Chapter 6s Statistical Process Control (SPC) PDF

Copyright © 2017 Pearson Education, Ltd. S6 - 1  Chapter 6s Statistical Process Control (SPC) Chapter 6s Copyright © 2017 Pearson Education, Ltd. S6 - 2  Learning Objectives When you complete t...

Copyright © 2017 Pearson Education, Ltd. S6 - 1  Chapter 6s Statistical Process Control (SPC) Chapter 6s Copyright © 2017 Pearson Education, Ltd. S6 - 2  Learning Objectives When you complete this supplement you should be able to : 1 Explain the purpose of a control chart 2 Build -charts and R-charts 4 List the five steps involved in building control charts Copyright © 2017 Pearson Education, Ltd. S6 - 3  Statistical Process Control (SPC) SPC: A process used to monitor standards by taking measurements and corrective action as a product or service is being produced. The objective of a process control system is to provide a statistical signal when assignable causes of variation are present. Such a signal can quicken appropriate action to eliminate assignable causes. Copyright © 2017 Pearson Education, Ltd. S6 - 4  Statistical Process Control (SPC) Statistical process control (SPC) is a methodology for establishing and maintaining high-quality output, and it is been heavily linked with Six Sigma. SPC includes a set of tools and principles for: Determining if a process is stable. Monitoring a process for possible changes in behavior. Assessing whether a process is capable of meeting production requirements and customer demands. Copyright © 2017 Pearson Education, Ltd. S6 - 5  Statistical Process Control (SPC) ► Uses statistics and control charts to tell when to take corrective action ► Drives process improvement ► Four key steps ► Measure the process ► When a change is indicated, find the assignable cause ► Eliminate or incorporate the cause ► Restart the revised process Copyright © 2017 Pearson Education, Ltd. S6 - 6  Inspection ► Involves examining items to see if an item is good or defective ► Detect a defective product ► Does not correct deficiencies in process or product ► It is expensive Copyright © 2017 Pearson Education, Ltd. S6 - 7  When & Where to Inspect 1. At the supplier’s plant while the supplier is producing 2. At your facility upon receipt of goods from your supplier 3. Before costly or irreversible processes 4. During the step-by-step production process 5. When production or service is complete 6. Before delivery to your customer 7. At the point of customer contact Copyright © 2017 Pearson Education, Ltd. S6 - 8  Control charts identify variation ► Source of variation, many problems can occurred from: ► Worker fatigue ► Measurement error ► Process variability ► Tactic to reduce variations: ► Robust design ► Empowered employees ► Quality at source Copyright © 2017 Pearson Education, Ltd. S6 - 9  Quality at source ► The next step in the process is your customer ► Ensure perfect product to your customer Quality at source involves the operator ensuring that the job is done properly. These operators are empowered to self-check their own work. Employees that deal with a system on a daily basis have a better understanding of the system than anyone else, and they can be very effective at improving the system. Copyright © 2017 Pearson Education, Ltd. S6 - 10  Quality at source Poka-yoke is the concept of error-proof devices or techniques designed to pass only acceptable products You can find a number of everyday examples of Poka-Yoke: Example: Look at the connector for your computer keyboard or mouse. Its shape prevents it from being connected in the wrong place or turned incorrectly, damaging your computer. Copyright © 2017 Pearson Education, Ltd. S6 - 11  Type of Variation 1. Natural or common causes 2. Special or assignable causes Copyright © 2017 Pearson Education, Ltd. S6 - 12  1. Natural Variations ► Also called common causes ► Inherent to the process or random and not controllable ► Expected amount of variation ► For any distribution there is a measure of central tendency and dispersion (xbar-R Chart) ► If the distribution of outputs falls within acceptable