INT 506/706: Total Quality Management Lec #6, Process Capability

Outline Individual values vs. averages Control limits vs. Specs 6σ spread versus specs Calculating Process Capability Indices 2

Process Capability

Individual vs. averages

The ability of X-bar to approximate μ is measured by the following equation:

Individual vs. averages IF the process can be assumed to be normal, the population standard deviation can be estimated from either the sample standard deviation (s) or the range (R).

Control limits vs Specifications A process under control exhibits: 1.2/3 of points near center 2.Few points close to the center 3.Points around centerline 4.Points balanced on both sides 5.No points beyond control limits 6.No patterns or trends

Control limits vs Specifications

6σ Spread versus Specs 3 Possible CASES 1)6σ < USL – LSL 2)6σ = USL – LSL 3)6σ > USL - LSL 3 Possible CASES 1)6σ < USL – LSL 2)6σ = USL – LSL 3)6σ > USL - LSL

CASE #1 6σ < USL – LSL

CASE #2 6σ = USL – LSL

CASE #3 6σ > USL – LSL

Calculating 6σ Assuming process is STABLE and IN CONTROL 1.20 subgroups of n=4 2.Calculate sample std dev, s i, for each sample 3.Calculate average sample std dev, 4. Calculate pop std dev 5.Multiply pop std dev *6

Example

Capability Index C p

EXAMPLE INTERPRETATION: Process NOT capable (case 3)

Capability Ratio, C r Inverse of C p so larger the ratio, the LESS capable the process is of meeting specifications

C pk C p and C r do not take into account the centering of the process Where Z(min)=

C pk

Review Review pdf file in blackboard –“CapabilityCaseStudy” –Put into Minitab and run capability modules to see what you come up with Is it the same as the case study? Do you understand the interpretation of the case study?