PROCESS CAPABILITY

RANGE OF NATURAL VARIATION OF A PROCESS

‘NATURAL VARIATION’ IS USUALLY DEFINED AS +/- 3 SIGMA

ASSUMES ONLY COMMON CAUSE VARIATION

ADDRESS HOW WELL PROCESS WILL MEET DESIGN TOLERANCES

FOUR WAYS IN WHICH DESIGN TOLERANCE MAY INTERACT WITH PROCESS CAPABILITY

• process capability = design tolerance

• process capability > design tolerance

• process capability < design tolerance

• center of process capability is not equal to nominal

PROCESS CAPABILITY STUDIES ARE OFTEN UNDERTAKEN TO IMPROVE PROCESSES

NEED TO HAVE AN IDEA OF THE DISTRIBUTION OF THE PROCESS

• HISTOGRAM

• NORMAL SCORES PLOTS

• MTB> NSCORES C1 C2

• MTB> PLOT C2 C1

IF HISTOGRAM AND NORMAL SCORES INDICATE NORMAL DISTRIBUTION - CAN MAKE STATEMENTS ABOUT PERCENT OF PROCESS OUTPUT WITHIN DESIGN TOLERANCE

EXAMPLE:

• UTL=10.4; LTL=9.6

• PROCESS MEAN = 10.0

• PROCESS STD DEV = .1667

• PROCESS IS NORMALLY DISTRIBUTED

• WHAT IS PROCESS CAPABILITY?

• WHAT IS PROPORTION DEFECTIVE?

• WHAT IS PPM DEFECTIVE?

PROCESS CAPABILITY INDEX

PROVIDES A NUMERICAL RATIO OF DESIGN TOLERANCE / PROCESS VARIABILITY

Cp = (UTL-LTL)/( 6 X SIGMA)

• Cp is for ‘centered’ processes

• What is Cp for prior example?

• What is relationship between design tolerance and process variability when Cp = 1, >1, <1

 

For non-centered process use Cpk

• Cpk = MIN(Cpl, Cpu)

• Cpl = (MEAN - LTL)/(3 X SIGMA)

• Cpu = (UTL - MEAN)/(3 X SIGMA)

EXAMPLE

• UTL = 10.4; LTL = 9.6

• MEAN = 10.2; SIGMA = .1667

• WHAT IS PROCESS CAPABILITY?

• WHAT IS PROCESS CAPABILITY INDEX?

• WHAT IS PROPORTION DEFECTIVE?

• WHAT IS PPM DEFECTIVE?

USE OF PROCESS CAPABILITY AND CONTROL CHARTS

ESTABLISH CAPABILITY:

say Cp or Cpk = 2 (Motorola’s 6 sigma quality philosophy goal)

this means process mean and process variability are acceptable

monitor and control with CONTROL CHARTS

X-BAR CHART TO MAINTAIN PROCESS MEAN AT DESIRED LOCATION

R CHART TO MAINTAIN PROCESS VARIABILITY AT DESIRED LEVEL

MOTOROLA 6 SIGMA

GOAL IS Cp = 2

(DESIGN TOLERANCE)/(PROCESS VARIABILITY) = 2

NOTE: NUMERATOR OF Cp WILL BE SOME NUMBER THAT REPRESENTS CUSTOMER REQUIREMENTS (DESIGN TOLERANCE)

THEREFORE DENOMINATOR MUST BE SUFFICIENTLY SMALL THAT Cp EVALUATES TO 2 (OR LARGER IS OK TOO)

SINCE DENOMINATOR WILL BE +/- 3 STANDARD DEVIATIONS, THE NUMERATOR (DESIGN TOLERANCE) MUST BE +/- 6 STANDARD DEVIATIONS

WHY IS THIS 3.4 PPM?