limits, the process is said to be "in control" Copyright © 2017 Pearson Education, Ltd. S6 - 13  2. Assignable Variations ► Also called special causes of variation ► Generally this is some change in the process ► Variations that can be traced to a specific reason ► The objective is to discover when assignable causes are present ► If present, the process is “out of control” ► Eliminate the root causes Copyright © 2017 Pearson Education, Ltd. S6 - 14  Control charts to monitor processes To monitor output, we use a control chart We check things like the mean, range, standard deviation To monitor a process, we typically use two control charts (x-bar chart & R chart) Mean (or some other central tendency measure) X-Bar Chart Variation or dispersion (typically using range or standard deviation) R-Chart Control Chart is the primary tool of SPC. Copyright © 2017 Pearson Education, Ltd. S6 - 15  FYI Samples To measure the process, we take samples and analyze the sample statistics following these steps Each of these (a) Samples of the product, represents one say five boxes of cereal sample of five taken off the filling machine line, vary from each other boxes of cereal in weight # # Frequency # # # # # # # # # # # # # # # # # # # # # # # # Weight Figure S6.1 Copyright © 2017 Pearson Education, Ltd. S6 - 16  FYI Samples To measure the process, we take samples and analyze the sample statistics following these steps The solid line (b) After enough samples represents the are taken from a stable distribution process, they form a pattern called a distribution Frequency Weight Figure S6.1 Copyright © 2017 Pearson Education, Ltd. S6 - 17  FYI Samples To measure the process, we take samples and analyze the sample statistics following these steps (c) There are many types of distributions, including the normal (bell- shaped) distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shape Figure S6.1 Central tendency Variation Shape Frequency Weight Weight Weight Copyright © 2017 Pearson Education, Ltd. S6 - 18  FYI Samples To measure the process, we take samples and analyze the sample statistics following these steps (d) If only natural causes of variation are present, the output of a process forms a distribution that Prediction is stable over time and is Frequency predictable e Tim Weight Figure S6.1 Copyright © 2017 Pearson Education, Ltd. S6 - 19  FYI Samples To measure the process, we take samples and analyze the sample statistics following these steps ? ?? ?? (e) If assignable causes are ? ? ? ? present, the process output ? ? ? ? is not stable over time and ?? ? ?? ? is not predicable Frequency Prediction e Tim Weight Figure S6.1 Copyright © 2017 Pearson Education, Ltd. S6 - 20  Control Charts A control chart is a statistical tool used to distinguish between variation in a process resulting from common causes and variation resulting from special causes. It presents a graphic display of process stability or instability over time Every process has variation. Some variation may be the result of causes which are not normally present in the process. This could be special cause variation. Some variation is simply the result of numerous, ever-present differences in the process. This is common cause variation. Control Charts differentiate between these two types of variation. Copyright © 2017 Pearson Education, Ltd. S6 - 21  Control Charts One goal of using a Control Chart is to achieve and maintain process stability. And that by: Determining if a process is stable. Monitoring a process for possible changes in behavior. Separating common and special causes of variation UCL Target LCL Copyright © 2017 Pearson Education, Ltd. S6 - 22  FYI Process Control (a) In statistical control and capable of producing within Frequency control limits Lower control limit Upper control limit (b) In statistical control but not capable of producing within control limits (c) Out of control Size (weight, length, speed, etc.) Figure S6.2 Copyright © 2017 Pearson Education, Ltd. S6 - 23  Control Charts for Variables (x-bar & R chart) ► Characteristics