Objectives • Define, select, and calculate process capability. • Define, select, and calculate process performance.

3. Process Capability • Process capability is defined as the inherent variability of a characteristic of a product. • It represents the performance of the process over a period of stable operations. • A process is said to be capable when the output always conforms to process specifications.

4. Process Capability Indices • Three process capability indices commonly used are Cp, Cpk, and Cpm . • 1. Cp = (USL – LSL) / 6 σ = Tolerance / Natural process variation • Where USL is the upper specification limit • LSL is the lower specification limit • 6 σ is the natural process variation

5. Process Capability Indices • 2. Cpk= Min (CpkU , CpkL ) • Where CpkUis the upper process capability index as given by CpkU= (USL – xbar) / 3 σ • and CpkLis the lower process capability index as given by CpkL= (xbar - LSL) / 3 σ • Xbar = process average • σ = process standard deviation • USL = upper specification limit • LSL = lower specification limit • 3 σ = half of the process capability • See examples on page 169.

6. Process Capability Indices • 3. Cpm = (USL - LSL)/2 /3 √ σ 2 + ( μ – T) 2 = (USL – LSL) / 6 √ ∑ (xi – T) 2 / (n-1) • Where μ = process average • σ = process standard deviation • USL = upper specification limit • LSL = lower specification limit • T = target value (center of tolerance) • X = sample readings • n = number of sample readings • See example on page 173

7. Process Capability for Non Normal Data • Find another distribution that fits the data – exponential, chi square, Weibull, and F distributions. • A statistical software package is helpful in choosing the function and parameters that will provide the best fit for the data. • Use non linear regression to fit a curve to the data.

8. Process Capability • The customary method for defining the process capability for attributes data is to use the mean rate of nonconformity. • The purpose of a capability study is to determine whether a process is capable of meeting customer specifications and to devise a course of action if it cannot.

9. Steps of a Process Capability Study • 1. Select a quality characteristic on a specific process for study. • 2. Confirm the measurement system used to acquire the process data. • 3. Gather the data. • 4. Verify process stability and ensure the process is in control. This can be accomplished using control charts. If the process is out of control, identify and eliminate variation. • 5. Verify that the individual data are normally distributed. • 6. Determine process capability. • 7. Update process control plan.

10. Process Performance vs. Specification • Natural Process Limits: Refers to the +- 3σ limits (6σ spread) around a process average. Such limits include 99.73% of the process variations. • Process Specification Limits: Are customer determined and are used to define acceptable limits of process performance.

11. Summary • Process capability is defined as the inherent variability of a characteristic of a product. • A process is said to be capable when the output always conforms to process specifications. • Three process capability indices commonly used are Cp, Cpk, and Cpm . • A statistical software package is helpful in choosing the function and parameters that will provide the best fit for the data. • Verify process stability and ensure the process is in control. This can be accomplished using control charts. If the process is out of control, identify and eliminate variation. • Process Specification Limits: Are customer determined and are used to define acceptable limits of process performance.

12. Home Work • 1. Define process capability. • 2. What package can help find the best fit for the data? • 3. What is the purpose of a capability study? • 4. How do you verify process stability? What do you do if it is out of control?