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Statistical Process Control Evolution of Quality Control Acceptance Process Continuous Sampling Control Improvement Inspection of materials Corrective Quality before and product action during built into after production production the process reactive proactive Cereal Manufacturer Example Your company produces boxes of cereal Each box of cereal is supposed to be 16.0 oz How cereal boxes are filled: an empty box is moved forward on a conveyer until it is positioned under the filling funnel a door at the base of the funnel is opened after a certain period of time the door is closed the conveyer moves the boxes forward again and the process repeats Will each box be exactly 16.0 oz, or will there be at least a little variation in the weight? How can we tell if the box filling machine is working properly or not? Getting Started Mark out this section of the notes: “How does variation relate to quality? “unusual”variation “too much” variation What we will cover … Statistical process control Used during processing by comparing measurements to standards Used to detect problems with the process (by looking at output of process) so process can be corrected Process capability Used before processing Used to determine if a particular process is able to meet customer specifications Difference between them? Purpose & when used Basis (what is examined) Getting started … Penny placement – round 1 Place penny on paper and trace outline of it Now pick it up, hold it about 6 inches above the paper and try to place it in exactly the same place 5 times Was it in exactly the same place every time? Penny placement – round 2 Close your eyes and pick up the penny Now try to place the penny in exactly the same place 5 times in a row (open your eyes to check your placement each time but close them before picking it up again) Was it in exactly the same place every time? Is there a difference between the 1st and 2nd rounds? What accounts for that difference? Why use samples in SPC? Individual observations tend to be too erratic to make trends quickly visible Only natural variation present Output from process forms distributions that are stable and predictable over time Same mean and standard deviation Day 1 – Day 4 samples from the same population Day 1 Day 2 Day 3 Day 4 Process is considered “in control” (operating as expected) Distribution of sample (n=5) means from day 1 Assignable cause of variation present Output from process forms distributions that are not stable or predictable over time Vary in central tendency (mean), standard deviation (variation) and shape Day 4 samples not from the same population as Day 1 Day 1 Day 2 Day 3 Day 4 Process considered “out of control” (not performing as expected) Statistical Process Control Chart A graphic representation of process data over time Time-ordered sequence of sample statistics Upper limit Target Lower limit SPC – monitor a process by comparing sample statistics to standards (limits) that are based on natural variation being present What sample statistic? X -chart (mean) X R-chart (range) R P-chart (% defective) p C-chart (# defective) c Statistical Process Control Chart 3σ X UCL 2σ X Natural or inherent 1σ X variation X 1σ X Natural or inherent variation 2σ X - 3σ X LCL U,LCL = target value + “acceptable” variation = overall mean + (# of std deviations)(std deviation) Statistical Process Control Chart Day 1 Day 2 Day 3 Day 4 If only natural variation present where should most sample values fall? Day 1 Day 2 Day 3 Day 4 If assignable causes of variation present where should at least some sample values fall? Statistical Process Control Chart 1. Establish control limits based on prior samples 2. Use control chart to monitor process by comparing sample values to established control limits Let’s play “Is it a variable or an attribute?” Diameter of a steel bar # of lawn mowers per 20 that start on 1st pull # of complaints at a fast-food joint per week Length of a piece of metal # of bolts of fabric with too little fabric per week Which chart? How is quality assessed? Measured Defects are (variable data) counted (weight, length, (attribute data) Density, etc.) X and R-charts Is the count out of some known or set number? Yes No (# of defects out of a (# of defects each day or sample of n units – so # of defects in a windshield - you can determine the so you do not know the % defective) sample size and can’t calculate the % defective) P-chart C-chart Control Charts for Variables shift in mean shift in variation Variable Charts X-chart – detect shift in central tendency If process (population) standard deviation known If process (population) standard deviation not known (not enough data) R-chart – detect shift in the variation What is a standard deviation? 