that can take any real value ► May be in whole or in fractional numbers ► Continuous random variables (i.e. the variable can be measured on a continuous scale (e.g. height, weight, length, time etc.) X- Bar chart tracks changes in the central tendency “Indicates how the average or mean changes over time” R-chart indicates a gain or loss of dispersion “Indicates how the range of the subgroups changes over time.” X-Bar and R-Charts are typically used when the subgroup size (n) lies between 2 and 10 Copyright © 2017 Pearson Education, Ltd. S6 - 24  Control Charts for Variables ► Characteristics that can take any real value ► May be in whole or in fractional numbers ► Continuous random variables x-chart tracks changes in the central tendency R-chart indicates a gain or lossheofse two e T u st b dispersion rts m cha together used Copyright © 2017 Pearson Education, Ltd. S6 - 25  FYI Central Limit Theorem Regardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curve 1) The mean of the sampling distribution will be the same as the population mean m 2) The standard deviation of the sampling distribution ( ) will equal the population standard deviation (s ) divided by the square root of the sample size, n Copyright © 2017 Pearson Education, Ltd. S6 - 26  FYI Population and Sampling Distributions Population Distribution of distributions sample means Beta Mean of sample means = Standard deviation of Normal the sample means Uniform | | | | | | | 95.45% fall within ± Figure S6.3 99.73% of all fall within ± Copyright © 2017 Pearson Education, Ltd. S6 - 27  FYI Sampling Distribution Figure S6.4 Sampling distribution of means Process distribution of means =m (mean) Copyright © 2017 Pearson Education, Ltd. S6 - 28  FYI Sampling Distribution As the sample size increases, Figure S6.4 the sampling distribution narrows n = 100 n = 50 n = 25 Mean of process Copyright © 2017 Pearson Education, Ltd. S6 - 29  Setting Chart Limits For x-Charts when we know s Where = mean of the sample means or a target value set for the process z = number of normal standard deviations = standard deviation of the sample means s = population (process) standard deviation n = sample size Copyright © 2017 Pearson Education, Ltd. S6 - 30  FYI Standard deviation calculation The standard deviation is a little more difficult to understand – and to complicate things, there are multiple ways that it can be determined – each giving a different answer. If you are interested to learn more about the standard deviation calculation, please follow the below links. https://www.spcforexcel.com/knowledge/control-chart-basics/estimated-standard-deviation-and-control-charts Copyright © 2017 Pearson Education, Ltd. S6 - 31  The weight of boxes of cookies within a large production lot are sampled each hour for the past 4 hours. The operation Setting Control manager wants to set control limit that include 99.73% i.e Z=3 of the sample mean. The standard deviation is = 1 ounce. Limits Approach: The operation manager randomly selected and weight five samples each hour (i.e n=5) for the past 4 hours. Find the upper and lower control limits Here are the 5 boxes choses for hour 1 to hour 4 SAMPLE SAMPLE SAMPLE SAMPLE SAMPLE HOUR #1 #2 #3 #4 #5 1 17 13 16 17 14 2 16 15 14 12 16 3 15 17 14 16 12 4 16 16 15 17 13 Copyright © 2017 Pearson Education, Ltd. S6 - 32  Setting Control Limits ▶Randomly select and weigh nine (n = 5) boxes each hour sampl sampl sampl sampl sampl Hour e1 e2 e3 e4 e5 1 17 13 16 17 14 for the 1st sample (hour 1) = = 15.4 2 16 15 14 12 16 for the 2nd sample (hour 2) = = 14.6 3 15 17 14 16 12 for the 3rd sample (hour 3) = = 14.8 4 16 16 15 18 11 for the 4th sample (hour 4) = = 15.2 Copyright © 2017 Pearson Education, Ltd. S6 - 33  Setting Control Limits = 15 n= 5 z=3 s = 1 Ounce Number of samples 4 Average mean of 4 samples = = 15 =/ = / = 0.45 UCL = 15 + (3*0.45) = 16.35 = -z LCL = 15 - (3*0.45) = 13.65 Copyright © 2017 Pearson Education, Ltd. S6 - 34  Setting Control Limits Control Chart for samples Variation of 5 boxes due to assignable causes 16.35 = UCL Variation