ASME - Paper

Process Capability Index (PCI) and SPC Control Limits

INTRODUCTION PCI is common metric in industry to measure and predict capability of manufacturing processes Communication tool:

Shop floor personnel Company management Customer, and certification organizations

SPC is a primary tool for process capability analysis SPC can detect cause of output in real time Control limits - critical decisions for control charts Common control charts: X-bar and Range charts

Proceedings of NAMRI/SME, Vol. 39, 2011 1

2

Manufacturing Process Capability

Process Capability: σ = Standard Deviation (sigma) µ = Mean USL = Upper Specification Limit LSL = Lower Specification Limit Cp = Process Capability Ratio Cpk= Process Capability Index

Process Capability ratio (Cp) is the ability of the process to manufacture the product that meets engineering specifications.

Cp = (USL – LSL) / 6σ

Process Capability Index (Cpk) determinates the efficiency of the process. It measures how close the process is to target.

Proceedings of NAMRI/SME, Vol. 39, 2011

3

Manufacturing Control Charts


4

CMM and SPC Analysis

Results from CMMs are automatically sent to Statistical Software , such as ProLink QC CALC Real time or MINITAB.


5

Localization is known as a relationship between part and CMM coordinate system.

Six contact 3-2-1 approach is required. 3 points define XY plane – primary datum 2 points define a line which lies on the XZ

plane – secondary datum. final point defines YZ plane – tertiary

datum. point of intersection of these 3 planes is

the origin of the system X=0, Y=0, and Z=0.

Six touch points needed to create coordinate system.


CMM - Part Alignment

Task-Specific Measurement Uncertainty

Machine Components (CMM Errors)

Part Component

(feature form error)

Sampling Patterns

Probe Components

(probe system error)

Fitting Algorithms

Repeatability Component

Environmental Factors

6 Proceedings of NAMRI/SME, Vol. 39, 2011

CMM - Measurement

7

EXPERIMENTAL WORK

OBJECTIVE Three experiments have been conducted to evaluate the effect of this decision on some important parameters and metrics used in the industrial community such as: the process capability index (Cpk), and Statistical Process Control (SPC) control limits. Estimate and compare the calculations of Process Capability Index (PCI) and Statistical Process Control (SPC) limits.

INSPECTION TOOLS Coordinate Measuring Machine (CMM), Computer Aided Design (CAD) based software PC-DIMIS to generate and simulate the inspection program. Digital Height gage (accuracy 0.000050 inch) Digital caliper (accuracy 0.0005 inch)


8

Experimental Work – 3 CASES


9

Set up and Alignment – CASE 1 The data collection for 19 parts was measured with CMM and Height Stand Indicator for 2 critical characteristics.

Diameter 3.812 +/- .002 Center Line 2.120 +/- .005

Fixturing - CMM Part Alignment - CMM


10

CASE 1 – Sampling Strategy CMM Diameter 3.812 was measured with two levels with off set of .100 form the bottom and the top surface of cylinder. 8 probing samples were taken to establish diametrical shape of each level.

Center Line 2.120 was established by measuring diameter .752 +/- .001, and line (datum –K –) that was established during the alignment.

-K-

3.812 ± .002

2.120± .002


11

Set Up and Alignment – CASE 2 The data collection for 19 parts was measured with CMM and Height Stand Indicator for 2 critical characteristics.

True Position .004 to datum – DEA- Perpendicularity .001 to datum – D- (at datum L)


-D-

-F-

-A-

-E-


12

CASE 2 – Sampling Strategy CMM Perpendicularity .001 to datum – D- (at datum L) - 17 probing samples were taken to establish Plane of datum - D - , and 16 points to establish perpendicularity relationship between datum – D- and - L -

True Position .004 to datum DEA - 10 probing samples taken to establish slot contour of datum - F-

-L-

-D-

-E-

-D-

-A- Proceedings of NAMRI/SME, Vol. 39, 2011

13

Set up and Alignment – CASE 3 (Rear Penal)

The data collection for 30 parts was measured with CMM and caliper for defined characteristics.

The BOSS Cylinder .52±.005 Inside Diameter .940±.005 Inside Packet Square DIM 1.20±.005 Extruded Square DIM 1.360±.005



14

CASE 3 – Sampling Strategy CMM Boss Cylinder measured with two levels with off set of .100 form the bottom & top, 8 probing samples were taken at each level.

Inside Diameter .940±.005 was established with 8 probing hit samples

Extruded Square DIM was established with 2 probing hits on each side of square

Inside Packet Square was established with 2 probing hits on each side of square


15

CASE 3 – Sampling Strategy Caliper Boss Cylinder was measured 60º apart at the top and bottom average recorded.

Inside Diameters was measured at 3 locations 60º apart, average recorded.

Inside Packet Square measured at two locations (top & bottom) average recorded.

Extruded Square measured at two locations (top & bottom) average recorded.


