Quality and Education Business has made progress toward quality over the past several years. But I don’t believe we can truly make quality a way of life … until we make quality a part of every student’s education Edwin Artzt, Chairman and CEO, Proctor & Gamble Co., Quality Progress, October 1992, p. 25

Quality and Competitive Advantage Better price The better customers judge the quality of a product, the more they will pay for it Lower production cost It is cheaper to do a job right the first time than do it over Faster response A company with quality processes for handling orders, producing products, and delivering them can provide fast response to customer requests

Quality and Competitive Advantage Reduced Inventory When the production line runs smoothly with predictable results, inventory levels can be reduced Improved competitive position in the marketplace A customer who is satisfied with quality will tell 8 people about it; a dissatisfied customer will tell 22 (A.V. Feigenbaum, Quality Progress, February 1986, p. 27)

TQM Wheel Customer satisfaction This slide presents the TQM Wheel from page 141. This can be left on the screen while you discuss whatever aspects of the wheel you choose. The Employee Involvement section is presented in more detail on a subsequent slide. 2

Customer-Driven Definitions of Quality Conformance to specifications Conformance to advertised level of performance Value How well the purpose is served at a particular price. For example, if a $2.00 plastic ballpoint pen lasts for six months, one may feel that the purchase was worth the price. These are the five dimensions of quality as listed and defined on page 142. We build on this slide as we advance so each definition can be discussed in depth. Note: This list adds the important element of Value to what is essentially a simplified version of Garvin’s 8 dimensions of quality. 3

Customer-Driven Definitions of Quality Fitness for use Mechanical feature of a product, convenience of a service, appearance, style, durability, reliability, craftsmanship, serviceability Support Financial statements, warranty claims, advertising Psychological Impressions Atmosphere, image, aesthetics “Thanks for shopping at Wal-Mart”

Defectives and Defect In the popular sense, a defect is some characteristic that makes a product unsatisfactory for its intended purpose Technically, a defect is a failure to conform to some specification e.g., 0.140  0.003 in. To avoid ambiguity, following words are suggested Nonconformity or Nonconformance: defect Nonconforming: defective

Quality Costs Prevention costs Customer requirements/expectations market research Product design/development reviews Quality education programs Equipment and preventive maintenance Supplier-rating program administration

Quality Costs Appraisal costs Testing/inspection equipment Inspection costs Audits

Quality Costs Internal failure costs Rework, scrap, repair External failure costs Returned goods, warranty costs, liability costs, penalties Intangible costs Customer dissatisfaction, company image, lost sales, loss of customer goodwill

Process Final testing Customer When defect is detected Costs of Detecting Defects Cost of detection (dollars) Process Final testing Customer When defect is detected

Statistical Quality Control Introduction Control charts and sampling Simple and R charts Variation Common and assignable causes

Control Chart Viewpoint Variation due to Common or chance causes Assignable causes Control chart may be used to discover “assignable causes”

Scientific Sampling Inspection Incoming materials, in-process products, finished goods JIT inventory control makes formal sampling impractical except for quality audit purposes The supplier performs sampling inspection and provides statistical evidence of conformance to specifications 100% inspection may be impractical or uneconomical

Some Terms Run chart - without any upper/lower limits Specification/tolerance limits - not statistical Control limits - statistical

Weakness of Plotting Individual Measurements against Specification/Tolerance Limits If individual measurements are plotted against specification/tolerance limits, following problems may occur If specification/tolerance limits are too wide, the systems may fail to detect some variations that are less likely to be caused by chance and more likely to be caused by some problems in the production system (see Example 1.1) If specification/tolerance limits are too narrow, unavoidable random variations may be considered as defects and too many items may be rejected (see Example 1.2)

Control Charts Take periodic samples from a process Plot the sample points on a control chart Determine if the process is within limits Correct the process before defects occur

Types of Data Variable data Product characteristic that can be measured Length, size, weight, height, time, velocity Attribute data Product characteristic evaluated with a discrete choice Good/bad, yes/no

Process Control Chart Upper control limit Process average Lower 1 2 3 4 5 6 7 8 9 10 Sample number

Constructing a Control Chart Decide what to measure or count Collect the sample data Plot the samples on a control chart Calculate and plot the control limits on the control chart Determine if the data is in-control If non-random variation is present, discard the data (fix the problem) and recalculate the control limits

Control Charts For Variables Mean chart (X-Bar Chart) Measures central tendency of a sample Range chart (R-Chart) Measures amount of dispersion in a sample Each chart measures the process differently. Both the process average and process variability must be in control for the process to be in control. The mean or X-bar chart indicates how sample results relate to the process average or mean. The range or R chart reflects the amount of dispersion that is present in each sample. These charts are normally used together to determine if a process is in control.

