# LOM 4326/5326 - Quality Assurance in Business

This description will be updated and will become more detailed for the Winter 2007 semester.

# Statistics Resources on the web

Paper syllabus

Robert J. "Bud" Banis, Ph.D.,C.M.A.
CCB 230 314-516-6136; 636-394-4950
E-mail rbanis@jinx.umsl.edu
MW 8-9:15 am in SSB 102
Prerequisites: Math 100 - Basic Calculus
Math 105 - Basic Probability and Statistics
BA 103 - Computers and Information Systems
minimum 2.0 Campus GPA

#### COURSE DESCRIPTION & OBJECTIVES:

This is primarily an applied statistics course dealing with philosophy and mechanics of statistical approaches to quality management.  It is assumed that the student is acquainted with basic probability and statistics, and basic use of a PC-Compatible computer, including navigating on the web, fundamental concepts of spreadsheets, and e-mail. We will review material from the prerequisites and then build on those to survey the tools of Statistical Quality Management and their application to practical cases. Emphasis is placed on problem definition, construction of statistical models, analysis of data, and interpretation of  results. Students will develop a report at the end describing application of the tools in local organizations.

#### Prerequisites:

BA3320/5320 or Graduate standing. Familiarity with basic statistics and PC-compatible computers, spreadsheets, email, and use of the internet..

Two Exams 400 points
Group Quizzes and cases 200
Case exercises 200
Application oral & written reports (last two weeks) 200
Total      1000 points

Exams are closed book, one page (2-sides) notes, multiple choice, short answer.  All Case exercises are individual effort only.  Submissions very similar in form and /or content will result in zeroes. The application Report may be small groups with individual parts identified. Letter grade breaks are expected to be around 90, 80, 70, 60%. Plus & minus grades are rare. Application Report quality will be used to decide on borderline cases.

#### Required:

You shouldn't need a complex statistical calculator as complex calculations will be done mostly in EXCEL

#### Tentative  Schedule:

Group Quiz one will be finished in class on January 25. This is the only quiz given out ahead of time, the rest will be in class.

#### Approx. date                                                                             Topic

Jan-16-18                       Introduction & Overview of tools
Powerpoint overview 6-Sigma,
Taguchi Quality function
Quality Masters (Ch2)

Data manipulation and cleanup in EXCEL,
Sorting, graphing, statistical functions

## Variance and Standard Deviation:

Measures of central tendency dispers.xls  : dispersity example with calculations of variance dispersolver.xls
Areas under the normal curve-- the Z score table. as an excelfile, ztblcalc.xls
Applications to normallized scores--the IQ Score examples

## Central Limit Theorem

• Google search on Central Limit Theorem
• Sampling Statistics and confidence limits on estimates of parameters.
Sampling from Airplane empty seats data airseats.htm
videotutorial on sampling,  samplek.html
Other videos on excel analysis of characteristics of the distribution of sample means:
Finished spreadsheet results show Central Limit Theorem on distribution of sample means.

 Exercise 1: Sampling and the central limit theorem.  Due Thursday February 8 using the random sampling procedure, collect 20 samples of size n=25 from the airplane empty seat data.  airseats.htm derive means, standard deviations and 95% confidence intervals for estimates of the population mean for each of the 20 samples.  compare histograms of the original distribution and the distribution of sample means.  Turn in the resulting spreadsheet printed to be 1 page (legible) with your name, section and student number printed at the top of the sheet. You can accomplish this by printing a selected range that leaves out some of the original data. video on print to 1 page Also submit a file via the  dropbox I put in Mygateway under course documents. 1) How many of your samples had intervals including the true mean?  2) How many gave an erroneous estimate?  3) What is the expected frequency of errors in estimating the population mean when you use a 95% confidence interval? Was your observed result close to that expectation?  4) State the three characteristics we expect to see in the distribution of sample means from the Central Limit Theorem.  5) Are your results reasonably consistent with those expectations?
probabilities of multiple errors in the sampling experiment. Normal approximation to binomial distribution.
Evidence for carcinogenicity of Dioxin.

