ENGM 720 Statistical Process Control 4/27/2016. REVIEW SHEET FOR FINAL Topics

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1 REVIEW SHEET FOR FINAL Topics Introduction to Statistical Quality Control 1. Definition of Quality (p. 6) 2. Cost of Quality 3. Review of Elementary Statistics** a. Stem & Leaf Plot b. Histograms c. Box Plots, Box & Whisker d. Mean, Mode, Median computations e. Variance, Standard Deviation, & Range computations f. Discrete / Continuous Distributions Simple Comparisons 1. Terms a. Statistic b. Mean / Average c. Variance & Standard Deviation d. Sampling Distributions e. Normal Dist f. Chi-square Dist g. t-dist h. F-Dist 2. Null hypothesis & Alternate hypotheses a. One-sided b. Two-sided 3. Type I & Type II Error a. Power of a Test b. Significance of a Test c. P-value d. Critical Region e. Confidence Interval 4. Hypothesis Testing a. Means tests i. Table ii. Mean Known iii. Mean Estimated iv. Variance / Standard Deviation Known v. Variance / Standard Deviation Estimated b. Variance tests i. Table ii. Variance / Standard Deviation Known iii. Variance / Standard Deviation Estimated 5. Assumption Assessment a. Normal Probability Plots b. Normality c. Equal Variance Methods & Philosophy of SPC 2. Terms a. Chance (common) Causes b. Assignable Causes c. Population / Sample mean, variance, grand mean d. Statistical Control e. Specification Limits Final Review Sheet Page 1 of 7 6:17 PM

2 3. Magnificent Seven tools a. Histogram / Stem & Leaf b. Check Sheet c. Pareto Chart d. Cause & Effect (Fishbone) Diagram e. Defect Concentration Diagram f. Scatter Diagram g. Control Chart 4. Statistical Basis for Control Charts b. Rational Subgroups c. Error Interpretation a) Risk b) Risk d. Analysis of Patterns on Control Charts a) Western Electric Rules b) Sensitizing Rules 5. Implementing SPC a. Elements of a Successful SPC Program Variables Control Charts 2. X-bar & R Charts from Standards from Point Estimates c. Process Capability a.) PCR Cp d. Sampling Size & Frequency a) Operating Characteristic Curves 1. Choice of Sample Size 2. Expected Shift 3. Risk b) Average Run Length & Curves 1. In-Control ARL 2. Out-of Control ARL 3. Average Time to Signal 2. X-bar & S Charts from Standards from Point Estimates c. Control Limits for Individual Measurements Process Capability Analysis a. Natural Tolerance Limits b. Specification Limits c. Fraction Non-Conforming 3. Process Capability a. PCR Cp a.) Two-sided b.) One-sided c.) Recommended Minimum Values b. PCR Cpk c. PCR Cpkm Final Review Sheet Page 2 of 7 6:17 PM

3 Attributes Control Charts a. Variables (Continuous) b. Attributes (Discrete) d. Sampling Distributions a.) Binomial b.) Poisson c.) Ordinate & Cumulative Probability b. Error Interpretation a) Risk b) Risk 2. p-chart a.) Mean b.) Standard Deviation a.) Standards Given b.) Estimates a.) Interpretation b.) Applicable Rules c.) Trial Limits Process d. Sample Size a.) Method 1: n large enough to get at least 1 defective per sample b.) Method 2: pick n so that LCL > 0 c.) Variable Sample Size Options 1. Variable Width Control Limits 2. Average Sample Size Control Limits 3. np-chart a) Mean b) Standard Deviation a) Standards Given b) Estimates 4. c-chart a) Mean b) Standard Deviation a) Standards Given b) Estimates Final Review Sheet Page 3 of 7 6:17 PM

4 5. u-chart a) Mean b) Standard Deviation a) Standards Given b) Estimates Individuals Control Charts 1. Use & Abuse a. When / why to use 2. X & Moving Range Charts a) X Chart Limits b) Moving Range Limits 1. Calculations 3. Moving Average Charts a) Chart Limits b) Calculations 1. m i 4. EWMA Chart c) Standards Given d) Estimates e) Calculations 1. z i 2. z 3. Choice of 5. CUSUM Chart f) Standards Given g) Estimates h) Calculations 1. C + i, N + 2. C - i, N - 3. Choice of K, H Final Review Sheet Page 4 of 7 6:17 PM

5 Short Run SPC Charts* 1. Use & Abuse a. When / why to use 2. DNOM (Deviation from Nominal) Charts a) DNOM x-bar Chart Limits 1. calculations b) DNOM R Chart Limits 1. calculations 1. x i calculation 2. Sample x-bar point calculation 3. Sample R point calculation 3. Standardized Control Charts a) Standardized x-bar Chart Limits b) Standardized R Chart Limits c) Standardized p, np, c, and u Chart Limits d) Calculations 1. Standardized x bar plotted point calculation 2. Standardized R plotted point calculation 3. Standardized p plotted point calculation 4. Standardized np plotted point calculation 5. Standardized c plotted point calculation 6. Standardized u plotted point calculation Gage Capability Studies* 1. Gage Capability a. Components of variability a.) Total b.) Product c.) Gage 1. Repeatability 2. Reproducibility b. Precision to Tolerance Ratio c. X-bar & R charts for Gage Capability a.) Interpretation of out-of-control points on x-bar Chart b.) Interpretation of out-of-control points on R-Chart Final Review Sheet Page 5 of 7 6:17 PM

6 Acceptance Sampling* a. Lot Tolerance Percent Defective b. Acceptable Quality Level c. Error Interpretation a) Risk b) Risk 2. Considerations a. Why / why not (w/rt other SPC methods) b. Lot Formation c. Random Sampling 3. Single Sampling Plan a. Process description in terms of parameters a) N b) n c) c d) P A e) p b. OC Curve a) Probability of Acceptance (P A ) computation b) Description of Ideal vs Practical OC Curves 1. n effect 2. c effect c) Error Interpretation 1. Risk 2. Risk d) Use of Binomial Nomograph 3. MIL STD 105E a. Terms a) Normal Inspection (Level II) b) Reduced Inspection (Level I) c) Tightened Inspection (Level III) d) AQL e) LTPD f) MIL STD Acceptance Number (A c ) g) MIL STD Rejection Number (R e ) h) Montgomery Text s Acceptance Number (c) b. Use of tables and process description with switching rules Intro to Designed Experiments* a. Design Factors = Primary Factors b. Nuisance Factors d. Treatments = Levels e. Blocking f. Replications g. Repeated Measures h. Control a) Blocking b) Randomization c) Replications i. Observation a) Main Effects b) Interaction Effects c) Estimation Final Review Sheet Page 6 of 7 6:17 PM

7 2. Visual Comparisons a. Stragglers a) Right Stragglers b) Left Stragglers c) Total Stagglers b. Tukey s Quick Test c. Three Straggler Rule d. Modified Quick Test 3. ANOVA Models a. Assumptions a) Residuals b) Normality c) Equal Variance b. Factorial Experiments c. Two Factor Designs a) ANOVA Model b) ANOVA Table d. Three Factor Designs*** a) ANOVA Model * Not covered on Midterm exams, covered on Final ** Assumed from previous coursework, calculation is incidental to the exams. ***Not covered on any exam. Final Review Sheet Page 7 of 7 6:17 PM