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ISEN 220 Introduction to Production and Manufacturing Systems Dr. Gary Gaukler

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6 – 2 Quality and Profit Profit = Revenue – Cost Quality impacts on the revenue side: Quality impacts on the cost side:

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6 – 3 3 Defining Quality The totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs American Society for Quality

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6 – 4 4 Costs of Quality Prevention costs - reducing the potential for defects Appraisal costs - evaluating products, parts, and services Internal failure - producing defective parts or service before delivery External costs - defects discovered after delivery

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6 – 5 5 Costs of Quality There is a tradeoff between the costs of improving quality, and the costs of poor quality Philip Crosby (1979): “Quality is free”

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6 – 6 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 Issues When to inspect Where in process to inspect

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6 – 7 7 Inspection Many problems Worker fatigue Measurement error Process variability Cannot inspect quality into a product Robust design, empowered employees, and sound processes are better solutions

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6 – 8 8 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

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6 – 9 9 An SPC Chart Upper control limit Coach’s target value Lower control limit Game number |||||||||123456789|||||||||123456789 20% 10% 0% Plots the percent of free throws missed Figure 6.7

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6 – 10 10 Control Charts Constructed from historical data, the purpose of control charts is to help distinguish between natural variations and variations due to assignable causes

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6 – 11 11 Variability is inherent in every process Natural or common causes Special or assignable causes Provides a statistical signal when assignable causes are present Detect and eliminate assignable causes of variation Statistical Process Control (SPC)

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6 – 12 12 Natural Variations Also called common causes Affect virtually all production processes Expected amount of variation Output measures follow a probability distribution For any distribution there is a measure of central tendency and dispersion If the distribution of outputs falls within acceptable limits, the process is said to be “in control”

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6 – 13 13 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 Eliminate the bad causes Incorporate the good causes

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6 – 14 14 Samples To measure the process, we take samples and analyze the sample statistics following these steps (a)Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight Frequency Weight # ## # ## ## # ### #### ######### # Each of these represents one sample of five boxes of cereal Figure S6.1

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6 – 15 15 Samples To measure the process, we take samples and analyze the sample statistics following these steps (b)After enough samples are taken from a stable process, they form a pattern called a distribution The solid line represents the distribution Frequency Weight Figure S6.1

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6 – 16 16 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 Weight Central tendency Weight Variation Weight Shape Frequency Figure S6.1

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6 – 17 17 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 is stable over time and is predictable Weight Time Frequency Prediction Figure S6.1

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6 – 18 18 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 Weight Time Frequency Prediction ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Figure S6.1

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6 – 19 19 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 (x) will be the same as the population mean x = n x = 2.The standard deviation of the sampling distribution ( x ) will equal the population standard deviation ( ) divided by the square root of the sample size, n

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6 – 20 20 Population and Sampling Distributions Three population distributions Beta Normal Uniform Distribution of sample means Standard deviation of the sample means = x = n Mean of sample means = x |||||||-3x-2x-1xx+1x+2x+3x|||||||-3x-2x-1xx+1x+2x+3x 99.73% of all x fall within ± 3 x 95.45% fall within ± 2 x Figure S6.3

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6 – 21 21 Control Charts for Variables For variables that have continuous dimensions Weight, speed, length, strength, etc. x-charts are to control the central tendency of the process R-charts are to control the dispersion of the process These two charts must be used together

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6 – 22 22 Setting Chart Limits For x-Charts when we know Upper control limit (UCL) = x + z x Lower control limit (LCL) = x - z x wherex=mean of the sample means or a target value set for the process z=number of normal standard deviations x =standard deviation of the sample means = / n =population standard deviation n=sample size

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6 – 23 23 Setting Control Limits Hour 1 BoxWeight of NumberOat Flakes 117 213 316 418 517 616 715 817 916 Mean16.1 =1 HourMeanHourMean 116.1715.2 216.8816.4 315.5916.3 416.51014.8 516.51114.2 616.41217.3 n = 9 LCL x = x - z x = 16 - 3(1/3) = 15 ozs For 99.73% control limits, z = 3 UCL x = x + z x = 16 + 3(1/3) = 17 ozs

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6 – 24 24 17 = UCL 15 = LCL 16 = Mean Setting Control Limits Control Chart for sample of 9 boxes Sample number |||||||||||| 123456789101112 Variation due to assignable causes Variation due to natural causes Out of control

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6 – 25 25 Setting Chart Limits For x-Charts when we don’t know Lower control limit (LCL) = x - A 2 R Upper control limit (UCL) = x + A 2 R whereR=average range of the samples A 2 =control chart factor found in Table S6.1 x=mean of the sample means

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6 – 26 26 Control Chart Factors Table S6.1 Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D 3 21.8803.2680 31.0232.5740 4.7292.2820 5.5772.1150 6.4832.0040 7.4191.9240.076 8.3731.8640.136 9.3371.8160.184 10.3081.7770.223 12.2661.7160.284

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6 – 27 27 Setting Control Limits Process average x = 16.01 ounces Average range R =.25 Sample size n = 5

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6 – 28 28 Setting Control Limits UCL x = x + A 2 R = 16.01 + (.577)(.25) = 16.01 +.144 = 16.154 ounces LCL x = x - A 2 R = 16.01 -.144 = 15.866 ounces Process average x = 16.01 ounces Average range R =.25 Sample size n = 5 UCL = 16.154 Mean = 16.01 LCL = 15.866

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Statistical Process Control

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