MOREHEAD STATE UNIVERSITY

Individual Project 2 IET 603

Travis Fisher

2/25/2013

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Individual Project II (50 points): Please solve and Submit your completed project by 2-25-2013 at 10:00 p.m. 1. Explain the foundation of Shewhart’s notion of scientific approach and the basic

activities involved in developing means for satisfying the customers (in approximately 100 words)

Shewhart framed the problem in terms of assignable-cause and chance-cause variation and introduced the control chart as a tool for distinguishing between the two. Shewhart stressed that bringing a production process into a state of statistical control, where there is only chance-cause variation, and keeping it in control, is necessary to predict future output and to manage a process economically. Dr. Shewhart created the basis for the control chart and the concept of a state of statistical control by carefully designed experiments. While Dr. Shewhart drew from pure mathematical statistical theories, he understood data from physical processes never produce a "normal distribution curve". He discovered that observed variation in manufacturing data did not always behave the same way as data in nature. Dr. Shewhart concluded that while every process displays variation, some processes display controlled variation that is natural to the process, while others display uncontrolled variation that is not present in the process causal system at all times. (Encyclopedia, 2013)

2. Explain the Juran Trilogy, in approximately 50 words:

JURAN’S TRILOGY – consists of three managerial processes: planning, control, and improvement. With similar analogy for better quality results, quality trilogy consists of the same managerial processes aimed at improving quality of products and services. They are Quality Planning, Quality Control, and Quality Improvement. 1. Quality Planning- refers to the activities that establish the objectives and requirement for quality.

It comprised of following steps: 1. Determine who your customers are. 2. Discover your customers’ needs. 3. Develop a product whose features are align with the customers’ needs. 4. Develop a process whose features are capable of producing these products along with accompanying features. 5. Hands these plans off to the operations.

2. Quality Control- the operational techniques and activities that are used to fulfill the requirements for quality. It is the inspection or appraisal of products and services to ensure that the stated requirements are fulfilled. It comprised of following steps:

1. Evaluate the actual operating performance. 2. Compare actual performance to operating goals. 3. Take actions in response to differences.

3. Quality Improvement – aimed at attaining unprecedented levels of performance, which are significantly better than the past level. It comprised of following steps:

1. Establish the infrastructure needed to facilitate the continuous quality improvement. 2. Identifies the project improvement. 3. For each project, establish the team that is clearly in charge with the responsibility of bringing a successful resolution to the project.

3. Briefly describe the purpose for basic tools for quality improvement (Basic

Process Improvement Toolbox).

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Once the basic problem-solving or quality improvement process is understood, the addition of

quality tools can make the process proceed more quickly and systematically. Seven simple

tools can be used by any professional to ease the quality improvement process: flowcharts,

check sheets, Pareto diagrams, cause and effect diagrams, histograms, scatter diagrams,

and control charts.

The concept behind the seven basic tools came from Kaoru Ishikawa, a renowned quality

expert from Japan. According to Ishikawa, 95% of quality-related problems can be resolved

with these basic tools. The key to successful problem resolution is the ability to identify the

problem, use the appropriate tools based on the nature of the problem, and communicate the

solution quickly to others. Inexperienced personnel might do best by starting with the Pareto

chart and the cause and effect diagram before tackling the use of the other tools. Those two

tools are used most widely by quality improvement teams.

4. Explain the properties of random variables

A random variable's possible values might represent the possible outcomes of a yet-to-be-performed experiment or an event that has not happened yet, or the potential values of a past experiment or event whose already-existing value is uncertain (e.g. as a result of incomplete information or imprecise measurements). They may also conceptually represent either the results of an "objectively" random process (e.g. rolling a die), or the "subjective" randomness that results from incomplete knowledge of a quantity.

5. The data shown below are the times in minutes that successive customers had to wait for service at an oil change facility. Using hand calculation and formula 1) find sample mean and standard deviation, 2) construct a histogram, and 3) use MINITAB to validate your findings and the histogram. 9.93 10.13 9.98 9.92 9.98 9.92 9.78 10.07 9.84 10.01

9.97 9.97 9.92 10.09 10.09 9.96 10.08 10.01 9.84 10.08

9.91 10.15 9.94 9.98 10.00 9.90 9.93 9.88 9.92 10.02

10.09 9.99 10.05 10.01 10.03 10.07 9.91 10.06 9.86 10.03

10.01 10.05 10.21 9.95 10.02 10.10 9.88 10.13 9.83 9.97

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6. If the probability that any individual will react positively to a drug is 0.8, what is

the probability that 4 individuals will react positively from a sample of 10 individuals?

f(x) = P(X = 4) = (10!/4!(10-4)!)0.8

4(1-0.8)

10-4

f(x) = P(X = 4) = 3628800/17280 (.4096(.000064)) f(x) = P(X = 4) = 209.81(.00002621) f(x) = P(X = 4) = 0.0055

7. Suppose the average number of customers arriving at ATM during the lunch

hour is 12 customers per hour. The probability of exactly two arrivals during the lunch hour is:

8. In a sample of 100 items produced by a machine that produces 2% defective

items, what is the probability that 5 items are defective? (Calculate with binomial distribution formula and verify your response using MINITAB). Solve the question #8 using Poisson distribution formula and verify your response using MINITAB.