95.45% of values will lie within + 2 standard deviations 99.73% of values will lie within + 3 standard deviations 95.45% of area under the curve 99.73% of area under the curve -3 -2 -1 0 +1 2 +3 In-class example Based on 100 samples of 5 cereal boxes each collected over time, you have estimated the population mean as 16.0 oz and the population standard deviation as 1 oz. Determine 3s control limits for an X-chart X-chart: 1 U,LCL= μ zσ X 16.0 3 5 16.0 1.3 Hint: If you have 5 samples, In-class example what is your sample size? You have 5 samples that have been collected for the cereal-box filling line Sample Weights Time Box 1 Box 2 Box 3 Box 4 9 am 15.8 16.2 15.9 16.2 10 am 16.1 16.2 15.9 15.8 11 am 15.9 16.0 16.3 16.1 Noon 15.7 15.8 16.1 16.2 1 pm 15.7 16.1 15.9 16.1 Determine control limits for all necessary charts In-class example Sample Weight Time Box 1 Box 2 Box 3 Box 4 Mean Range 9 am 15.8 16.2 15.9 16.2 16.02 0.4 10 am 16.1 16.2 15.9 15.8 16.00 0.4 11 am 15.9 16.0 16.3 16.1 16.08 0.4 n4 Noon 15.7 15.8 16.1 16.2 15.95 0.5 X 16.0 1 pm 15.7 16.1 15.9 16.1 15.95 0.4 R 0.42 Factors for 3s Control Limits Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3 2 1.880 3.268 0 3 1.023 2.574 0 4 .729 2.282 0 5 .577 2.115 0 6 .483 2.004 0 7 .419 1.924 0.076 8 .373 1.864 0.136 9 .337 1.816 0.184 10 .308 1.777 0.223 12 .266 1.716 0.284 In-class example Sample Weight Time n4 Box 1 Box 2 Box 3 Box 4 Mean Range 9 am 15.8 16.2 15.9 16.2 16.02 0.4 X 16.0 10 am 16.1 16.2 15.9 15.8 16.00 0.4 R 0.42 11 am 15.9 16.0 16.3 16.1 16.08 0.4 A 2 0.729 Noon 15.7 15.8 16.1 16.2 15.95 0.5 D 4 2.282 1 pm 15.7 16.1 15.9 16.1 15.95 0.4 D3 0 U, LCLX X A 2 R 16.0 .729.42 UCL R D 4 R 2.282(.42) 0.96 LCLR D3 R 0(.42) 0 In-class Example – Munchkins What reflects quality? Set up control chart Take samples when you think process is working properly Calculate appropriate sample statistics Determine control limits for all appropriate charts Using the control chart Draw samples of pre-defined size at pre-determined time intervals Plot appropriate sample statistics on control chart Draw conclusion – what type of variation is present? If “out of control”, what could be assignable cause of variation? What can be done to fix it? Did corrective action remove assignable cause? “In control” Process both central tendency and variation must be “in control” for process to be “in control” Mean = 1.0 Mean = 1.0 Variation = 0.2 Variation = 0.2 Using the Control Chart √ Set control limits based on data collected in prior periods Use control charts to monitor process Take sample of size n at pre-specified time intervals Calculate the appropriate sample statistic for that sample Plot sample values on appropriate charts Draw conclusion and take appropriate action Repeat process What are you trying to accomplish with SPC charts? Which chart? How is quality assessed? Measured Defects are (variable data) counted (weight, length, (attribute data) Density, etc.) X and R-charts Is the count out of some known or set number? Yes No (# of defects out of a (# of defects each day or sample of n units – so # of defects in a windshield - you can determine the so you do not know the % defective) Sample size and can’t Calculate the % defective) P-chart C-chart Examples Telephone inquiries of IRS customers are monitored daily (5 days in total). Incidents of incorrect information or other nonconformities (such as impoliteness to customers) are recorded. The data for 5 sample days are below. Construct the 3s control chart for nonconformities. Day 1 2 3 4 5 # of nonconformities 5 10 23 20 15 Detroit Central Hospital is trying to improve its image by providing a positive experience for its patients and their relatives. A 100-patient sample of questionnaires that accompanied meals had the following results. Construct 3s control limits. Day 1 2 3 4 5 6 7 # of unsatisfied 8 5 4 7 8 4 6 customers Examples Telephone inquiries of IRS customers are monitored daily (5 days in total). Incidents of incorrect information or other nonconformities (such as impoliteness to customers) are recorded. The data for 5 sample days are below. Construct the 3s control chart for nonconformities. Day 1 2 3 4 5 # of nonconformities 5 10 23 20 15 U , LCL c z c 14.6 3 14.6 UCL 26.06 LCL 3.14 Examples Detroit Central Hospital is trying to improve its image by providing a positive experience for its patients and their relatives. A 100-patient sample of questionnaires that accompanied meals have the following