## Hypothesis testing and sample means

See Lean Six Sigma Pocket Toolbook, pp.156-165

Example one-sample t-test: Is hospital length of stay < 5 days?
video on 1-sample t-test Beta error & sample size losbeta.xls

## T-test two sample means:

gender and height data from statistics class
video on 2-sample t-test
height data 2 sample t test completed

Hypothesis testing, General overview h0test.pdf
Quiz 2 review

## Analysis of Variance

Concepts of ANOVA , "explaining variance" Where does it come from and how can you mathematically separate out the sources of variation?
Ho: all means are the same
Ha: at least two differ from each other.
If Ho is rejected, Which ones are different from which?
Least Significant Difference (LSD) good discussion at http://helios.bto.ed.ac.uk/bto/statistics/tress6.html
basically, LSD= t(alpha,dferror)*sqrt((2*MSE)/n) also see the Multiple Range test with a studentized range.
Summers Text, p. 133 clutch plate keyways ungrouped and grouped data.
Is there evidence that the keyways differ in depth?
Completed keyway sheet with grouped data histograms and ANOVA
Analysis of Variance (ANOVA), Toolbook, pp.173-179
Capsule summary of concept of ANOVA, Summers, p339

### Two-way ANOVA:

golf ball data --correcting for the effect of other variables
Videos on the golf ballcase with one-factor and two-factor ANOVA
What is "Interaction"?
Finished sheet for golf ball data and  Discussion of results
Recorded classes from Statistics course on the golf-ball case Winter 2006 Statistics course

EXCEL model showing partition of Variance by averaging out different effects.  Be sure to set Tools  >Macro >security at  "medium" and enable the macros so the drop down list works.

 I'll run through all this in class to show exactly how I would do it before you do it. Exercise 2:  Problem 9-4 p.172 plastic trim The question is whether Mary and Jack are trimming the same amount from the parts coming from Press #1. To look at this thoroughly: 1) We'll do a histogram of combined data vs. data separated into Jack's and Mary's products. Use bin size of 0.0005 from 0.6530 to 0.6600 (15 bins)  2) We'll consider whether time of the sample gives a huge contribution to variance by doing a one way ANOVA (4 times represented) separately for Jack and Mary. 3) produce descriptive statistics for the distribution of values produced by each worker, including upper and lower 95% confidence limits. In order to do this, data will have to be reconfigured to be all in one row for each. Is there evidence that the two have significantly different means from these results? 4) We'll do an F test, 2-sample for variances to determine if the two operators have significantly different variances, followed by the appropriate t-test. Interpret the F-test output and the T-test output. What do you conclude about the difference between the two operators?

## The paired sample t-test--correcting for unknown common factors

Blood pressure readings- comparison of two methods:
Paired t-Test versus t-Test without pairing. Diastolic blood pressures (DBP) Readings were made by two devices. The diastolic blood pressures (DBP) of 60 patients were determined using two techniques: the standard method used by medical personnel and a method using an electronic device with a digital readout. The results are given in a TXT file bpdigi.txt
We will analyze these data to determine if the two techniques give significantly different results.
First, we'll use the t-test for comparison of two means, ignoring the pairing of the data, then we will analyze differences between the pairs, using each individual as his own control for variables other than the reading technique. This is also used as a "before and after" type experiments. Finished sheet for the BPDigi paired t-test.

## Chapter 10: Variable Control Charts

Data table on Clutch plate thickness from Summers Book (p176, again on p138, again on p218) sheet in progress on clutch plate control charts
We plotted a time series of the clutch plate thickness sample (n=5) averages and added in lines for LCL and UCL where these are = mean +/- 3SEM
We also plotted an R-barchart using Shewhart's D3 and D4 factors from the table in the book X-bar&R-barcharts
Shewhart Factors table scanned from book
Roller shaft length data p184-185    with a Sheet in process

 Mar 24-Apr 1 spring break

## Different ways to arrive at Limits and use of Standard deviations for S charts:

Process Capability, Chapter 11.

Control Chart Patterns and Process Capability Powerpoint
Process Capability Ratio,  Cp and Process Capability Index, Cpk figure

 Exercise 3 (due Thursday, April 12): X-bar and R-charts Data from Question 10-3, p212 datatable in EXCEL Setup X-bar and R charts as I did in class where: X-bar chart: centerline = Xbarbar use R-bar calculated as the mean of sample R's. The UCL and LCL are Xbarbar+/- A2*Rbar Range Chart: Centerline= Rbar which is calculated as the average of the sample Ranges. LCL=D3*Rbar UCL=D4*Rbar 1) Interpret the charts. Does the process seem in control? 2) Are there some points that probably have assignable causes that might be eliminated once those causes were identified?  3) If the Average fill of the bags is supposed to be 50.0 pounds, how does the process history compare to that goal?

