1. Process Capability Studies Before performing a process capability study the process must be stable. The natural behavior of a process is termed its process capability. Once the process capability study is completed, process improvement studies can start (PDSA) cycle. For attributes, process capability studies are carried out with control charts and rational subgrouping as discussed previously. We will concentrate on Variables process capability studies

2. Natural Limits - indicate what a process is capable of producing. That is they provide an indication of the variability that is inherent in the process. They are calculated as follows: Upper Natural Limit (UNL) = process centerline + 3(process standard deviation) Lower Natural Limit (LNL) = process centerline - 3(process standard deviation) Note: it is assumed that the measurements follow a normal distribution

3. Example A process is stable, centered, and distributed normally with an average of 30 lbs. And an average range of 4.8 lbs. Find the natural limits(assume n = 5):

4. Process capability indices Process capability indices are used to state a process’s ability to meet specifications in one summary statistic. Assumptions: –Process is stable –Variables data –Process is normally distributed C p : Used to summarize the processes ability to meet a two sided specification limit. –It is assumed that the process average (x bar bar) is centered on nominal

5. CPU: Used to summarize a process’s ability to meet a one sided upper specification limit. CPL: Used to summarize a process’s capability to meet a one sided lower specification limit.

6. C pk Used to summarize a process’s ability to meet a two-sided specification without assuming the process is centered on nominal. Note: –If a process is unstable process capability studies are meaningless –If a process is not normally distributed, out-of-spec fraction can be incorrectly calculated.

7. Example (Problem 2 chapter 11) The ABC Co. produces steel tubes. The steel tube process is a stable cut-to-length operation that generates tubes that are distributed normally with a mean of 12.00 inches and a standard deviation of 0.10 inch. The LMN Co. wishes to but tubes from the ABC Co. The LMN Co. requires steel tubes 11.95 inches long with a tolerance of ±.30 inches. Compute C p, CPU, CPL and C pk