Tiger Tools company, a subsidiary of the Drillmore Industries, was about to launch a new product. In this regard, the Production Manager asked her assistant Jim Peterson to evaluate the capability of the existing equipment used in the process. He proceeded to obtain eighteen random samples and the results of these samples were put in a table. His subsequent conclusion after analyzing the data would be that the process was not capable. This was on the basis of the width specification of 1.44 cm.
Given the ambition that the company had, of introducing the new product, using the same equipment, this analysis proved a major setback. This is despite the fact that the ...view middle of the document...
Also, we evaluate the extent to which the samples and methods used are able to capture the random changes realized in the data obtained.
Finally, we determine and recommend what would have been the best techniques to use, in terms of the selection of samples and choice of the sample size in determining the capability and the capability potential of the equipment and production process.
Evaluating the first data set from the table, for n = 20, A2 = 0.18. Using the hint provided, the estimated standard deviation is 0.234. The process capability as obtained is 1.03. This is below 1.33, which means that the process is not capable.
As a production manager, Michelle York was disappointed with this conclusion and decided to consult a professor on the best solution to this dilemma, after futile efforts to establish a sampling technique that would yield the desired improvement and results. Previously, the samples were carried under different settings since the company had to freeze on capital expenditures of a significant amount, and still, the replacement would have cost many times that amount. The professor’s advice was that the company should have used smaller sample sizes and taken more samples. After conferring with the professor, the company took twenty seven samples of five observations each. In their second sampling, the company got results with a sample mean range that indicated less deviation.
As is norm, the size of the sample size determines the precision or level of confidence that is attributed to the particular sample estimates. Similarly, in this case, the level of certainty of the findings depended on the underlying variability of the data and size of the sample used. The more variable the samples are, the greater the associated with the estimates. Having a smaller sample size deprived the company of the ability to detect the differences that would have otherwise have been affected by the random aspect of the study. This is because any difference in the data obtained would have been within the confidence intervals set by the company, therefore making it difficult to detect (Joglekar, 2003).
Also, it is equally important to consider the manner in which the samples were selected. In order for the data to reflect the true status and potential capability of the equipment in question, an unbiased sample selection technique ought to have been used. In this case, there has not been any specific mention of the process of selecting the samples.
It is common practice that sampling is used to inspect the quality of products, especially in companies that massively manufacture products. For example, if an inspector controls quality of products in China, he or she is not able to check the whole batch. Therefore, he or she probably checks a proportion of the entire batch. However, owing to the fact that the products are sold far and wide across the globe, the sampling of products for inspection is just as of importance as any other...