## Attributes Control Charts:

### Confidence interval on Population Proportions:

The same tools apply as for continuous variables except that the mean of a population is approximated by the proportion of "successes" in the sample data, and the variance is estimated by p*(1-p).
Thus the equivalent of sample distribution SEM is the sqrt((p*(1-p))/n). Because we assume an approximation to a continuous variable, it's important the p not be near 0 or 1.0. The test for appropriateness is that a 99% confidence interval doesn't include 0 or 1.0.
New Jersey Drug Testing

### Attributes Charts (Chapter 13):

1) Fraction Defective (p) Charts (constant sample size).
Proportion defective = p = np/n  where np=number defective, n= sample size.
Centerline = pbar
3-sigma control limits = pbar +/- 3 * sqrt(pbar(1-pbar) / sqrt (n)
example: Credit Card Data, pp 259-260and265
If sample sizes vary, it is best to calculate pbar as a weighted average.
Percent defective = exactly the same, but everything multiplied times 100
Number defective = exactly the same, but just count the number defective each sample and plot that.
3-sigma limits calculated as npbar +/- 3* sqrt( npbar*(1-pbar)) is the same as calculating everything using pbar,
then multiplying all terms times n.
2) C-Chart: Counts of Defects per piece with n=1
Sample size is one unit. centerline = cbar avceraged over all samples.
Control Limits = cbar +/- 3 * Sqrt (cbar)
Example: Rolls of paper p.271-272
3) U-Chart Average of Defects per Unit (n>1) Constant sample size.
u = c/n . Centerline = ubar
Control limits = ubar +/- 3 * sqrt(ubar) / sqrt(n)
Example: hose connectors p276
If sample sizes vary, it is best to calculate ubar as a weighted average.

### Joint Probabilities and Independence:

• Joint events rain
• Independence and the Chi-Square test.
• Categorical Analysis Chi Square tests of independence-- drinking and smoking.
• U. Cal. Berkeley Graduate School Admission Sex-bias Data analysis by pivottable and Chi-square
•  Exercise 4: Simpson's Paradox: Due Thursday April 19. Use the Berkeley partial dataset provided set up the pivottable and Chi-squared analysis as described. Use the page variable to filter the data and record the admission percents for males and females and Pvalues for each department. Discuss the the results of departmental analysis versus aggregate analysis. refer to the references and any others you find useful to explain what happened and what it means.
• You could also add conditional formatting to highlight which sex is favored.

### Acceptance Sampling:

Powerpoint show from Heizer-Render (start slide 64)
Operating Characteristics Curve from Ng (2003) J. Stats Ed
EXCEL File for sampling strategy and Operating Characteristic

### Failure Modes and Effects Analysis (FMEA) Ch15

FMEA Powerpoint Show from Summers textbook
Links to Many other examples on FMEA
Wikipedia Description FMEA
FMEA InfoCenter Mainpage
http://www.fmeainfocentre.com/presentations1.htm

### Outstanding Site on Six Sigma tools in general:

Six Sigma First

### Design of Experiments (Ch16):

Powerpoint from Summers Book DOE

### Lean Manufacturing (ch17):

Powerpoint from Summers Book Lean Mfg.

### Book Report on Beyond Lean by Darrell Bender:

Due Last class, May 3.
about a page, please send it in electronic form in the dropbox I put in mygateway under assignments.

Read the book and comment on:
1) What kinds of things can go wrong in a Lean Implementation.
2) Managment usually buys into quality/efficiency programs such as Lean, Six Sigma expecting reductions in costs. Many people feel cost reductions necessarily equate to eliminating people from the organization. Some people assume "Lean"="Mean". Is that necessarily true? explain?
3) How is it possible for business leaders to both pursue profit for the shareholders as well as a beneficial and humane environment for the employees?

Last Class Thursday,  May 3

## Text books:

 ISBN 0-13-171680-8 Six Sigma-Basic Tools and Techniques by Donna C.S. Summers (2007) Prentice Hall ISBN 0-07-144119-0 Lean Six Sigma Pocket Toolbook by George, Rowlands, Price, Maxey (2005) McGraw-Hill ISBN 1-59630-016-7 Beyond Lean- Lessons for Leading Organizational Change by Darrell Bender (2006) Heuristic Books
 Exam 1: Tuesday March 20  Exam 1 answer key

E-mail: bud_banis (at) umsl.edu
Campus office CCB 230
On-campus phone 314-516-6136
Off-campus 636-394-4950