Description: The purpose of Phase III is to finally conclude "accept" or "reject" for the machine by predicting long-term stability and capability. The main difference from Phase II is that the 125 parts ( n = 125) are collected over a much greater time period (at least 8 hours). The increased time period of data collection gives the study more validity in predicting future production performance. The reason for the increased validity in Phase III is that potentially additional sources of special variation are allowed into the data collection time frame.
Objectives: The objectives of Phase III are to
Analyze data to determine control and potential capability (using an Xbar and R chart with 5 parts per subgroup ).
Confirm investigations of distribution shape.
Predict long-term production performance of process.
Phase III participants include the
Machine acceptance team
Supplier of the machine
Maintenance and setup personnel
Material suppliers
Phase III method (Figure 16.10): Before data collection, set up the process using all the information that was collected in Phase I and any additional information from Phase II. Make sure to use the same gages and measurement process as in Phases I and II.
Data collection: Collect 125 parts ( n = 125) over a period of at least 8 hours. The parts are to be collected in groups of five consecutive parts spaced evenly over the 8 hours (number the subgroups in time order). Measure the 125 parts and record them in their time order.
Data analysis: Plot the parts on an Xbar and R chart with the subgroup sizes of five. Assess control or out of control with the best possible chance of performing competently in production. If the control chart exhibits out-of-control conditions, an action plan must be developed with the supplier and the 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 exhibits control, then investigate the distribution of the 125 parts. If they appear to have a normal distribution, then calculate C pk . If the distribution is not normal, calculate the capability with appropriate techniques such as mirror imaging and probability paper for 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 distribution needs to be centered on the middle of the specification. In either case, do not recommend acceptance of this machine. If the supplier can correct the problem, then go back to a Phase I study (after the vendor has made appropriate changes).
If the process shows potential capability (i.e., C pk > 1.33 99.994% in specifications), then recommend accepting the machine. A good way to make sure that Phase III has met all the requirements is to use a checklist such as the one in Table 16.4.
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 data were collected during a Phase III study (continuing the previous example). The Xbar and R charts show control, and the histogram indicates that a normal distribution is appropriate for a model of the population. Notice that the +4 sigma interval is not contained inside of the specification of 16 to 17; hence, this process would not be deemed potentially capable (i.e., C pk < 1.33). The distribution is too wide for the specifications, so just centering the process would not solve the problem. Because there is a wider window to the data collection in this study as compared with that in the Phase II study, more common variability was picked up. Material changes or ambient temperature changes are two examples of variables that change over longer periods of time. In any case, the variability of the process must be reduced, and an action plan for the supplier must be created and executed before any more work can be done.
