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1 Statistics -Quality Control Alan D. Smith Statistics -Quality Control Alan D. Smith

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2 UpComing Events Complete CD-ROM certifications Review Final Examination

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3 Statistical Quality Control Statistical Quality Control CD-ROM ASSIGNMENT

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4 TO DISCUSS THE ROLE OF STATISTICAL QUALITY CONTROL TO DEFINE THE TERMS CHANCE CAUSES, ASSIGNABLE CAUSES, IN CONTROL, & OUT OF CONTROL. TO CONSTRUCT AND DISCUSS VARIABLES CHARTS: MEAN & RANGE. TO DISCUSS THE ROLE OF STATISTICAL QUALITY CONTROL TO DEFINE THE TERMS CHANCE CAUSES, ASSIGNABLE CAUSES, IN CONTROL, & OUT OF CONTROL. TO CONSTRUCT AND DISCUSS VARIABLES CHARTS: MEAN & RANGE. GOALS

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5 GOALS (next class) TO CONSTRUCT AND DISCUSS ATTRIBUTES CHARTS: PERCENTAGE DEFECTIVE & NUMBER OF DEFECTS. TO DISCUSS ACCEPTANCE SAMPLING. TO CONSTRUCT OPERATING CHARACTERISTIC CURVES FOR VARIOUS SAMPLING PLANS. TO CONSTRUCT AND DISCUSS ATTRIBUTES CHARTS: PERCENTAGE DEFECTIVE & NUMBER OF DEFECTS. TO DISCUSS ACCEPTANCE SAMPLING. TO CONSTRUCT OPERATING CHARACTERISTIC CURVES FOR VARIOUS SAMPLING PLANS.

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6 Statistical Quality Control emphasizes in-process control with the objective of controlling the quality of a manufacturing process or service operation using sampling techniques. Statistical sampling techniques are used to aid in the manufacturing of a product to specifications rather than attempt to inspect quality into the product after it is manufactured. Control Charts are useful for monitoring a process. Statistical Quality Control emphasizes in-process control with the objective of controlling the quality of a manufacturing process or service operation using sampling techniques. Statistical sampling techniques are used to aid in the manufacturing of a product to specifications rather than attempt to inspect quality into the product after it is manufactured. Control Charts are useful for monitoring a process. CONTROL CHARTS

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7 There is variation in all parts produced by a manufacturing process. There are two sources of variation: Chance Variation - random in nature. Cannot be entirely eliminated. - Assignable Variation - nonrandom in nature. Can be reduced or eliminated. There is variation in all parts produced by a manufacturing process. There are two sources of variation: Chance Variation - random in nature. Cannot be entirely eliminated. - Assignable Variation - nonrandom in nature. Can be reduced or eliminated. CAUSES OF VARIATION

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8 The purpose of quality-control charts is to determine and portray graphically just when an assignable cause enters the production system so that it can be identified and be corrected. This is accomplished by periodically selecting a small random sample from the current production. PURPOSE OF QUALITY CONTROL CHARTS

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9 The mean or the x-bar chart is designed to control variables such as weight, length, inside diameter etc. The upper control limit (UCL) and the lower control limit (LCL) are obtained from equation: The mean or the x-bar chart is designed to control variables such as weight, length, inside diameter etc. The upper control limit (UCL) and the lower control limit (LCL) are obtained from equation: TYPES OF QUALITY CONTROL CHARTS - VARIABLES

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11 The range chart is designed to show whether the overall range of measurements is in or out of control. The upper control limit (UCL) and the lower control limit (LCL) are obtained from equations: The range chart is designed to show whether the overall range of measurements is in or out of control. The upper control limit (UCL) and the lower control limit (LCL) are obtained from equations: TYPES OF QUALITY CONTROL CHARTS - VARIABLES

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13 EXAMPLE A manufacturer of ball bearings wishes to determine whether the manufacturing process is out of control. Every 15 minutes for a five hour period a bearing was selected and the diameter measured. The diameters (in mm.) of the bearings are shown in the table below.

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14 Compute the sample means and ranges. The table below shows the means and ranges. EXAMPLE (continued)

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15 Compute the grand mean (X double bar) and the average range. Grand mean = (25.25 + 26.75 +... + 25.25)/5 = 26.35. The average range = (5 + 6 +... + 3)/5 = 5.8. average Determine the UCL and LCL for the average diameter. UCL = 26.35 + 0.729(5.8) = 30.58. LCL = 26.35 - 0.729(5.8) = 22.12. Compute the grand mean (X double bar) and the average range. Grand mean = (25.25 + 26.75 +... + 25.25)/5 = 26.35. The average range = (5 + 6 +... + 3)/5 = 5.8. average Determine the UCL and LCL for the average diameter. UCL = 26.35 + 0.729(5.8) = 30.58. LCL = 26.35 - 0.729(5.8) = 22.12. EXAMPLE (continued)

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17 Determine the UCL and LCL for the range diameter. UCL = 2.282(5.8) = 30.58. LCL = 0(5.8) = 0. Is the process out of control? Observe from the next slide that the process is in control. No points are outside the control limits. Determine the UCL and LCL for the range diameter. UCL = 2.282(5.8) = 30.58. LCL = 0(5.8) = 0. Is the process out of control? Observe from the next slide that the process is in control. No points are outside the control limits. EXAMPLE (continued)

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19 EXAMPLE (continued) X-bar and R Chart for the Diameters

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20 Control Charts W. Edwards Deming Control Charts W. Edwards Deming Short Video Clip

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21 The percent defective chart is also called a p-chart or the p-bar chart. It graphically shows the proportion of the production that is not acceptable. TYPES OF QUALITY CONTROL CHARTS - ATTRIBUTES

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22 The equation below gives the UCL and LCL for the p-chart. The equation below gives the UCL and LCL for the p-chart. TYPES OF QUALITY CONTROL CHARTS - ATTRIBUTES

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23 A manufacturer of jogging 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

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24 c-c-bar The c-chart of the c-bar chart is designed to control the number of defects per unit. The UCL and LCL are found by: c-c-bar The c-chart of the c-bar chart is designed to control the number of defects per unit. The UCL and LCL are found by: TYPES OF QUALITY CONTROL CHARTS - ATTRIBUTES

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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 2. Construct the appropriate control limits. EXAMPLE

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26 Acceptance sampling is a method of determining whether an incoming lot of a product meets specified standards. It is based on random sampling techniques. A random sample of n units is obtained from the entire lot. 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 is a method of determining whether an incoming lot of a product meets specified standards. It is based on random sampling techniques. A random sample of n units is obtained from the entire lot. 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

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27 An OC curve, or operating characteristic curve, is developed using the binomial probability distribution, in order to determine the probabilities of accepting lots of various quality levels. OPERATING CHARACTERISTIC CURVE

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28 EXAMPLE 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? P(r n = 10, p = 0.05) = 0.599 + 0.315 = 0.914. P(r n = 10, p = 0.1) = 0.349 + 0.387 = 0.736 etc. 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? P(r n = 10, p = 0.05) = 0.599 + 0.315 = 0.914. P(r n = 10, p = 0.1) = 0.349 + 0.387 = 0.736 etc.

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29 Statistical Quality Control Homework Complete CD-ROM exercises

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