PHASE II: PRELIMINARY STUDY INVESTIGATING PROCESS STABILITY AND CAPABILITY


PHASE II: PRELIMINARY STUDY INVESTIGATING PROCESS STABILITY AND CAPABILITY

Description: The purpose of Phase II is to establish short- term stability. This is performed after determining the process setup and warmup periods in Phase I. The main difference from Phase I is that 125 parts ( n = 125) are collected sequentially and recorded in time order.

Objectives: The objectives of Phase II are to

  • Analyze data to determine control as in Phase I (using an Xbar and R chart with five parts per subgroup ).

  • Further investigate distribution shape.

  • If process is in control, calculate C pk to quantify and predict potential capability.

Phase II participants include:

  • Machine acceptance team

  • Supplier of the machine

  • Maintenance and setup personnel

Phase II method (Figure 16.9): Before data collection, set up the process using all the information that was collected in Phase I. Have maintenance personnel check the machine over to make sure that nothing has broken down. Make sure to use the same gauge and measurement process as in Phase I.

click to expand
Figure 16.9: Phase II flow chart.

Data collection: Collect 125 parts ( n = 125) consecutively (numbered in time order). Measure the 125 parts for all critical characteristics and record them in time order.

Data analysis: Plot the parts on an Xbar and R chart with subgroup sizes of five. As in Phase I, look for any and every possible out-of-control situation. Do not cheat yourself by calling something in control that is not. If there are any out-of-control signals, categorize them as good or bad processes. It is the responsibility of the supplier to eliminate the causes of the "bad" special variation. Expenses incurred during the problem-solving effort (time, energy, human resources, and money) should be incurred by the machine builder. If there are any good out-of-control situations, then have the supplier incorporate the causes into the process. Following this procedure will give you a machine with the best possible chance of achieving long-term capability under production conditions.

If the control chart exhibits out-of-control conditions, an action plan must be developed with the supplier and customer team. Using the action plan, the problem needs to be identified and removed from the process. After the changes, start back at Phase I.

If the control chart shows control, then investigate the distribution of the 125 parts. If it appears to follow the normal distribution, then calculate capability indices (C p , C pk ). If the distribution does not seem to follow the normal distribution, proceed with the mirror imaging and nonnormal probability plotting techniques that are used with nonnormal data.

If C p and C pk are < 1.33, instruct the supplier to reduce the variation (reduce Rbar) in the process. If C p > 1.33 but C pk < 1.33, then the process needs to be centered on the middle of the specification. In either case, do not accept this machine or proceed to repeat a Phase II study until after the supplier has made appropriate changes.

If the process shows potential capability (i.e., C pk > 1.33 or 99.994% in specifications), then proceed to Phase III. A good way to make sure that Phase II has met all the requirements is to use a checklist such as the one in Table 16.3.

Table 16.3: A Typical Checklist Before Moving to Phase III

If at least 99.994% of the distribution is not within the specification limits, then develop an action plan based on the following questions.

 

Yes

No

Action Required

Is the lack of capability because of the average?

_____

_____

__________

Is the lack of capability because of the range?

_____

_____

__________

Were there any trends or patterns over the time window of the study?

_____

_____

__________

Does the histogram suggest any unusual conditions such as nonnormality?

_____

_____

__________

Does the study log show any unusual occurrences that would help explain apparent incapability?

_____

_____

__________

Does either of the control charts give signals of unusual variation that would suggest stratification?

_____

_____

__________

Should the study be rerun?

_____

_____

__________

PHASE II EXAMPLE

These Phase II data were collected after the warmup period determined in Phase I. One hundred twenty-five parts ( n = 125) were collected sequentially and grouped by five. The control chart and histogram of all the parts are shown. The distribution of the data seems to follow the shape of the normal distribution very well. The Xbar and R charts show control. Note that the +4 ƒ range falls within the specification of 16 to 17. This means that at least 99.994% of the parts are predicted to fall within specification; hence, this is at least 4 ƒ capable (i.e., C pk and C p > 1.33).

Statistical (SQC) Data Analysis Phase II Example

Sample size

125

Actual

EST 99.730%

Limits

 

Target

16.5000

Low

16.2196

16.1872

16.0000

Average

16.4987

High

16.7612

16.8101

17.0000

Std. Dev.