Sample size | 125 | Actual | EST | Limits | |
---|---|---|---|---|---|
99.730% | |||||
Target | 16.5000 | Low | 15.9275 | 15.6634 | 16.0000 |
Average | 16.4808 | High | 17.1796 | 17.2981 | 17.0000 |
Std. Dev. | 0.2724 | Range | 1.2520 | 1.6346 | 1.0000 |
Skewness | 0.3247 | % < Low limit | 3.20 | 3.88 | |
Kurtosis | -0.2329 | % > High limit | 4.80 | 2.83 | |
Normality test made | % Out of range | 8.00 | 6.71 | ||
Normality assumed | C P | 0.6118 | |||
Subgroup size = 5 | C pk | 0.5883 |
Cum Prob | Midpoint | Frequency |
---|---|---|
0.001 | 15.6000 | 0 + |
0.002 | 15.7000 | 0 + |
0.006 | 15.8000 | 0 + |
0.017 | 15.9500 | 1 + *. |
0.039 | 16.0000 | 7 + *** *** ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” |
0.081 | 16.1000 | 5 + ***** . |
0.151 | 16.2000 | 14 + **********. *** |
0.253 | 16.3000 | 14 + **************. |
0.383 | 16.4000 | 19 + ***************.** |
0.528 | 16.5000 | 19 + ****************.* |
0.669 | 16.6000 | 15 + **************. |
0.790 | 16.7000 | 13 + ***********. |
0.879 | 16.8000 | 4 + ****. |
0.938 | 16.9000 | 6 + *****. |
0.972 | 17.0000 | 4 + **.* ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” ” |
0.988 | 17.1000 | 2+.* |
0.996 | 17.2000 | 2 +.* |
0.999 | 17.3000 | 0 + |
1.000 | 17.4000 | 0 + |
1.000 | 17.5000 | 0 + |
Note: Histogram 1 "*" = 1 sample (actual data); "." = estimated distribution. |
LCL = 16.1070 Center = 16.4808 UCL = 16.8546 | ||||||||
---|---|---|---|---|---|---|---|---|
Subgroup size used: 5 | ||||||||
Mean | SN | 15.9200 | 16.3200 | 16.7200 | ||||
+ ” ” ” ” ” + ” ” ” ” ” + ” ” ” ” ” + ” ” ” ” ” + ” ” ” ” | ||||||||
16.5719 | I | : | + | * | : | |||
16.2993 | I | : | * | + | : | |||
16.5259 | I | : | + * | : | ||||
16.4122 | I | : | * | + | : | |||
16.4357 | 5 | I | : | * + | : | |||
16.3791 | I | : | * | + | : | |||
16.5422 | I | : | + | * | : | |||
16.5326 | I | : | + * | : | ||||
16.3176 | I | : | * | + | : | |||
16.4736 | 10 | I | : | * | : | |||
16.6442 | I | : | + | * | : | |||
16.5625 | I | : | + | * | : | |||
16.4957 | I | : | * | : | ||||
16.6789 | I | : | +* | : | ||||
16.4741 | 15 | I | : | * | : | |||
16.3787 | I | : | * | + | : | |||
16.4047 | I | : | * | + | : | |||
16.6267 | I | : | + | * | : | |||
16.4170 | I | : | * | + | : | |||
16.5325 | 20 | I | : | + | * | : | ||
16.4492 | I | : | * + | : | ||||
16.3410 | I | : | * | + | : | |||
16.5392 | I | : | + * | : | ||||
16.6133 | I | : | + | * | : | |||
16.3708 | 25 | I | : | * | + | : |
LCL = 0.000 Center = 0.6445 UCL = 1.3599 | ||||||||
---|---|---|---|---|---|---|---|---|
Subgroup size used: 5 | ||||||||
Range | SN | 0.0000 | 0.4000 | 0.8000 | 1.2000 | |||
+ ” ” ” ” ” + ” ” ” ” ” + ” ” ” ” ” + ” ” ” ” ” + ” ” ” ” ” | ||||||||
0.9349 | I | + * | : | |||||
0.4814 | I | * + | : | |||||
0.7988 | I | + * | : | |||||
0.4467 | I | * + | : | |||||
0.5174 | 5 | I | * + | : | ||||
0.8532 | I | + * | : | |||||
1.1206 | I | + | * | : | ||||
0.4441 | I | * | + | : | ||||
0.6426 | I | * | : | |||||
0.4631 | 10 | I | * | + | : | |||
0.8453 | I | + | * | : | ||||
0.5785 | I | * | + | : | ||||
0.7972 | I | + | * | : | ||||
0.7131 | I | + | * | : | ||||
0.2194 | 15 | I | * | + | : | |||
0.8213 | I | + | * | : | ||||
1.0042 | I | + | * | : | ||||
0.5416 | I | * + | : | |||||
0.5488 | I | * + | : | |||||
1.0093 | 20 | I | + | * | : | |||
0.3880 | I | * | + | : | ||||
0.3068 | I | * | + | : | ||||
0.6682 | I | + * | : | |||||
0.1909 | I | * | + | : | ||||
0.7767 | 25 | I | + | * | : |