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.
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.
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? | _____ | _____ | __________ |
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).
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. |
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 | : | * + | : |
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 | + | * : |