Report

Process Control Charts VOCABULARY • IMPORTANT TERMS: – Nominal: Data at expected value – Discrete: Data with only a finite number of values – Indiscrete: Data of Acceptable vs. Unacceptable – Variable: Property being measured – Under Control: Variables fall in a nominal range – Data Points: Measurements taken – Datum: A fixed reference point for measurements Process Control Charts • Used to test if the process is in control • Used to see if significant changes have occurred in the process over time “Indiscrete” or “Continuous Data Chart” or “X-R Chart” • Measurement at time intervals • Measurements compare the control over time Example units of measurement to Use: Length (mm) Volume (cc) Weight (gm.) Power (kwh) Time (sec, min, hr.) Pressure (psi) Voltage (v) “Discrete Data Charts” or “PN-P Charts” • Inspection on lot or batch of parts; • Notation of the number of good and defective parts Variable representation: The number of parts inspected in the lot = n Fraction of defective in lot = p Number of defectives = pn X- R CHART CONSTRUCTION Indiscrete Chart Classroom Example In the manufacturing process, car engine valve stems are being machined with a nominal diameter of 13 mm. Samples are taken at the following times of day: 6:00, 10:00, 14:00, 18:00 and 22:00, for 25 consecutive days. The diameter measurements (data) from these samples are presented in the table on the next slide. 5 Steps to formulating the chart: Step 1: Collect the data Step 2: Sort the data into subgroups, such as lots, order number, or days Step 3: Identify the values for the variables “n” and “k”, where n = the size of the sub group (i.e., five times) k = the number of sub groups (i.e., 25 days) Steps to formulating the chart: Step 4: Calculate the mean for each group that will be represented by X Formula: = = + + ⋯⋯+ .+.+.+.+. = . Steps to formulating the chart: Step 5: Calculate the range for each subgroup represented by R Formula: = − = − . = . Upper & Lower Control Limits The Upper Control Limit and the Lower Control Limit set the tolerance level for the control of the manufacture of a product. Learning how to plot two separate charts: o X Control Chart o R Control Chart 9 Steps to Calculating the Upper & Lower Control Limits Step 6: Find the Overall Mean – noted by the double bar X or is the sum of all the means determined in Step 4 divided by the total number of sub groups denoted by the variable, k , which in this example is 25. Formula: + + + ⋯ ⋯ = . + ? ? +? ? + = Continuation of Calculating the Upper & Lower Control Limits Step 7: Find the Average Value of the Range – noted by the bar R or is the sum of all the ranges determined in Step 5 divided by the total number of sub groups denoted by the variable, k , which in this example is 25. Formula: + + + ⋯ ⋯ + = Manufacturing Statistics Step 8: Complete the control limits for each chart: • For X Control Chart: Central Line (CL) = Upper Control Limit (UCL) = + Lower Control Limit (LCL) = − • For R Control Chart: Central Line (CL) = Upper Control Limit (UCL) = Lower Control Limit (LCL) = A2 is from the table based on the size of the subgroup (i.e., Five reading times) D4 & D3 is from the table based on the size of the subgroup (i.e., Five reading times) = ∑ x bar ∑R X double bar R bar CLx UCLx LCLx CLr UCLr LCLr Step 8: Plot Chart Plot Chart Chart Variations Future Prediction P-Control Chart Construction Classroom Example An inspector of car wheel rims, working at the end of a manufacturing line, near the end of each shift must inspect the lot of wheel rims made during that shift. On good days when the welder is running properly, over 400 wheel rims are made per batch. On poor days, as low as 50 to 60 wheel rims are made per batch. The inspector marks on the “check sheet” for each batch the total number of wheels inspected and the number of defects returned for rework for each lot. 18 Steps to Calculating P-Control Chart Step 1. Collect data Step 2. Divide the data into sub groups (i.e., usually days or lot). Each sub group size should be larger than 50 units, where n = the number in each subgroup pn = the number of defects in each sub group Calculating Fraction of Defectives Step 3. Calculate the fraction of defective parts using the following formula: Formula = Where p = fraction (decimal) of the number of defectives pn = number of defects in each subgroup n = number in each subgroup NOTE: To convert result to percentage(%), multiply the result by 100 Calculating Average Fraction of Defectives Step 4. Calculate the Average Fraction of Defectives using the following formula: Formula = = Where = average of fraction of defectives = summation (total) number of defects in each subgroup = summation (total) number in each subgroup Calculating Control Limits Step 5. Calculating the Control Limit for each Subgroup: Formulas: Central Line (CL) = Upper Control Limit (UCL) = + Lower Control Limit (LCL) = − (−) (−) 23 Step 6: Draw P Control Chart Plot Chart PN Control Chart Classroom Example On an assembly line of windshield wiper motors, the inspector selects randomly 100 motors per hour to examine. The inspector notes on the “check sheet” the number of defective motors in each 100 selected. The inspector samples 100 samples for a total of 30 sampling events. PN Control Data Chart Calculating the PN Control Values Step 1. Collect Data – Lot size is set constant Step 2. Calculate the Average Fraction of Defectives, the Center Line, and Upper and Lower Control Limits Formulas: = = = + 3 (1 − ) = − 3 (1 − ) Step 3: Plot the Chart 27 Plotting of PN Control Chart 28 Check For Understanding Please Develop a Control Chart for This Valve Manufacturing line: Your Company makes gate valves which you guarantee to flow water at 3 gallons per minute when fully open. Any restriction or misplaced gaskets in the opening will alter this flow rate. Your inspector at the end of the line tests one valve each hour by measuring the flow for one minute in sample valves. The flow rate is recorded for several days in the table in the next slide. Is this operation in control ? Check For Understanding Flow Rate in Gate Valve Inspection (gal/min) Day 9 AM 10 AM 11 AM Noon 1 PM 2 PM 3 PM 1 3.11 3.20 2.99 2.85 3.00 3.08 2.90 2 2.98 3.01 2.86 2.55 3.06 3.18 3.11 3 2.86 2.99 3.01 3.10 3.03 2.99 3.10 4 3.05 3.04 2.95 3.08 3.01 2.96 2.89 5 2.58 3.25 3.16 3.08 3.01 2.99 2.98 6 3.09 3.03 3.06 3.02 2.99 2.95 3.01 7 3.12 3.04 2.65 2.99 3.30 3.03 2.99 8 3.01 2.97 2.98 3.01 3.00 3.01 3.02