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 C p, C pk, and C pm. 1. C p = (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. C pk = Min (C pkU, C pkL ) Where C pkU is the upper process capability index as given by C pkU = (USL – xbar) / 3 σ and C pkL is the lower process capability index as given by C pkL = (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. C pm = (USL - LSL)/2 /3 √ σ 2 + ( μ – T) 2 = (USL – LSL) / 6 √ ∑ (x i – 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 C p, C pk, and C pm. 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?