0.1038

Range

0.5416

0.6229

1.0000

Skewness

0.1190

% > Low limit

0.00

0.00

 

Kurtosis

0.1803

% > High limit

0.00

0.00

 

Normality test made

 

% Out of range

0.00

0.00

 

Normality assumed

         

Subgroup size = 5

     

Cp

1.6054

       

Cpk

1.6014

Cum Prob

Midpoint

Frequency

0.000

16.0000

0 ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ”

0.000

16.0500

0 +

0.000

16.1000

0 +

0.000

16.1500

0 +

0.002

16.2000

1 + *

0.008

16.2500

2+.*

0.028

16.3000

2+ **.

0.076

16.3500

10 + ******** *

0.171

16.4000

16 + *************** *

0.320

16.4500

18 + ******************

0.505

16.5000

25 + *********************** *

0.689

16.5500

21 + ********************.

0.835

16.6000

16 + ************** *

0.928

16.6500

9+ ******* *

0.974

16.7000

4+ ***.

0.992

16.7500

1 +.

0.998

16.8000

0 +

1.000

16.8500

0 +

1.000

16.9000

0 +

1.000

16.9500

0 +

1.000

17.0000

0 + ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ”

1.000

17.0500

0 +

1.000

17.1000

0 +

1.000

17.1500

0 +

Note: Histogram 1 "*" = 1 sample (actual data); "." = estimated distribution.

Statistical (SQC) Data Analysis Xbar chart

LCL = 16.3523 Center = 16.4987 UCL = 16.6451

Subgroup size used: 5

Mean

SN

16.2000

 

16.4000

16.6000

   

+ ” ” ” ” + ” ” ” ” + ” ” ” ” + ” ” ” ” + ” ” ” ”

16.5277

 

I

:

 

+*

   

:

16.5026

 

I

:

 

*

   

:

16.4934

 

I

:

 

*

   

:

16.5009

 

I

:

 

*

   

:

16.5322

5

I

:

 

+

*

 

:

16.5435

 

I

:

 

+

*

 

:

16.4616

 

I

:

 

* +

   

:

16.5006

 

I

:

 

*

   

:

16.4348

 

I

:

*

+

   

:

16.5144

10

I

:

 

+*

   

:

16.5363

 

I

:

 

+ *

   

:

16.5234

 

I

:

 

+ *

   

:

16.4201

 

I

:

 

* +

   

:

16.4771

 

I

:

 

* +

   

:

16.5493

15

I

:

 

+

*

 

:

16.5036

 

I

:

 

*

   

:

16.4773

 

I

:

 

* +

   

:

16.4783

 

I

:

 

* +

   

:

16.5707

 

I

:

 

+

 

*

:

16.3873

20

I

:

 

*+

   

:

16.4585

 

I

:

 

* +

   

:

16.5353

 

I

:

 

+

*

 

:

16.5468

 

I

:

 

+

*

 

:

16.5333

 

I

:

 

+

*

 

:

16.4580

25

I

:

 

* +

   

:

Range Chart

LCL = 0.000 Center = 0.2524 UCL = 0.5326

Subgroup size used: 5

Mean

SN

0.0000

0.2000

0.4000

0.6000

   

+ ” ” ” ” + ” ” ” ” + ” ” ” ” + ” ” ” ” + ” ” ” ”

0.2699

 

I

     

*

   

:

0.2022

 

I

   

*

+

   

:

0.3670

 

I

     

+

*

 

:

0.2560

 

I

     

*

   

:

0.1984

5

I

   

*

+

   

:

0.2590

 

I

     

*

   

:

0.1211

 

I

 

*

 

+

   

:

0.2952

 

I

     

+*

   

:

0.2473

 

I

     

* +

   

:

0.4121

10

I

     

+

*

 

:

0.2136

 

I

   

*

+

   

:

0.2752

 

I

     

+*

   

:

0.3888

 

I

     

+*

   

:

0.2148

 

I

*

   

+

   

:

0.3033

15

I

     

+*

   

:

0.0922

 

I

 

*

 

+

   

:

0.1731

 

I

   

*

+

   

:

0.2173

 

I

*

   

+

   

:

0.2951

 

I

     

+ *

   

:

0.1007

20

I

     

*+

   

:

0.2139

 

I

     

* +

   

:

0.3419

 

I

     

+*

   

:

0.2131

 

I

     

* +

   

:

0.1139

 

I

 

*

 

+

   

:

0.5251

25

I

     

+

   

* :




Six Sigma and Beyond. Statistical Process Control (Vol. 4)
Six Sigma and Beyond: Statistical Process Control, Volume IV
ISBN: 1574443135
EAN: 2147483647
Year: 2003
Pages: 181
Authors: D.H. Stamatis

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