¶ … upper and lower control limits for a sample size of 100?
Ratio when process in under control: 10 to 1,000,000 = .00001
Thus:
Upper Control Limit: .009497
Control Limit: .00001
Lower Control Limit: .
(Shmueli, 2005)
(Defects per sample, 100)
UCL = 0.009497
CL = 0.000010
LCL = 0.
Recompute the upper and lower control limits for a sample size of 10,000?
Ratio when process in under control: 10 to 1,000,000 = .00001
Thus:
Upper Control Limit: .030100
Control Limit: .000100
Lower Control Limit: .
(Shmueli, 2005)
(Defects per sample, 10,000)
UCL = 0.030100
CL = 0.000100
LCL = 0.
Which of these two sample sizes would you recommend? Explain.
While an ideal quality control program would test all work for defects or damage, this process would be highly expensive and time consuming. Thus, by gathering an average defect rate for a sample, and then by applying that rate to a smaller sample, the interpretation of results using statistical analysis can provide conclusions of an entire batch (Hendrickson, 1998). The only question, then, is one of sample size, and its effect on upper and lower control limits.
It should be noted, however, that small sample sizes could be misleading, without proper data analysis. Since sample selection is random, the results of the sample selection can vary greatly. For example, in the above instance, the baseline sample showed only five defects per million. If, using a single sample of 100, we find that five are defective, a direct inference drawn that indicated the entire batch was bad would be incorrect, since it is possible these five were the only five defects. It is only through statistical...
At the same time, the sample should be small enough to be economically and practically feasible. In order for this to be true, the time and effort required to collect the sample must be minimal (Ishikawa, 1982). Careful balance must be met between cost and variances.
Larger groups have some advantages, in that large groups allow the central limit theorem to apply, meaning that the means will be more equally distributed. Further, larger groups allow for a higher level of sensitivity in the detection of a control condition outside the mean (Ishikawa, 1982). In other words, the larger the sample, the more likely a shift in the process mean will be detected. According to some researchers, the balance between cost and variation is best achieved with a sample size of 1/5th to 1/10th the size of the original control condition, particularly in the case of process control by attribute, or number of defects per batch (Ishikawa, 1982).
Based on the information above, the best sample size in the first example would be 10,000 units. A sample size of only 100 units, when compared to the control condition, is less likely to achieve a balanced sample, where variations in the process are detected based on means alone, since the sample size is so small compared to the control condition. On the other hand, a sample of 10,000 would be large enough to detect a change in the process mean while still being small enough to be economically viable.
Q4. What would the upper and lower control limits be for the resulting control charts (average and range)?
Target mean: 3.1, Sample…
