Probability and Statistics for Reliability Benbow and Broome (Ch 4 and Ch 5)

1. Probability and Statistics for ReliabilityBenbow and Broome (Ch 4 and Ch 5) Presented by Dr. Joan Burtner Certified Quality Engineer Associate Professor of Industrial Engineering and Industrial Management

2. Overview • Chapter 4 Basic Concepts • Measures of central tendency • Measures of dispersion • Discrete and continuous probability distributions • Statistical process control • Chapter 5 Statistical Inference • Point estimate for failure rate • Confidence intervals • Parametric hypothesis testing • Nonparametric hypothesis testing • Type I and Type II errors • Bayes’s theorem for reliability Dr. Joan Burtner, Associate Professor of Industrial Engineering

3. Statistical Analysis • Measures of Central Tendency • Mean • Median • Mode • Measures of Dispersion (aka Variation or Spread) • Range • Standard Deviation • Variance Dr. Joan Burtner, Associate Professor of Industrial Engineering

4. Probability Distributions • Widely-used discrete distributions • Poisson • Binomial • Negative Binomial • Hypergeometric • Widely-used continuous distributions • Normal • Exponential • Weibull • Lognormal • Skewness and Kurtosis Dr. Joan Burtner, Associate Professor of Industrial Engineering

5. Statistical Process Control (SPC) • Central tool is the control chart • Provides an early signal when a process changes • Basic chart consists of an upper control limit, lower control limit, and process mean • Trial control charts are based on historic data • The process is monitored and control limits are modified as needed • Evaluation of control charts is based on probability distribution of the characteristic being monitored • Normal (variables) • Binomial or Poisson (attributes) Dr. Joan Burtner, Associate Professor of Industrial Engineering

6. SPC - Theory of Variation • Common Cause • Stable and predictable causes of variation • Inherent in all processes • Managers, not workers, are responsible for common cause variation • Special Cause • Unexpected or abnormal causes of variation • May result in sudden or extreme departures from normal • May also result in gradual shifts (trends) Dr. Joan Burtner, Associate Professor of Industrial Engineering

7. SPC - Control Chart Types • Control Charts • Variables – based on continuous data • X bar and R (mean and range) • X bar and S (mean and standard deviation) • Attributes - based on discrete data • P (proportion) • C (count) • U (count per unit) Dr. Joan Burtner, Associate Professor of Industrial Engineering

8. Control Chart Calculations for Xbar and R Charts • Xbar and R Control Chart Constants • Control Chart Calculations Dr. Joan Burtner, Associate Professor of Industrial Engineering

9. Control Chart Interpretation We will use Minitab to build / interpret control charts • Building Control Charts • Collect at least 25 samples • Enter data in Minitab using appropriate formatting • Use pull-down menu to select the desired type of chart • Interpretation of Control Charts • Use Minitab to identify the tests Dr. Joan Burtner, Associate Professor of Industrial Engineering

10. Parametric Hypothesis Testing (used for ‘known’ distributions) • Basic Hypothesis Testing for Means • One Sample t or Z Tests • Two Sample t or Z Tests • Hypothesis Tests for Population Standard Deviation • Hypothesis Tests for Population Proportion • Advanced Designs for Hypothesis Testing (Covered in Chapter 6 of Benbow and Broome) • One Factor ANOVA • Two Factor ANOVA • Full Factorial Experiments Dr. Joan Burtner, Associate Professor of Industrial Engineering

11. Nonparametric Hypothesis Testing • Kruskal-Wallis • Nonparametric equivalent to one factor ANOVA • Does not require the assumption that the population is normal • Hypothesizes about medians unless population known to be “mound-shaped and symmetric” • Minitab hypotheses- medians • Benbow and Broome hypotheses - means • Wilcoxon Signed Rank Test • Nonparametric equivalent to single sample test for mean • Used when we can’t assume that the population is normal • Used when we can’t assume the Central Limit Theorem applicable • Examples in Minitab Dr. Joan Burtner, Associate Professor of Industrial Engineering

12. References • Course Text: • Benbow, D.W. and Broome, H.W., Ed. (2009). The Certified Reliability Engineer Handbook . Milwaukee,WI: ASQ Quality Press. • Additional Sources • Christensen, E.H., Coombes-Betz, K.M., and Stein, M.S. (2006). The Certified Quality Process Analyst Handbook. Milwaukee: ASQ Quality Press. • Westcott, R.T., Ed. (2006). Certified Manager of Quality/Organizational Excellence Handbook (3rd ed.). Milwaukee: ASQ Quality Press. Dr. Joan Burtner, Associate Professor of Industrial Engineering

13. Contact Information • Email: Burtner_J@Mercer.edu • US Mail: Mercer University School of Engineering 1400 Coleman Avenue Macon, GA • Phone: (478) 301- 4127 Dr. Joan Burtner, Associate Professor of Industrial Engineering