due to 15 = Mean natural causes 13.65 = LCL Variation due to assignable | | | | | | | | | | | | causes 1 2 3 4 Sample number The process is in control because all samples fall between the UCL & LCL Copyright © 2017 Pearson Education, Ltd. S6 - 35  Setting Control Limits Control Chart for samples Out of Variation of 5 boxes control due to assignable causes 16.35 = UCL Variation due to 15 = Mean natural causes 13.65 = LCL Variation due to assignable | | | | | | | | | | | | causes 1 2 3 4 Out of Sample number control Assume that we have smaple above or below the UCL & LCL. In that case, the process is out of control because NOT all of the samples fall between the UCL &© LCL Copyright 2017 Pearson Education, Ltd. S6 - 36  Setting Chart Limits For x-Charts when we don't know s where average range of the samples A2 = control chart factor found in Table S6.1 = mean of the sample means Ri = range for sample i Copyright © 2017 Pearson Education, Ltd. S6 - 37 k = total number of samples  Control Chart Factors TABLE S6.1 Factors for Computing Control Chart Limits (3 sigma) 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 Copyright © 2017 Pearson Education, Ltd. S6 - 38  Setting Control Limits Super Cola example Process average = 12 ounces labeled as "net weight Average range =.25 ounces 12 ounces" Sample size = 5 UCL = 12.144 Mean = 12 From Table S6.1 LCL = 11.856 Copyright © 2017 Pearson Education, Ltd. S6 - 39  R – Chart ► Type of variables control chart ► Shows sample ranges over time ► Difference between smallest and largest values in sample ► Monitors process variability ► Independent from process mean Copyright © 2017 Pearson Education, Ltd. S6 - 40  Setting Chart Limits For R-Charts where Copyright © 2017 Pearson Education, Ltd. S6 - 41  Restaurant Control Limits For salmon fillets at Darden Restaurants x Bar Chart 11.5 – UCL = 11.524 Sample Mean 11.0 – = 10.959 10.5 – | | | | | | | | | LCL = 10.394 1 3 5 7 9 11 13 15 17 Range Chart 0.8 – Sample Range UCL = 0.6943 0.4 – = 0.2125 0.0 – | | | | | | | | | LCL = 0 1 3 5 7 9 11 13 15 17 Copyright © 2017 Pearson Education, Ltd. S6 - 42  Setting Control Limits Average range = 8 minutes Sample size = 4 From Table S6.1 D4 = 2.282, D3 = 0 UCL = 18.256 Mean = 8 LCL = 0 Copyright © 2017 Pearson Education, Ltd. S6 - 43  FYI Mean and Range Charts (a) These (Sampling mean is sampling shifting upward, but distributions range is consistent) result in the charts below UCL (x-chart detects x-chart shift in central tendency) LCL UCL (R-chart does not R-chart detect change in mean) LCL Figure S6.5 Copyright © 2017 Pearson Education, Ltd. S6 - 44  FYI Mean and Range Charts (b) These sampling (Sampling mean distributions is constant, but result in the dispersion is charts below increasing) UCL (x-chart indicates x-chart no change in central tendency) LCL UCL (R-chart detects R-chart increase in dispersion) LCL Figure S6.5 Copyright © 2017 Pearson Education, Ltd. S6 - 45  Steps In Building Control Charts 1. Collect 20 to 25 samples, often of n = 4 or n = 5 observations each, from a stable process, and compute the mean and range of each 2. Compute the overall means ( and ), set appropriate control limits, usually at the 99.73% level, and calculate the preliminary upper and lower control limits Copyright © 2017 Pearson Education, Ltd. S6 - 46  Steps In Creating Control Charts 3. Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits 4. Investigate points or patterns that indicate the process is out of control – try to assign causes for the variation, address the causes, and then resume the process 5. Collect additional samples and, if necessary, revalidate the control limits using the new data Copyright © 2017 Pearson Education, Ltd. S6 - 47  FYI Setting Other Control Limits TABLE S6.2 Common z Values Z-VALUE (STANDARD DEVIATION REQUIRED DESIRED CONTROL FOR DESIRED LEVEL OF LIMIT (%) CONFIDENCE) 90.0 1.65 95.0 1.96 95.45 2.00 99.0 2.58 99.73 3.00 Copyright © 2017 Pearson Education, Ltd. S6 - 48  FYI Control Charts for Attributes ► For variables that are categorical ► Defective/nondefective, good/bad, yes/no, acceptable/unacceptable ► Measurement is typically counting defectives ► Charts may measure 1. Percent defective (p-chart) 2. Copyright © 2017 Number Pearson Education, Ltd. of defects (c-chart) S6 - 49  FYI Control Limits for p-Charts Population will be a binomial distribution, but applying the central limit theorem allows us to assume a normal distribution for the sample statistics Copyright © 2017 Pearson Education, Ltd. S6 - 50  FYI p-Chart for Data Entry NUMBER NUMBER SAMPLE OF FRACTION SAMPLE OF FRACTION NUMBER ERRORS DEFECTIVE NUMBER ERRORS DEFECTIVE 1 6.06 11 6.06 2 5.05 12 1.01 3 0.00 13 8.08 4 1.01 14 7.07 5 4.04 15 5.05 6 2.02 16 4.04 7 5.05 17 11.11 8 3.03 18 3.03 9 3.03 19 0.00 10 2.02 20 4.04 80 Copyright © 2017 Pearson Education, Ltd. S6 - 51  FYI p-Chart for Data Entry NUMBER NUMBER SAMPLE OF FRACTION SAMPLE OF FRACTION NUMBER ERRORS DEFECTIVE NUMBER ERRORS DEFECTIVE 1 6.06 11 6.06 2 5.05 12 1.01 3 0.00 13 8.08 4 1.01 14 7.07 5 4.04 15 5.05 6 2.02 16 4.04 7 5.05 17 11.11 8 3.03 18 3.03 9 3.03 19 0.00 10 2.02 20 4.04 80 e c annot us ew (bec a ne gative a have defective) nt perce Copyright © 2017 Pearson Education, Ltd. S6 - 52  FYI p-Chart for Data Entry.11 –.10 – UCLp = 0.10.09 – Fraction defective.08 –.07 –.06 –.05 –.04 – p = 0.04.03 –.02 –.01 – LCLp = 0.00.00 – | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 Sample number Copyright © 2017 Pearson Education, Ltd. S6 - 53  FYI p-Chart for Data Entry Possible assignable causes present.11 –.10 – UCLp = 0.10.09 – Fraction defective.08 –.07 –.06 –.05 –.04 – p = 0.04.03 –.02 –.01 – LCLp = 0.00.00 – | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 Sample number Copyright © 2017 Pearson Education, Ltd. S6 - 54  FYI Control Limits for c-Charts Population will be a Poisson distribution, but applying the central limit theorem allows us to assume a normal distribution for the sample statistics Copyright © 2017 Pearson Education, Ltd. S6 - 55  FYI c-Chart for Cab Company UCLc = 13.35 14 – Number defective 12 – 10 – 8 – 6 – c= 6 4 – 2 – LCLc = 0 0 – | | | | | | | | | 1 2 3 4 5 6 7 8 9 be a Cannot mber Day e nu negativ Copyright © 2017 Pearson Education, Ltd. S6 - 56  FYI Managerial Issues and Control Charts Three major management decisions: ► Select points in the processes that need SPC ► Determine the appropriate charting technique ► Set clear and specific SPC policies and procedures Copyright © 2017 Pearson Education, Ltd. S6 - 57  FYI Which Control Chart to Use TABLE S6.3 Helping You Decide Which Control Chart to Use VARIABLE DATA USING AN x-CHART AND R-CHART 1. Observations are variables 2. Collect 20 – 25 samples of n = 4, or n = 5, or more, each from a stable process and compute the mean for the x-chart and range for the R-chart 3. Track samples of n observations Copyright © 2017 Pearson Education, Ltd. S6 - 58  FYI Which Control Chart to Use TABLE S6.3 Helping You Decide Which Control Chart to Use ATTRIBUTE DATA USING A P-CHART 1. Observations are attributes that can be categorized as good or bad (or pass–fail, or functional–broken), that is, in two states 2. We deal with fraction, proportion, or percent defectives 3. There are several samples, with many observations in each ATTRIBUTE DATA USING A C-CHART 1. Observations are attributes whose defects per unit of output can be counted 2. We deal with the number counted, which is a small part of the possible occurrences 3. Defects may be: number of blemishes on a desk; flaws in a bolt of cloth; crimes in a year; broken seats in a stadium; typos in a chapter of this text; or complaints in a day Copyright © 2017 Pearson Education, Ltd. S6 - 59  FYI Patterns in Control Charts Upper control limit Target Lower control limit Normal behavior. Process is "in control." Figure S6.7 Copyright © 2017 Pearson Education, Ltd. S6 - 60  FYI Patterns in Control Charts Upper control limit Target Lower control limit One plot out above (or below). Investigate for cause. Process is "out of control." Figure S6.7 Copyright © 2017 Pearson Education, Ltd. S6 - 61  FYI Patterns in