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Christian D.

Advanced mathematics, statistics, and business applications

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Quality Management

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Question:

Name a benefit of implementing a quality management system?

Christian D.

Answer:

A mature quality management system follows an established system of standards based upon the ISO 9001 principles. Following the ISO 9001 standards enables a company to managed well defined processes that deliver outcomes in alignment with ISO 9001. The ISO 9001 requires a company to document their processes, requires the company to demonstrate that they are following their documented processes, and to provide evidence they are compliant through records. The best way to monitor the maturity of the quality management system is to perform internal audits.

Industrial Engineering

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Question:

How would an Industrial Engineer determine how long an operator takes to perform a task on the manufacturing (of back office) process?

Christian D.

Answer:

An Industrial Engineer would use a method called work sampling to estimate this duration. The first step is to identify list of operators that represent the full range of the task performance. This would include operators who would demonstrate a below average, average, and above average performance. The Engineer would observe a sample of 25 observations per operator. The average of the total sample size would represent the average time to complete this task.

Statistics

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Question:

The Production Manager is interested in monitoring the average width of widgets being manufactured. He wants to know if the average width of widgets has shifted during his shift. A random sample of 25 widgets was collected from a production line at 1:00 pm had sample statistics of mean of 3 inches with standard deviation of 0.25 inches. Another random sample of 25 was collected at 3:00 pm with sample statistics of mean 3.5 inches and standard deviation of 0.25 inches. Has the manufacturing line shifted the average width of the widgets?

Christian D.

Answer:

To answer this question, we first convert the question from a practical problem to a statistical problem. The practical problem is "Has the line shifted the average width of the widget over time?" The statistical problem is, "Has the mean width of the widgets increased, or decreased, in a statistically significant way?" To answer the statistical question, we determine if the difference in the sample means has deviated greater than average sample deviation, thus beyond pure random chance. A random sample size of 25 allows us to use the normal (of Gaussian) distribution to analyze this problem. This method assumes random variation around a population mean, and since the sample standard deviations are equal, they are of constant population variance. We solve this problem by dividing the difference of sample means by the square root of the average sample variation. This calculated statistic gives us the a value of how many standard units (i.e. the number of standard deviations that can fit between the difference of sample means). As a general rule, if the statistic is greater than 2.5, then there is less than a 5% probability the difference in the sample means is due to random chance. So, if the value is 2.5+. we would state that there is statistical evidence to conclude that the mean of the widgets has shifted. If the value is not greater than 2.5, we would state that there is no statistical evidence to conclude that the mean of the widgets has shifted. The difference we experience is consistent with random chance.

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