results. Construct 3s control limits. Day 1 2 3 4 5 6 7 # of unsatisfied customers 8 5 4 7 8 4 6 p .08 .05 .04 .07 .08 .04 .06 U , LCL p z p 1 p n .06.94 0.06 3 100 .06 3(.0237 ) UCL .13 LCL .01 0 Control Charts for M&M’s Two situations – what chart for each? monitor M&M processing based on # of defects per bag monitor mix of colors per sample of 55 M&M’s Managerial Considerations where to use control charts where might process go “out of control”? where in the process is critical? type of chart variable or attribute data trade-off between them – ease vs richness of data when to stop process a single sample value outside limits trends or patterns sample size time and cost effectiveness Sample Size In-Class Demonstration No food this time Need 8-10 volunteers to come up front and bring something with which to write Customer specifications: all rolls must be between 4 and 10, inclusive Is the process capable of meeting customer specifications essentially 100% of the time? What is needed to make it capable? Number Production Process with only natural variation 2 3 4 5 6 7 8 9 10 11 12 Cannot meet customer’s specifications of 4-10 – process is not capable Side note: this is what Deming meant by 85% of quality problems have to do with materials and/or processes, not employee performance Number Production Change process to reduce natural variation 4 5 6 7 8 9 10 Every roll will meet specifications – process is capable Process Control vs Capability In control only natural variation present Capable Process with natural variation is able to meet specs – process variation is “small” enough such that output meets specifications essentially 100% of the time Process Variation Natural process variation – range for all units produced process distribution -3s +3s 6s 99.73% of area under curve falls within + 3s Measure as process width = + 3s (= 6s) Specifications range of acceptable values established by design engineer or customers Measure as specification width + x (= 2x) upper specification – lower specification x x Process Capability Natural variability compared to specifications– can we meet specs given the inherent variability? Lower spec 2x Upper spec 99.74% process distribution -3s +3s Specification width spec width Cp = = process width 6s Customer specs Process is “not capable” That means 4.6% of the units produced Only 95.4% of the area under will not meet specs process distribution the curve is between specs -3s -2s -1s +1s +2s +3s C = 0.67 You make improvements to the process to reduce the natural variation p Process as it currently operates (ex: manual welding) Customer specs Process is “capable” That means 0.3% Cp = 1.00 Customer specs Process is “capable” That means 0.27% of the units produced will not meet specs Now 99.73% of the area under process distribution the curve is between specs -3s -2s -1s +1s +2s +3s Make improvements to process to reduce the natural variation (ex: automated welding) of the units produced Now 99.7% of the area under will not meet specs process distribution the curve is between specs -3s -2s -1s +1s +2s +3s Cp = 2.00 You make more improvements to the process to further reduce the natural variation Customer specs Process is “capable” That means 0.0003% and almost perfect of the units produced (Motorola’s goal) Now 99.9997% of the area under will not meet specs process distribution the curve is between specs -6s -4s -2s +2s +4s +6s Make further Improvements to process (ex: improved equipment for automated process) Process Control and Capability Process Control Process Capability Based on sample values and Based on individual observations sampling distribution and process distribution Done on an on-going basis to Done to evaluate a process before monitor process production (e.g., new specification, Natural vs assignable variation new technology available) Natural variation in process compared to specs – is process capable of meeting specs given the natural variation of the process Process Control and Capability Control Chart UCL Sample statistic LCL Each Xi Design specifications Process Control and Capability Process is … Capable Not capable Try to reduce In control Good! natural variation Find assignable Out of control Yuck! cause of variation

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Statistical Process Control, control charts, control limits, process capability, control chart, process control, SPC software, Six Sigma, standard deviation, statistical control

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posted: | 7/8/2011 |

language: | English |

pages: | 47 |

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