Selection of sample frequency for variable data: There is no absolute rule for how large a subgroup size should be or how often we should sample. The rule of thumb is that we should always sample with the following in mind: balance the value of the data obtained with the cost of sampling. In general, it is best to sample quite often at the beginning and reduce the sample frequency when the process permits (when it has become stabilized). Any time the process becomes unstable (out of control), the sampling frequency should be increased to help identify the assignable source of variation. A guideline that may be used for estimating the initial amount of sampling required for variable data is shown in Table 13.3.
Pieces per Shift | Total Number of Pieces To Be Sampled |
---|---|
1 “65 | 5 |
66 “110 | 10 |
111 “180 | 15 |
181 “300 | 25 |
301 “500 | 30 |
501 “800 | 35 |
801 “1300 | 40 |
1301 “3200 | 50 |
3201 “8000 | 60 |
8001 “22000 | 85 |
For example, if the process is expected to produce 250 pieces per shift, the table says that we should begin sampling a total of 25 pieces per shift. If we collect the data in subgroups of sizes n = 5, then 5 subgroups (25/5) need to be taken during the shift. On an 8-hour shift, there are 480 min (8 hours — 60 min/ hour ). Because we wish to sample at approximately equal time intervals, we need to collect a subgroup of 5 every 96 min (480/5 = 96). At this point, we will instruct the operator to collect 5 consecutive pieces about every 96 minutes throughout the shift.
Selection of sample frequency for attribute data: For attribute data, the subgroup size is determined by the expected percentage nonconforming (pbar) rather than the population size. Use Table 13.4 to estimate the initial subgroup size.
Percentage Nonconforming ( p ) | Sample Size |
---|---|
50.0 | 5 |
35.0 | 7 |
25.0 | 9 |
20.0 | 11 |
15.0 | 15 |
10.0 | 23 |
7.5 | 35 |
5.0 | 45 |
3.0 | 70 |
2.5 | 90 |
2.0 | 115 |
1.0 | 240 |
0.5 | 500 |
0.27 | 1,000 |
With traditional attribute charts , the pieces within a subgroup must all be the same part number. If lot sizes are small (as in short run), we have trouble collecting a large enough subgroup for statistically valid results. Try testing the product at higher stress levels so that a higher defect rate is obtained (higher defect rates require smaller subgroup sizes). Another method is to use an X and MR chart to monitor the number of conforming parts between nonconforming parts .