International operations strategy and management

¶ … 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 methods of chance, or upper and lower control limits, that the true level of defects can be measured using smaller samples (Hendrickson, 1998).

That being noted, the idea behind sample selection is to use a sample size in such a way that the variances found are attributable to the process variation only. 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 Size: 5, R = 1.2

(Shmueli, 2005a)

Q5. Five samples of voltage are taken with the results in the table below. What action should be taken if any?

Presuming that mean and variance of the process does not change, the samples taken should be distributed normally around the mean. By applying the central limit theorem, we know that the sample means should fall within the limits approximately 99% of the time. Additionally, according to experts, a single point outside of the control limits, or variations in clusters of data indicate out of control processes (Tague, 2004). In the above graph, one can note that there is a high level of variation between points three and four, and that four is above the upper control limit. Thus, one would assume that this sample represents a process not within the control limits. As a result, the production manager would need to find the course of this deviation from the mean, and take corrective action based on those findings. If the source is found to be a discrepancy in activity, such as an altered process or faulty machinery, the defect can be quickly avoiding by repairing the problem. If instead the deviation is found to be caused by faulty parts, basic corrective action, such as a reevaluation of suppliers, may be in order (Allen, 1998).

Q6. Discuss the pros and cons of using this variables control chart vs. The control chart discussed in the first part of the assignment. Which do you prefer?

Attribute control charts are beneficial in that in using one, supervisors can quickly summarize the quality of the products. This in turn can save time and money by alleviating the need for more specific, time-consuming testing measures. Further, this type of chart is easy to understand, and does not require extensive mathematical ability or computerized calculation, which furthers the usefulness. On the other hand, attribute charts are less sensitive, and thus, cannot alert a supervisor to problem areas prior to actual defects of product (Tague, 2004).