Control Charts Upper control limit Target Lower control limit Trends in either direction, 5 plots. Investigate for cause of progressive change. Figure S6.7 Copyright © 2017 Pearson Education, Ltd. S6 - 62  FYI Patterns in Control Charts Upper control limit Target Lower control limit Two plots very near lower (or upper) control. Investigate for cause. Figure S6.7 Copyright © 2017 Pearson Education, Ltd. S6 - 63  FYI Patterns in Control Charts Upper control limit Target Lower control limit Run of 5 above (or below) central line. Investigate for cause. Figure S6.7 Copyright © 2017 Pearson Education, Ltd. S6 - 64  FYI Patterns in Control Charts Upper control limit Target Lower control limit Erratic behavior. Investigate. Figure S6.7 Copyright © 2017 Pearson Education, Ltd. S6 - 65  FYI Patterns in Control Charts Run test Identify abnormalities in a process Runs of 5 or 6 points above or below the target or centerline suggest assignable causes may be present Process may not be in statistical control There are a variety of run tests Copyright © 2017 Pearson Education, Ltd. S6 - 66  FYI Process Capability ► The natural variation of a process should be small enough to produce products that meet the standards required ► A process in statistical control does not necessarily meet the design specifications ► Process capability is a measure of the relationship between the natural variation of the process and the design specifications Copyright © 2017 Pearson Education, Ltd. S6 - 67  FYI Process Capability Ratio Upper Specification – Lower Specification Cp = 6s ► A capable process must have a Cp of at least 1.0 ► Does not look at how well the process is centered in the specification range ► Often a target value of Cp = 1.33 is used to allow for off-center processes ► Six Sigma quality requires a Cp = 2.0 Copyright © 2017 Pearson Education, Ltd. S6 - 68  FYI Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation s =.516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification Cp = 6s Copyright © 2017 Pearson Education, Ltd. S6 - 69  FYI Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation s =.516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification Cp = 6s 213 – 207 = = 1.938 6(.516) Copyright © 2017 Pearson Education, Ltd. S6 - 70  FYI Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process standard deviation s =.516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification Cp = 6s 213 – 207 Process is = = 1.938 6(.516) capable Copyright © 2017 Pearson Education, Ltd. S6 - 71  FYI Process Capability Index Upper Lower Specification – x x – Specification Cpk = minimum of ,, Limit Limit 3s 3s ► A capable process must have a Cpk of at least 1.0 ► A capable process is not necessarily in the center of the specification, but it falls within the specification limit at both extremes Copyright © 2017 Pearson Education, Ltd. S6 - 72  FYI Process Capability Index New Cutting Machine New process mean x =.250 inches Process standard deviation s =.0005 inches Upper Specification Limit =.251 inches Lower Specification Limit =.249 inches Copyright © 2017 Pearson Education, Ltd. S6 - 73  FYI Process Capability Index New Cutting Machine New process mean x =.250 inches Process standard deviation s =.0005 inches Upper Specification Limit =.251 inches Lower Specification Limit =.249 inches (.251) -.250 Cpk = minimum of , (3).0005 Copyright © 2017 Pearson Education, Ltd. S6 - 74  FYI Process Capability Index New Cutting Machine New process mean x =.250 inches Process standard deviation s =.0005 inches Upper Specification Limit =.251 inches Lower Specification Limit =.249 inches (.251) -.250.250 - (.249) Cpk = minimum of , (3).0005 (3).0005 Copyright © 2017 Pearson Education, Ltd. S6 - 75  FYI Process Capability Index New Cutting Machine New process mean x =.250 inches Process standard deviation s =.0005 inches Upper Specification Limit =.251 inches Lower Specification Limit =.249 inches (.251) -.250.250 - (.249) Cpk = minimum of , (3).0005 (3).0005 Both calculations result in.001 New machine is Cpk = = 0.67.0015 NOT