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Running head: INDIVIDUAL PROJECT II 1

Individual Project II

Laura M Williams, RN, CLNC, MSN

IET603: Statistical Quality Assurance in Science and Technology

Morehead State University

Dr. Ahmad Zargari

22 February 2014

A.Zargari - Instructor Page 2 2/23/2014

Laura Williams - Student

Individual Project II (50 points): Please solve and Submit your completed project by 2- 25-2014 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).

In 1924, Shewhart suggested that continual process-adjustment in reaction to non-conformance actually increased variation and degraded quality and stressed the importance of reducing variations in the manufacturing process. Shewhart developed the control chart which framed the problem in terms of assignable- cause and chance-cause variation 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. As a statistician, Shewhart drew from pure mathematical statistical theories. He discovered that observed variation in manufacturing data did not always behave the same way as data in nature and found that data from physical processes never produce a "normal distribution curve." 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. http://en.wikipedia.org/wiki/Walter_A._Shewhart

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

Juran exposed the cost of poor quality and asserted that without change, there will be a constant waste; however, during change there will be increased costs, but after the improvement, margins will be higher and the increased costs get recouped. To effect a change, Juran suggested a new approach to cross- functional management composed of three managerial processes: quality planning, quality control, and quality improvement – the “Juran Trilogy.”

Planning – establish objectives and requirements for quality

Control – operational techniques and activities used to fulfill requirements for quality

Improvement – systematic and continuous actions that lead to measurable improvement

http://en.wikipedia.org/wiki/Joseph_M._Juran

3. Briefly describe the purpose for basic tools for quality improvement (Basic Process Improvement Toolbox).

The Basic Tools of Quality are called basic because they are suitable for people with little formal training in statistics and because they can be used to solve the vast majority of quality-related issues. These tools are a fixed set of graphical techniques which were identified by Kaoru Ishikawa as being the MOST helpful when troubleshooting issues relate to quality. This toolbox includes the:

http://en.wikipedia.org/wiki/Walter_A._Shewhart http://en.wikipedia.org/wiki/Joseph_M._Juran

A.Zargari - Instructor Page 3 2/23/2014

Laura Williams - Student

Cause-and-effect diagram (alternately, “fishbone” or Ishikawa diagram)

Check sheet

Control chart

Histogram

Pareto chart

Scatter diagram

Stratification (alternately, flow chart or run chart)

These basic tools can be used separately or in conjunction with one or more of the other tools to identify weaknesses in the process. Ishikawa encouraged every member of an organization to learn these tools and become adept in their use so that the quality mentality was a shared vision within the company.

http://en.wikipedia.org/wiki/Seven_Basic_Tools_of_Quality

4. Explain the properties of random variables

A random variable is a function that associates a unique numerical value with every outcome of an experiment. The value of the random variable will vary from trial to trial as the experiment is repeated, and cannot be predicted with complete certainty. Their values are subject to variations due to chance and do not have a fixed value. This allows the random variable to assume a set of possible different values, each with an associated probability outcome of a random process. The numerical values of a random variable can be manipulated to construct summary values for the variable, allowing for an observation of a moment of the random variable. Once the random variable has been defined, the process can be examined using probability distribution (discrete random variable) or probability density function (continuous random variable). http://www.stats.gla.ac.uk/glossary/?q=node/410

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

http://en.wikipedia.org/wiki/Seven_Basic_Tools_of_Quality http://www.stats.gla.ac.uk/glossary/?q=node/410

A.Zargari - Instructor Page 4 2/23/2014

Laura Williams - Student

Mean = 9.9890 Standard Deviation = 0.0918

A.Zargari - Instructor Page 5 2/23/2014

Laura Williams - Student

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? (note to self: reference slide 30 from PPT by Ding & Yang)

P10(4) = C 4 10 x 0.8

4 x (1 – 0.8) 10-4

= 10! x 0.84 x (1 – 0.8) 10-4 4! x (10-4)!

= 3628800 x 0.4096 x 0.000064 720 = 209.81 x 0.00002621 = 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: P(x; μ) = (e-μ) (μx) / x! X=2, μ=12

P(x=2) = (e-12) (122) / 2! P(x=2) = 0.0004424

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).

b (x; n, P) = nCx * P x * (1 - P)n – x

n=100, x=5, p=0.02

b (x=5) = 100C5 * 0.02 5 * (1 – 0.02)100 – 5

b(x=5) = 0.0353468047277209

A.Zargari - Instructor Page 6 2/23/2014

Laura Williams - Student

Solve the question #8 using Poisson distribution formula and verify your response using MINITAB. P(x; μ) = (e-μ) (μx) / x! P(5; 0.02) = (e-5) (50.02) / 5! p = 0.007

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. P(a

A.Zargari - Instructor Page 7 2/23/2014

Laura Williams - Student

10. Explain Null Hypothesis, Alternative Hypothesis, Types of error, Significance

Level, Risk Level in hypothesis testing.

Null Hypothesis – (H0 : μ) represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved.

Alternative Hypothesis – (H1 : μ) the alternative hypothesis (or maintained hypothesis or research hypothesis) . It is a statement of what a statistical hypothesis test is set up to establish.

Type I Error –incorrect rejection of a true null hypothesis.

Type II Error - failure to reject a false null hypothesis.

Significance Level - is a statistical assessment of the probability of wrongly rejecting the null hypothesis, if in fact, it is true. (The probability of having a Type I error).

Risk Level in hypothesis testing - The level of risk that the researcher wishes to assume in the analysis is represented by the probability of Type I and Type II errors. Given a specific test design (sample size, hypothesis), the researcher specifies the level of Type I risk, referred to as the significance level. The compliment of the significance level is the confidence level.

A.Zargari - Instructor Page 8 2/23/2014

Laura Williams - Student

11. Formulate the appropriate null hypothesis and alternative hypothesis for testing that the starting salary for gradua

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