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Process Capability
Capability Indices
The capability index is defined as:
Cap is equal to Upper Specification Limit (USL) minus Lower Specification Limit (LSL) divided by 6 Standard Deviations.
As a rule of thumb:
CP > 1.33 Capable
CP = 1.00 to 1.33 Capable with tight control
CP < 1.00 Incapable
The capability ratio is defined as:
CR is equal to six standard deviations divided by upper specification limit (USL) minus lower specification limit (LSL).
As a rule of thumb:
CR < 0.75 Capable
CR = 0.75 to 1.00 Capable with tight control
CR > 1.00 Incapable
Note: The above formulas only apply if the process is centered, stays centered within the speciﬁcations, and CP=Cpk.
Performance Indices
The performance index is defined as:
Pp is equal to Upper Specification Limit (USL) minus Lower Specification Limit (LSL) divided by 6 Standard Deviations.
The performance ratio is defined as:
PR is equal to six standard deviations divided by upper specification limit (USL) minus lower specification limit (LSL). σi is a measure of total sigma and generally comes from a calculator or computer. Ppk is the ratio giving the smallest answer between:

Ppk is equal to Upper Specification Limit minus Mean divided by 3 standard deviations or

Ppk is equal to mean minus Lower Specification Limit divided by 3 standard deviations
Shortterm and Longterm Capability
When a process capability is determined using one operator on one shift, with one piece of equipment, and a homogeneous supply of materials, the process variation is relatively small. As factors for time, multiple operators, variouslots of material, environmental changes, etc. are added, each of these contributes to increasing the process variation.
Control limits based on a shortterm process evaluation are closer together than control limits based on the longterm process. When a small amount of data is available, there is generally less variation than is found with a larger amount ofdata. Control limits based on the smaller number of samples will be narrower than they should be, and control charts will produce false outofcontrol patterns.
Relationship between Short Term and Long Term
Process Capability Z short term is equal to Z long term plus 1.5
Instrument Selection
The terms measuring tool, instrument, and gage are often used interchangeably in this text. Appropriate gage should be used for the required measurement. The Adjustable snap gages are usually accurate with 10% of the tolerances and its application is that it measures diameters on a production basis where an exact measurement is needed. The air gages have an accuracy that depends upon gage design. Measurements of less than 0.000005 inches are possible. It is used to measure the diameter of a bore or hole.
The Automatic sorting gages are accurate within 0.0001 inches and is used to sort parts by dimension. The combination square is accurate within onedegree and is used to make angular checks. The coordinate measuring machines has accuracy that depends upon the part. Its axis inaccuracies are within 35 millionths and T.I.R. within 0.0000005 inches. It can be used to measure a variety of characteristics, such as contour, taper, radii, roundness,
The Dial bore gages have Accuracy within 0.00001 inch using great care and used to measure bore diameters, tapers, and outofroundness. The Dial indicator has Accuracy that depends upon the part. Axis accuracies are within 0.00001 inch and Measures a variety of features such as: flatness, diameter, concentricity, taper, height, etc.
The Electronic comparator is Accurate from 0.00001 inch to 0.0000001 inch and is used where the allowable tolerance is 0.00001 inch or less. The Fixed snap gages has No set accuracy and is normally used to determine if diameters are within specifications. The Flush pin gages have Accuracy of about 0.002 inch and is used for high volume single purpose applications. The Gage blocks have Accuracy that depends upon the grade and normally the accuracy is 0.000008 inch or better. Gage blocks are best adapted for precision machining and as a comparison master. The Height verniers are Mechanical models measure to 0.0001inch.
Some digital models attain 0.000005 inch. They are used to check dimensional tolerances on a surface plate. The Internal and external thread gages cannot provide exact reading. They will discriminate to a given specification. They are set for measuring inside and outside pitch thread diameters. The Micrometer (inside) has Mechanical accuracy of about 0.001 inch. Some digital models are accurate to 0.00005 inch.They are normally used to check diameter or thickness. Special models can check thread diameters. The Micrometer (outside) has Mechanical accuracy of about 0.001 inch.
Some digital models are accurate to 0.00005 inch. They are normally used to check diameter or thickness. Special models can check thread diameters. The Optical comparator has the accuracy can be within 0.0002 inch. They measure difficult contours and part configurations. The Optical flat depending on operator skill and are accurate to a few millionths of an inch. They are used only for very precise tool room work. Best used for checking flatness.
The Plug gages have Accuracy that is very good for checking the largest or smallest whole diameter. They check the diameter or drilled or rimmed holes and will not check for out of roundness. The Precision straight edge have Visual 0.10 inch With a feeler gage 0.003 inch and are Used to check flatness,waviness or squareness of a face to a reference plane. The Radius and template gages have Accuracy that is no better than 0.015 inch and are used to check small radii, and contours.
The Ring gages will only discriminate against diameters larger or smaller than the print specification. The best application is to approximate a mating part in assembly. Will not check for out of roundness. The Split sphere and telescope have No betterthan 0.00005” using a micrometer graduated in 0.0001” and are used for measuring small whole diameters. The Steel ruler or scale are No better than0.015”. They are used to measure heights, depths, diameters, etc. The Surface plates have Flatness expected to be no better than 0.005” between any 2 points. They are used to measure the overall flatness of the object.
The Tapered parallels are using an accurate micrometer, the accuracy is about 0.005”. They are used to measure bore sizes in low volume applications. The Tool maker’s flat have Accuracy that is no better than 0.0005” depending upon the instrument used to measure the height. They are used with a surface plate and gage blocks to measure height. The Vernier calipers are about 0.001”. Some digital models are accurate to 0.00005”.
Reference/Measuring Surfaces
A reference surface is the surface of a measuring tool that is fixed. The measuring surface is movable. Both surfaces must be free from grit or damage, secure to the part and properly aligned for an accurate measurement.
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