¶ … 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...
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