Quality Assurance - Lecture - Process Capability , Lecture notes of Material Engineering

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Process Capability

Process capability

• Process capability is the range within which a

process is normally able to operate given

inherent variation due to:

• (^) Design
• (^) Materials
• (^) Equipment
• (^) People
• (^) Process steps
• (^) Others

• Also defined as the six standard deviation spread

in the process

Reasons for process capability

• Assess whether a quality characteristic or process

is able to meet requirements

• Monitors the continuous reduction in variation

• Monitors the continuous improvement in a process

• Measures the uniformity of the output of a process

• Identifies processes or quality characteristics that

need improvement

• Ensures that key customer requirements are met or

exceeded

• Selects between alternative machines or

processes to produce a product

• Aids in determining subgroup sampling frequency

for control charts

• Provides information to design engineering for

design and tolerance determination

• Determines whether defect reduction can be best

achieved by:

• Centering the process, or

• (^) Reducing process variation

Reasons for process capability (continuatio

Capability indexes

• Capability indexes are values that measure the

capability of a process

• Capability indexes are used to predict the

performance of a process by comparing the width

of process variation to the with of the specified

tolerance

• Process capability uses two indexes, Cp and Cpk,

to compare process variation and engineering

requirements

Capability indexes

• Cp

• (^) Called Process potential
• (^) Width of the engineering tolerance divided by the capability, or spread, in the output of the process
• (^) The Cp ratio does not take into account the relationship between the process average and the target specification

Cp =

Engineering tolerance Cpk = Min of

USL - X , X - LSL

USL= Upper specification limit LSL = Lower specification limit Engineering tolerance = USL – LSL X = Average of the individual measurements Xi = individual measurement  = True population standard deviation = S = Sample standard deviation n = Total number of measurements

Formulas for Capability indexes

 (^) =s= Sum(Xi – X) n- 2

Assumptions for calculating Cp and Cpk

• The process must be in “statistical control”

• (^) Process mean is stable and predictable
• (^) Process variation is stable and predictable

• Specification limits are independent of the process

• Targets being used are goals for the process

LSL USL

Process is off – target

Process with low variation

High potential for defects

Defects

Process spread and engineering tolerances

relationship

LSL (^) USL

Process is on - target

Process with high variation

High potential for defects

Defects

Process spread and engineering tolerances

relationship

Cp Defective PPM

Process fallout table (for centered processe

Exceeds spec. range Equals spec. range Uses less than specification range Process spread

**LSL USL

-1. -0. 0

998, 933, 500, 66, 1,

Cp** (^) Cpk Defective PPM LSL USL Nominal Nominal

Relationship between Cp and Cpk