Process Capability Studies

Comparison of Process Output to Product Requirements

Lynn Taylor – OISM 470W Section 002

Process Capability Studies3 Steps

• Gauge Capability• Process Characteristics

– Stability– Normality– Control

• Process Capability Analysis– Comparison of process output(s) to

requirements.

Process Capability StudiesDefinitions

• Process – Work performed on a set of inputs to produce a result.

• Capability – The predictable result(s) of a process allowed to operate without outside interference.

• Process Capability Study – Comparison of process output(s) to product requirements.

Process Capability StudiesUses In Our Plant

• Customer 1 < 407, Cpk > 1.25• Customer 1 > 407, Cpk > 1.50• Customer 2, Cpk > 1.33• With new clients, determine if tolerances are

reasonable, if our processes are capable and robust, and if improvements are needed.

Process Capability StudiesStep 1 – Gauge Capability

Six Measures• Gauge Accuracy

– Are the readings correct?

• Gauge Linearity– Are the readings correct over the measurement

range of the instrument?

• Gauge Stability– Does the gauge return similar values over time?

Process Capability StudiesStep 1 – Gauge Capability

Six Measures

• Gauge Repeatability– Does one operator return a similar result time after

time (gauge variability)?

• Gauge Reproducibility– Do different operators return similar results?

• Gauge Repeatability and Reproducibility– Total variability of a test result (operator &

gauge).

Process Capability StudiesStep 2 – Process Characteristics

Analyze Process Data

• Normality – Evidenced by the descriptive statistics skewness and kurtosis.

• Stability – The absence of shifts or trends over time.

• Control – Control chart analysis passing tests for special causes.

Process Capability StudiesTests for Normality

Process Capability StudiesTests for Stability and Control

Process Capability StudiesComparing Distributions to Specifications

Process Capability StudiesReal World Example – Part 504

Process Capability StudiesPart 504 Continued

Process Capability StudiesPart 504 Continued

Process Capability StudiesPart 613 - An Exercise

0.1083 0.10816 0.10778 0.10836 0.10802 0.10837 0.108090.10819 0.1081 0.10784 0.10809 0.10794 0.10846 0.108560.10827 0.10817 0.10789 0.10841 0.10802 0.10811 0.108460.10817 0.10801 0.10835 0.10807 0.10843 0.10834 0.10804

0.1084 0.10822 0.1082 0.10822 0.10785 0.108110.10838 0.10827 0.10817 0.10812 0.10809 0.108280.10836 0.10833 0.10833 0.10811 0.10811 0.107960.10835 0.10799 0.10824 0.10813 0.10822 0.10832

0.10794 0.10803 0.10819 0.10822 0.10826 0.108150.10838 0.10819 0.10808 0.10824 0.10803 0.108050.10797 0.10814 0.10793 0.10807 0.10817 0.108150.1078 0.10794 0.10819 0.10811 0.10794 0.10794

0.10816 0.10826 0.10814 0.1081 0.10813 0.107980.10802 0.10844 0.10816 0.10837 0.1082 0.108330.10797 0.10813 0.10817 0.10815 0.10802 0.107990.10833 0.10828 0.1081 0.10839 0.10849 0.10818

Process Capability StudiesPart 613 – An Exercise

0.110 Diameter Part 613

0

5

10

15

20

25

30

35

0.10

77

0.10

78

0.10

790.

108

0.10

81

0.10

82

0.10

83

0.10

84

0.10

85

0.10

86M

ore

dia - in.

Fre

qu

en

cy

Descriptive Statistics

Mean 0.1081636Standard Error 1.64535E-05Median 0.10816Mode 0.10817Standard Deviation 0.000164535Sample Variance 2.70718E-08Kurtosis 3.411886124 Max Kurtosis 4.49Skewness 0.017494357 Max Skewness 0.745Range 0.00078Minimum 0.10778Maximum 0.10856Sum 10.81636Count 100

Process Capability StudiesPart 613 – An Exercise

R Chart .110 Dia Part 613 n=4

0

0.0002

0.0004

0.0006

0.0008

1 3 5 7 9 11 13 15 17 19 21 23 25

Observation #

in.

UCLR

Rbar

R

LCLR

Xbar Chart .110 dia Part 613- n=4

0.10770.10780.10790.108

0.10810.10820.10830.10840.1085

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Observation #

in.

UCLXbarXbarbarXbarLCLXbar

Process Capability StudiesPart 613 – An Exercise

And the answer is:

Descriptive StatisticsLSL = 0.105

Mean 0.1081636 USL = 0.115Standard Error 1.64535E-05 Cp = 10.1Median 0.10816 CpL = 6.4Mode 0.10817 CpU = 13.8Standard Deviation 0.000164535 Cpk = 6.4Sample Variance 2.70718E-08Kurtosis 3.411886124Skewness 0.017494357Range 0.00078Minimum 0.10778Maximum 0.10856Sum 10.81636Count 100

Process Capability StudiesSummation

Three Steps:

• Gauge Capability

• Process Characteristics

• Process Capability Analysis

Process Capability StudiesBibliography

• Introduction to Statistical Analysis – sixth ed – Dixon and Massey

• Introductory Statistics – Weiss and Hassett, 1982

• AT&T Statistical Quality Control Handbook – 11th Printing – 1985• Experimental Statistics – Mary G. Natrella – 1966 (NBS Handbook 91)

• General Motors Statistical Quality Control Handbook – 1982

• LTV Steel Integrated Process Control Handbook – Norman Bresky and Joan Harley – 1986

• North American Refractories Co. SPC Handbook – 1988

• 1994 Annual ASTM Book of Standards- ASTM E 691 - 92