Review homeworkProblems: Chapter 5 - 2, 8, 18, 19Control chart handout problem Process capabilityOther variable control chartsWeek 11 College holidayWeek 12 AssignmentRead Chapter 8 ProbabilityHomeworkChapter 6: 1, 2, 3, 4, 12Chapter 7: 2, 5, 11Week 10Agenda

Process Capability

Process Capability

Chapter Six

Process Capability

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

Process Capability

Process capability analysisObjective is to determine how well the output from a process meets specification limitsCompare total process variation and tolerance.LSLUSL-3+3Target

Process Capability

Individual values compared with averagesWhen 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 dataThe 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 calculationIf 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 limitsXbar 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 limitsCase I: 6 < USL - LSLMost desirable; individual values fall within specification limitsCase II: 6 = USL - LSLOkay, as long as the process remains in controlCase III: 6 > USL - LSLUndesirable; process incapable of meeting specifications

Process Capability

Calculating process capability indicesProcess capability indices: ratios that quantify the ability of a process to produce within specifications

See example - page 290-292

Process Capability