 Review homework Problems: Chapter 5 - 2, 8, 18, 19 and control chart handout  Process capability  Other variable control charts  Week 11 Assignment Read Chapter 8 “Probability” Homework Chapter 6: 1, 2, 3, 4, 13 Chapter 7: 2, 5, 11 Week 10 Agenda

Process Capability Chapter Six

Process Capability Defining process capability  Process capability refers to the ability of the process to meet the specifications set by the customer or designer.

Process Capability Process capability analysis  Objective is to determine how well the output from a process meets specification limits  Compare total process variation and tolerance. LSL USL -3  +3  Target

Process Capability Individual values compared with averages  When distributions of averages are compared to distributions of individual values, the averages are grouped closer to the center value than are the individual values, as described by the central limit theorem.  What does this imply for averages in control limits versus individual values in specification limits?

Process Capability Estimation of population sigma from sample data  The relationship between the standard deviation for individual values and the standard deviation for their averages is given by the formula: Where n = subgroup sample size

Process Capability To simplify calculation  If the process can be assumed to be normal, the population standard deviation can be estimated from either the standard deviation associated with the sample standard deviation or the range: or

Process Capability Control limits and specification limits  Xbar charts do not reflect how widely the individual values composing the plotting averages spread.  The spread can only be seen by observing what is happening on the s or r chart.

Process Capability The Six sigma spread versus specification limits  Case I: 6  < USL - LSL Most desirable; individual values fall within specification limits  Case II: 6  = USL - LSL Okay, as long as the process remains in control  Case III: 6  > USL - LSL Undesirable; process incapable of meeting specifications

Process Capability Calculating process capability indices  Process capability indices: ratios that quantify the ability of a process to produce within specifications  See examples - pages