TM 720: Statistical Process Control IENG 451 - Lecture 04 Quality Matters: Cost of Quality, Yield and Variance Reduction 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Quality is a multifaceted entity. TM 720: Statistical Process Control Quality is a multifaceted entity. Traditional (OLD) definition of Quality: Fitness for Use (i.e., products must meet requirements of those who use them.) 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Two Aspects of “Fitness for Use” TM 720: Statistical Process Control Two Aspects of “Fitness for Use” Quality of Design – all products intentionally made in various grades of quality. (e.g., Autos differ with respect to size, options, speed, etc.) Quality of Conformance – how well the product conforms to specifications. (e.g., If diameter of a drilled hole is within specifications then it has good quality.) 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

What's Wrong with "Fitness for Use" Definition of Quality? TM 720: Statistical Process Control What's Wrong with "Fitness for Use" Definition of Quality? Unfortunately, quality as “Fitness for Use” has become associated with the "conformance to specifications" regardless of whether or not the product is fit for use by customer. Common Misconception: Quality can be dealt with solely in manufacturing - that is, by "gold plating" the product 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Cost of Quality Myth: Higher Quality  Higher Cost TM 720: Statistical Process Control Cost of Quality Myth: Higher Quality  Higher Cost $ Defect Rate Quality Cost Total Cost Failure Cost 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Reduction of Variability TM 720: Statistical Process Control Reduction of Variability Modern Definition of Quality: Quality is inversely proportional to variability If variability of product decreases  quality of product increases Quality Improvement – Reduction of variability in processes and products 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Cost of (Poor) Quality: Higher Quality  Lower Cost TM 720: Statistical Process Control Cost of (Poor) Quality: Higher Quality  Lower Cost Example: Manufacture of Copier Part Manufacturing Process $20 / part 75% Conform 100 parts (75 good parts) 25% Non-conforming: (10 scrap parts) (25 parts) Re-work Process $4 / part (15 good parts)   1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Study finds excessive process variability causes high defect rate TM 720: Statistical Process Control Study finds excessive process variability causes high defect rate New process implemented NOW: manufacturing non-conformities = 5% SAVINGS: $22.89 – $20.53 = $2.36 / good part PRODUCTIVITY: 9% improvement   1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

Understanding Process Variation Three Aspects: Location Spread Shape Independence: changing Location does not impact Spread Frequently, the CLT lets us use Normal Curve 1/17/2019 IENG 451 Operational Strategies

IENG 451 Operational Strategies Shape: Distributions Distributions quantify the probability of an event Events near the mean are most likely to occur, events further away are less likely to be observed 35.0  2.5 30.4 (-3) 34.8 (-) 39.2 (+) 43.6 (+3) 32.6 (-2) 37 () 41.4 (+2) 1/17/2019 IENG 451 Operational Strategies

Standard Normal Distribution The Standard Normal Distribution has a mean () of 0 and a standard deviation () of 1 Total area under the curve, (z), from z = – to z =  is exactly 1 ( -or- 100% of the observations) The curve is symmetric about the mean Half of the total area lays on either side, so: (– z) = 1 – (z) (z) z  1/17/2019 IENG 451 Operational Strategies

Standard Normal Distribution How likely is it that we would observe a data point more than 2.57 standard deviations beyond the mean? Area under the curve from – to z = 2.5  is found by using the Standard Normal table, looking up the cumulative area for z = 2.57, and then subtracting the cumulative area from 1. (z) z  1/17/2019 IENG 451 Operational Strategies

IENG 451 Operational Strategies 1/17/2019 IENG 451 Operational Strategies

Standard Normal Distribution How likely is it that we would observe a data point more than 2.57 standard deviations beyond the mean? Area under the curve from – to z = 2.5  is found by using the table on pp. 716-717, looking up the cumulative area for z = 2.57, and then subtracting the cumulative area from 1. Answer: 1 – .99492 = .00508, or about 5 times in 1000 (z) z  1/17/2019 IENG 451 Operational Strategies

What if the distribution isn’t a Standard Normal Distribution? If it is from any Normal Distribution, we can express the difference from an observation to the mean in units of the standard deviation, and this converts it to a Standard Normal Distribution. Conversion formula is: where: x is the point in the interval,  is the population mean, and  is the population standard deviation. 1/17/2019 IENG 451 Operational Strategies

Example: Process Yield Specifications are often set irrespective of process distribution, but if we understand our process we can estimate yield / defects. Assume a specification calls for a value of 35.0  2.5. Assume the process has a distribution that is Normally distributed, with a mean of 37.0 and a standard deviation of 2.20. Estimate the proportion of the process output that will meet specifications. 1/17/2019 IENG 451 Operational Strategies

TM 720: Statistical Process Control Six Sigma - Motorola Six Sigma* = 3.4 defects per million opportunities! ± 6 standard deviations – after a 1.5 sigma shift! Every Motorola employee must show bottom line results of quality project – finance, mail room, manufacturing, etc. identify problem; develop measurement; set goal; close gap Long term process – 5 years to fully implement 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Questions & Issues There WILL be a lab tomorrow: It is a follow-on from last week, covering process improvement Variation effects Cost of (poor) Quality 1/17/2019 IENG 451 Operational Strategies (c) 2002-2006 D.H. Jensen & R.C. Wurl