17- 2 Chapter Seventeen Statistical Quality 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
17- 3 Chapter Seventeen 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- 4 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 Statistical Process Control
17- 5 Causes of Variation Assignable Variation Assignable Variation is not random in nature and can be reduced or eliminated by investigating the problem and finding the cause. There is variation in all parts produced by a manufacturing process. Sources of Variation Chance Variation Chance Variation is random in nature and cannot be entirely eliminated.
17- 6 A technique for tallying the number and type of defects that happen within a product or service Produce a vertical bar chart to display data. Diagnostic Charts: Pareto Chart Pareto Analysis Steps in pareto analysis Tally the type of defects. Rank the defects in terms of frequency of occurrence from largest to smallest.
17- 7 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. Example 1 Department staff pulled a sample of 100 vouchers and tallied errors in the various categories.
17- 8 Error TypeNumber found Wrong codes60 Incorrect employee identification number 25 Inaccurate math23 Inaccurate form placement 80 Incomplete documentation 42 Example 1 continued
17- 9 Error TypeNumberPercent Wrong codes6026 Incorrect employee identification number 2511 Inaccurate math2310 Inaccurate form placement 8035 Incomplete documentation 4218 Total Example 1 Pareto table
EXCELEXCEL Example 1 Pareto Chart
Major causes listed on left-hand side of diagram Diagnostic Fishbone Chart cause-and-effect diagram Also called cause-and-effect diagram Helps organize ideas and identify relationships Identifies factors that cause variability Usually considers four problem areas: methods, materials, equipment, and personnel Problem or effect is head of fish Fishbone chart
Suppose a family restaurant, such as those found along an interstate highway, has recently been experiencing complaints from customers that the food being served is cold. Example 2 In the following fishbone diagram, notice each of the subcauses are listed as assumptions. Each of these subcauses must be investigated to find the real problem regarding the cold food.
Purpose of Quality Control Charts Portray graphically when an assignable cause enters the production system so that it can be identified and corrected Monitoring accomplished by periodically selecting a random sample from the current production. Purpose of Quality-Control Charts
Types of Quality Control Charts-Variables where is the mean of the sample means Mean (x-bar) Chart Designed to control variables such as weight or length Limits How much variation can be expected for a given sample size UCL: upper control limit LCL: lower control limit
is the mean of the sample ranges where is the mean of the sample means Shortcut method for UCL and LCL A 2 is a constant used in computing the upper and lower control limits, factors found in Appendix B. Shortcut method
Types of Quality Control Charts-Variables Designed to show whether the overall range of measurements is in or out of control Range Chart
Example 3 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 3 continued Grand Mean ( ) 5 = Mean Range ( ) 5 =5.8 UCL and LCL for Mean UCL= (5.8)=30.58 LCL= (5.8)=22.12 UCL and LCL for the range diameter UCL=2.282(5.8) = LCL=2.282(0) = 0
UCL = Mean=26.35 LCL=22.12 UCL=30.58 Example 3 continued No points outside limits: Process in control
UCL = Mean =5.8 LCL = 0 Example 3 continued No points outside limits: Process in control
Types of Quality Control Charts-Attributes Percent Defective Chart (p-chart or p-bar chart) Graphically shows the proportion of the production that is not acceptable (p) UCLLCL The UCL and LCL computed as the mean percent defective plus or minus 3 times the standard error of the percents
Example 4 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?
Types of Quality Control Charts-Attributes C-chart (c-bar chart) C-chart (c-bar chart) UCL and LCL found by Designed to monitor the number of defects per unit
Example 5 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 2. Construct the appropriate control limits.
UCL = 7.44 c = 2.6 LCL = 0 Example 5
Acceptance Sampling 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 A method of determining whether an incoming lot of a product meets specified standards Based on random sampling techniques A random sample of n units is obtained from the entire lot.
Suppose a manufacturer and a supplier agree on a sampling plan with n=10 and acceptance number of 1. What is the probability of accepting a lot with 5% defective? A lot with 10% defective? Uses binomial probability distribution to determine the probabilities of accepting lots of various quality levels Operating Characteristic Curve Short form OC
Probability of accepting a lot that is 10% defective is.677 Example 6