17- Chapter Seventeen McGraw- © 2005 The McGraw-Hill Companies, Inc., All Chapter Statistical Quality Seventeen 17- Control GOALS When you have completed this chapter, you will be able to: ONE Discuss the role of quality control in production and service operations TWO Define and understand the terms chance causes, assignable cause, in control and out of control, and variable THREE Construct and interpret a Pareto chart FOUR Construct and interpret a Fishbone diagram Goals Chapter Seventeen 17- continued Statistical Quality Control GOALS When you have completed this chapter, you will be able to: FIVE Construct and interpret a mean chart and a range chart SIX Construct and interpret a percent defective chart and a c-bar chart SEVEN Discuss acceptance sampling EIGHT Construct an operating characteristic curve for various sampling plans Goals 17- Statistical Process Control A collection of strategies, techniques, and actions taken by an organization to ensure they are producing a quality product or providing a quality service Statistical Process Control 17- Sources of Variation There is variation in all parts produced by a manufacturing process Chance Variation is random in nature and cannot be entirely eliminated Assignable Variation is not random in nature and can be reduced or eliminated by investigating the problem and finding the cause Causes of Variation 17- Pareto Analysis A technique for tallying the number and type of defects that happen within a product or service Produce a Steps in pareto analysis vertical bar chart to display data Rank the defects in terms of frequency of occurrence from largest to smallest Tally the type of defects Diagnostic Charts: Pareto Chart The accounting department of a large organization is spending significant time correcting travel vouchers submitted by employees from its numerous locations Accounting staff noted that typical errors included wrong travel codes, incorrect employee identification numbers, inaccurate math, placing expenses on the wrong lines of the form, and failure to include proper documentation of expenses 17- Department staff pulled a sample of 100 vouchers and tallied errors in the various categories Example 17- Error Type Wrong codes Incorrect employee identification number Number found 60 25 Inaccurate math Inaccurate form placement 23 80 Incomplete documentation 42 Example continued 17- Error Type Wrong codes Incorrect employee identification number Number 60 25 Percent 26 11 Inaccurate math 23 10 Inaccurate form placement 80 35 Incomplete documentation 42 18 330 100 Total Example Pareto table 17- 10 E X C E L Example Pareto Chart 17- 15 Mean (x-bar) Chart Limits How much variation can be expected for a given sample size Designed to control variables such as weight or length U CL = X + s n LCL = X - s n where X is the mean of the sample means UCL: upper control limit LCL: lower control limit Types of Quality Control Charts-Variables 17- 16 Shortcut method for UCL and LCL UCL = X + A2 R and LCL = X − A2 R where X is the mean of the sample means R is the mean of the sample ranges A2 is a constant used in computing the upper and lower control limits, factors found in Appendix B Shortcut method 17- 17 Range Chart Designed to show whether the overall range of measurements is in or out of control UCL = D4 R and LCL = D3 R Types of Quality Control Charts-Variables 17- 18 A manufacturer of chair wheels wishes to maintain the quality of the manufacturing process Every 15 minutes, for a five hour period, a wheel is selected and the diameter measured Given are the diameters (in mm.) of the wheels Example Grand Mean EXAMPLE continued (25.25+26.75+ +25.25) 17- 19 = 26.35 UCL and LCL for Mean UCL=26.35+.729(5.8)=30.58 LCL=26.35-.729(5.8)=22.12 Mean Range (5+6+ +3) =5.8 UCL and LCL for the range diameter UCL=2.282(5.8) = 13.24 LCL=2.282(0) = 17- 20 UCL=30.58 Mean=26.35 UCL = 30.58 LCL=22.12 No points outside limits: Process in control Example continued 17- 21 Sample Range Range Charts for Diameters UCL = 13.24 14 12 10 Mean =5.8 LCL = 2 Hour No points outside limits: Process in control Example continued 17- 22 Percent Defective Chart (p-chart or p-bar chart) The UCL and LCL computed as the mean percent defective plus or minus times the standard error of the percents p(1 − p) UCL and LCL = p ± n Graphically shows the proportion of the production that is not acceptable (p) Sum of the percent defectives p= Number of samples Types of Quality Control Charts-Attributes 17- 23 08(1−.08) 08 ± 400 =.08±.041 A manufacturer of running shoes wants to establish control limits for the percent defective Ten samples of 400 shoes revealed the mean percent defective was 8.0% Where should the manufacturer set the control limits? Example 17- 24 C-chart (c-bar chart) Designed to monitor the number of defects per unit UCL and LCL found by UCL and LCL = c ± c Types of Quality Control Charts-Attributes 17- 25 A manufacturer of computer circuit boards tested 10 after they were manufactured The number of defects obtained per circuit board were: 5, 3, 4, 0, 2, 2, 1, 4, 3, and Construct the appropriate control limits c = 26 / 10 = 2.6 UCL and LCL = 2.6 ± 2.6 = 2.6 ± 4.84 Example 17- 26 Sample Count c-bar chart for Number of Defects per Circuit Board UCL = 7.44 Sample Number 10 c = 2.6 LCL = Example 17- 27 Acceptance sampling A method of determining whether an incoming lot of a product meets specified standards A random sample of n units is obtained from the entire lot Based on random sampling techniques c is the maximum number of defective units that may be found in the sample for the lot to still be considered acceptable Acceptance Sampling Operating Characteristic Curve 17- 28 Short form OC Uses binomial probability distribution to determine the probabilities of accepting lots of various quality levels Suppose a manufacturer and a supplier agree on a sampling plan with n=10 and acceptance number of What is the probability of accepting a lot with 5% defective? A lot with 10% defective? P ( X ≤ / n = 10, π = 05) = 599 + 315 = 914 P ( X ≤ / n = 10, π = 10) = 349 + 387 = 736 17- 29 Probability of accepting a lot that is 10% defective is 677 Example ... Variation is random in nature and cannot be entirely eliminated Assignable Variation is not random in nature and can be reduced or eliminated by investigating the problem and finding the cause Causes... Acceptance sampling A method of determining whether an incoming lot of a product meets specified standards A random sample of n units is obtained from the entire lot Based on random sampling techniques. .. c o rre c t s ta r tin g te m p e r a tu r e P a c k a g in g in s u la te s enough C o m p la in ts o f c o ld fo o d T h e rm o s ta t w o r k in g p r o p e r ly H e a t in g lig h ts a t c