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9. It is assumed that the inductance of particular inductors produced by ABC

Company is normally distributed. The of inductors is = 20,000 mH, and of 90 my. If acceptable inductance range is from 19,750 mH to 20,200 mH. Using both formula and MINITAB, determine the expected number of rejected inductors in a production run of 10,000 inductors.

10. E

x

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plain:

Null Hypothesis - 1.(in a statistical test) The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error

Alternative Hypothesis - the alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test. alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference.

Types of error - In statistics, a type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis. A type II error (or error of the second kind) is the failure to reject a false null hypothesis.

Significance Level - is a statistical assessment of whether observations reflect a pattern rather than just chance. When used in statistics, the word significant does not mean important or meaningful, as it does in everyday speech; with sufficient data, a statistically significant result may be very small in magnitude.

Risk Level in hypothesis testing - The importance of a risk as defined by its characteristics impact and likelihood. The level of risk can be used to determine the intensity of testing to be performed. A risk level can be expressed either qualitatively (e.g. high, medium, low) or quantitatively.

11. Formulate the appropriate null hypothesis and alternative hypothesis for testing

that the starting salary for graduates with a B.S. degree in electrical engineering

is greater than $38,000 per year. The significance, or risk, is: What does = 0.05 mean?

This means that there is a 0.05 probability that type 1 error will occur. 12. In a New York Times/CBS poll, 56 percent of 2,000 randomly selected voters in

New York City said that they would vote for the incumbent in a certain two-candidate race. Calculate a 95 percent confidence interval for the population proportion. Discuss its implication. Carefully discuss what is meant by the population, how you would carry out the random sampling, and what other factors could lead to differences between the responses to the surveys and the actual votes on the day of the election.

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13. A random sample of 50 teaching assistants at the University of Iowa in the fall of 1996 indicated that 30 of them were planning to join the union for teaching assistants. Calculate a 95 percent confidence interval for the proportion of University of Iowa teaching assistants who are in favor of joining a union.

14. The American Association of University Professors claims that the mean income

of tenured professors at public universities is $ 62,000. Our hypothesis is that the mean salary is actually lower than $62,000. In order to test whether or not the mean salary is lower than $ 62,000. We take a random sample of n=36 professors. Their salaries led to a sample average of $59,000 and a sample standard deviation s=$8,000.

(a) Calculate the test statistic and obtain its probability value.

(b) Assuming a significance level of 5 percent ( = 0.05), what is your conclusion?

15. Thirty light bulbs were selected randomly form among a very large production

batch, and they were put on test to determine the time until they burn out. The

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average failure time for these thirty bulbs was 1,080 hours; the sample standard deviation was 210 hours. The light bulbs are advertised as having a mean life length of 1200 hours. Test this hypothesis against the alternative that the mean life length of this batch is actually smaller than 1,200 hours. Follow the steps as

directed in class. Alpha

16. A manufacturing manager claims that on average it take it 22.0 minutes to build

a unit. How can you verify the claim having secured test data for 15 production

times? Average X = 25.8 and the standard deviation S = 4.70.

17. A software company wants to verify that the technical service help line answers

customers’ inquiries in less than two minutes. The results of the data are

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summarized as follows: Sample size, n = 120 Average, X = 1.9, Standard deviation, S = 0.28 Formulate the hypothesis and solve the problem. What is your conclusion?

18. A diet plan states that, on average, participants will lose 12 pounds in four

weeks. As a statistician for a competing organization, you want to test the claim. You sample 70 participants who have been on the subject diet plan for four weeks. You find that the average weight loss has been 1 1.4 pounds with a sample standard deviation of 1.6 pounds. What is your conclusion based on the data using a 5 percent level of significance (risk)?

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19. Consider a process variable I that has a standard deviation of sigma 1 and

a process variable 2 that has a standard deviation 2 (sigma 2). For example,

(might represent the standard deviation of the tablet weight of a

pharmaceutical product before attempts were made to reduce variability and 2 the standard deviation after efforts were made to reduce the variation. A sample of seven tablets is taken from the production line prior to the improvement, and five tablets are taken from the production line after implementation of the modification. Using F-test, decide on hypothesis that one of the variances is greater than the other variance. Considering the data in table below establish an appropriate hypothesis and draw conclusions on the process improvement

has reduced the variation. (Alpha) Risk = 0.05 (a confidence level of 95%).

The weights of tablets prior The weights of tablets after to process improvement: process improvement _______________________________________________________ 12.3 12.6 12.7 12.5 12.5 12.6 12.6 12.5 12.4 12.4 12.9 12.2 20. Two different methods of training have been evaluated to find out if there is a

difference between them. One test group consists of 16 participants, and the other consists of II. The respective standard deviations are 14.0 and 7. Assume a

risk, = 0.05.