capable Copyright © 2017 Pearson Education, Ltd. S6 - 76  FYI Interpreting Cpk Figure S6.8 Cpk = negative number Cpk = zero Cpk = between 0 and 1 Cpk = 1 Cpk > 1 Lower Upper specification specification limit limit Copyright © 2017 Pearson Education, Ltd. S6 - 77  FYI Acceptance Sampling ► Form of quality testing used for incoming materials or finished goods ► Take samples at random from a lot (shipment) of items ► Inspect each of the items in the sample ► Decide whether to reject the whole lot based on the inspection results ► Only screens lots; does not drive quality improvement efforts Copyright © 2017 Pearson Education, Ltd. S6 - 78  FYI Acceptance Sampling ► Form of quality testing used for incoming materials or finished goods Rejected lots can be: ► Take samples at random from a lot 1. Returned to the (shipment) of items supplier ► Inspect each of the items in the sample 2. Culled for defectives ► Decide whether to reject the whole lot (100% inspection) based on the inspection results 3. May be re-graded to a ► Only screens lots; does notspecification lower drive quality improvement efforts Copyright © 2017 Pearson Education, Ltd. S6 - 79  FYI Operating Characteristic Curve ► Shows how well a sampling plan discriminates between good and bad lots (shipments) ► Shows the relationship between the probability of accepting a lot and its quality level Copyright © 2017 Pearson Education, Ltd. S6 - 80  FYI The "Perfect" OC Curve Keep whole shipment P(Accept Whole Shipment) 100 – 75 – Return whole shipment 50 – Cut-Off 25 – | | | | | | | | | | | 0 – 0 10 20 30 40 50 60 70 80 90 100 % Defective in Lot Copyright © 2017 Pearson Education, Ltd. S6 - 81  FYI An OC Curve Figure S6.9  = 0.05 producer's risk for AQL Probability of Acceptance  = 0.10 | | | | | | | | | Percent 0 1 2 3 4 5 6 7 8 defective Consumer's AQL LTPD risk for LTPD Good Indifference Bad lots lots zone Copyright © 2017 Pearson Education, Ltd. S6 - 82  FYI AQL and LTPD ► Acceptable Quality Level (AQL) ► Poorest level of quality we are willing to accept ► Lot Tolerance Percent Defective (LTPD) ► Quality level we consider bad ► Consumer (buyer) does not want to accept lots with more defects than LTPD Copyright © 2017 Pearson Education, Ltd. S6 - 83  FYI Producer's and Consumer's Risks ► Producer's risk () ► Probability of rejecting a good lot ► Probability of rejecting a lot when the fraction defective is at or above the AQL ► Consumer's risk (b) ► Probability of accepting a bad lot ► Probability of accepting a lot when fraction defective is below the LTPD Copyright © 2017 Pearson Education, Ltd. S6 - 84  FYI OC Curves for Different Sampling Plans n = 50, c = 1 n = 100, c = 2 Copyright © 2017 Pearson Education, Ltd. S6 - 85  FYI Average Outgoing Quality (Pd)(Pa)(N – n) AOQ = N where Pd = true percent defective of the lot Pa = probability of accepting the lot N = number of items in the lot n = number of items in the sample Copyright © 2017 Pearson Education, Ltd. S6 - 86  FYI Average Outgoing Quality 1. If a sampling plan replaces all defectives 2. If we know the true incoming percent defective for the lot We can compute the average outgoing quality (AOQ) in percent defective The maximum AOQ is the highest percent defective or the lowest average quality and is called the average outgoing quality limit (AOQL) Copyright © 2017 Pearson Education, Ltd. S6 - 87  FYI Automated Inspection ► Modern technologies allow virtually 100% inspection at minimal costs ► Not suitable for all situations Copyright © 2017 Pearson Education, Ltd. S6 - 88  FYI SPC and Process Variability Lower Upper specification specification limit limit (a) Acceptance sampling (Some bad units accepted; the "lot" is good or bad) (b) Statistical process control (Keep the process "in control") (c) Cpk > 1 (Design a process that is in within specification) Process mean, m Figure S6.10 Copyright © 2017 Pearson Education, Ltd. S6 - 89  Videos SPC Software in Coca Cola Using Statistical Process Control (SPC) in Chinese Factori es Frito Lay Control Charts Copyright © 2017 Pearson Education, Ltd. S6 - 90