16

RESULTS CASE 1 – Process Capability


X AND R CHART FOR THE 2, 12 C/L DISTANCE FOR CASE STUDY (H. GAGE)

X AND R CHART FOR THE 2.12 C/L DISTANCE FOR CASE STUDY (CMM)

2.126

2.124

2.122

2.120

2.118

2.116

2.114

300

250

200

150

100

50

0

Data

Den

sity

2.120 0.002550 292.121 0.001303 29

Mean StDev N

(Layout)(CMM)

Variable

Normal Hist.of C/L 2.120 ± .005 (Layout), C.L. 2.120 ± .00

The Cpk index varies from 0.7 to .75 for the height gage, while it ranges from 1.17 to 1.4 for the CMM.

The experiment reveals that the measuring range of collected data collected from the CMM is almost half the size of data collected from the height gage and surface plate

The upper and lower statistical control limits calculated from the CMM data is also half the size of the conventional tool.

17



X AND R CHART FOR THE TRUE POSITION 0.004 STUDY II (HEIGHT GAGE)

X AND R CHART FOR THE TRUE POSITION 0.004 STUDY II (CMM)

0.0035

0.0030

0.0025

0.0020

0.0015

0.0010

1000

800

600

400

200

0

Data

Den

sity

0 .002047 0.0004208 190.002253 0.0006720 19

Mean StDev N

True Pos. .004(CMM)TP .004 (Layout)

Variable

Normal Hist. of True Pos. .004 -DEA- (CMM), TP .004 -DEA- (Layout)

The Cpk varies from 1.16 to 1.65 for CMM, while it varies from 0.65 to 0.78 for the height gage (Table).

The SPC process control limits for the X and R charts were 47 % less for the CMM data.

18



X and R Chart for the OD 0.52 Distance for Case Study (Caliper)

F X and R Chart for the OD 0.52 Distance for Case Study (CMM)

0.5230.5220.5210.5200.5190.5180.517

500

400

300

200

100

0

Data

Den

sity

0.5203 0.0008945 300.5202 0.001341 30

Mean StDev N

C MM O D .52C aliper O D .52_1

Variab le

Histogram of CMM OD .52, Caliper OD .52_1Normal

Cpk varies from 0.96 to 1.28 for digital caliper, while it ranges from 1.40 to 1.87 for the CMM for the same parts.

The SPC process control limits for the X and R charts shown in are 35% less for the CMM data.

19

Results Discussion


For all cases that the range of the measured data is larger for the height gage and caliper compared to the CMM.

This phenomenon may affect a SPC charts by either shrinking or expanding the region between the upper and lower statistical limits depending whether the measured data is collected from a CMM or conventional tool.

Suggested standard deviation monitoring graph is used to insure the integrity of the Cpk calculations.

Figure a shows the cumulative standard deviation for the 2.12 C/L distance (case study I)

Figure b is based on a window of the last ten points.

Figure c is based on a window of the last five points. The erratic behavior of the standard deviation of the height gage is noticed and this justifies the low Cpk value.

Using this graph will minimize false alarms and/or the need to re-calculate the upper and lower control limits for SPC charts; since this situation should be avoided (www.itl.nist.gov).

http://www.itl.nist.gov/

20

Results Discussion For all cases that the range of the measured data is

larger for the height gage and caliper compared to the CMM.

This phenomenon may affect a SPC charts by either shrinking or expanding the region between the upper and lower statistical limits depending whether the measured data is collected from a CMM or conventional tool.

Suggested standard deviation monitoring graph is used to insure the integrity of the Cpk calculations.

Figure a shows the cumulative standard deviation for the 2.12 C/L distance (case study I)

Figure b is based on a window of the last ten points.

Figure c is based on a window of the last five points. The erratic behavior of the standard deviation of the height gage is noticed and this justifies the low Cpk value.

Using this graph will minimize false alarms and/or the need to re-calculate the upper and lower control limits for SPC charts; since this situation should be avoided (www.itl.nist.gov).


http://www.itl.nist.gov/

21

Conclusions The analysis provided in this paper reveals that the CMM

measurement proved to be more accurate than manual gages.

The measurement data collected from manual gages is more spread around the mean, while in case of coordinate based metrology tool the collected data is more clustered around the mean or the target values.

There is major difference when calculating the Cpk and the SPC control chart limits based on selection of the measurement device. This will effect a percentage of non-conforming products.

The difference in the calculation of the X and R charts control limits may cause inconsistency, confusion, and may result in unnecessary false alarms.


22

Recommendation As a recommendation, if a checked dimension is

critical to the product functionality such as: bore diameter in an engine block, a CMM would be recommended, while if the dimension is non-critical, a conventional inspection tool may be considered convenient.

The suggested standard deviation monitoring graph provided in this paper is a part of larger scale study intended to provide a decision support system for the manufacturing and/or quality engineer to make better decisions regarding the control process monitoring and inspection process.


23

Thank You


Documents

ASME - Paper