Example: Control Charts for Variable Data Slip Ring Diameter (cm) Sample 1 2 3 4 5 X R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 Example4.3

Normal Distribution Review If the diameters are normally distributed with a mean of 5.01 cm and a standard deviation of 0.05 cm, find the probability that the sample means are smaller than 4.98 cm or bigger than 5.02 cm.

Normal Distribution Review If the diameters are normally distributed with a mean of 5.01 cm and a standard deviation of 0.05 cm, find a lower value and an upper value of the sample means such that 97% sample means are between the lower and upper values.

Normal Distribution Review Define the 3-sigma limits for sample means as follows: What is the probability that the sample means will lie outside 3-sigma limits?

Normal Distribution Review Note that the 3-sigma limits for sample means are different from natural tolerances which are at

Constructing a Range Chart Note: The control limits are only preliminary with 10 samples. It is desirable to have at least 25 samples.

Constructing A Mean Chart

3-Sigma Control Chart Factors Sample size X-chart R-chart n A2 D3 D4 2 1.88 0 3.27 3 1.02 0 2.57 4 0.73 0 2.28 5 0.58 0 2.11 6 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86

Common Causes The first set of slides presents the various aspects of common and assignable causes. This slide and the two following show a normal process distribution and how it allows for expected variability which is termed common causes. 2

Assignable Causes (a) Mean Average Grams The new distribution will look as shown in this slide. Grams (a) Mean 7

Assignable Causes (b) Spread Average Grams The new distribution has a much greater spread (higher standard deviation). Grams (b) Spread 9

Assignable Causes (c) Shape Average Grams A skewed (non-normal) distribution will result in a different pattern of variability. Grams (c) Shape 11

The Normal Distribution  = Standard deviation Mean -3 -2 -1 +1 +2 +3 Mean 68.26% 95.44% 99.74%  = Standard deviation And at +/- 3 sigma, the most common choice of confidence/control limits in quality control application, the area is 99.97%. 20

Control Charts Assignable causes likely UCL Nominal LCL 1 2 3 Samples However, the third sample plots outside the original distribution, indicating the likely presence of an assignable cause. LCL 1 2 3 Samples 24

Control Chart Examples UCL Nominal Variations LCL And finally, this chart shows a process with two points actually outside the control limits, an easy indicator to detect but not the only one. These rules, there are a few more, are commonly referred to as the Western Electric Rules and can be found in any advanced quality reference. Sample number 30

Control Limits and Errors Type I error: Probability of searching for a cause when none exists UCL Process average As long as the area encompassed by the control limits is less than 100% of the area under the distribution, there will be a probability of a Type I error. A Type I error occurs when it is concluded that a process is out of control when in fact pure randomness is present. Given +/- 3 sigma, the probability of a Type I error is 1 - 0.9997 = 0.0003, a very small probability. LCL (a) Three-sigma limits 32

Control Limits and Errors Type I error: Probability of searching for a cause when none exists UCL Process average When the control limits are changed to +/- 2 sigma, the probability of a Type I error goes up considerably, from 0.0003 to 1 - 0.9544 = 0.0456. While this is still a small probability, it is a change that should be carefully considered. In practice, this would mean more samples would be identified inappropriately as out-of-control. Even if they were subsequently ‘Okd’, there would be increased costs due to many more cycles through the four step improvement process shown previously. LCL (b) Two-sigma limits 33

Control Limits and Errors Type II error: Probability of concluding that nothing has changed UCL Shift in process average Process average Returning to the 3 sigma limits, we can see the probability of making a Type II error, in this case failing to detect a shift in the process mean. LCL (a) Three-sigma limits 34

Control Limits and Errors Type II error: Probability of concluding that nothing has changed UCL Shift in process average Process average By reducing the control limits to +/- 2 sigma, we see the probability of failing to detect the shift has been reduced. LCL (b) Two-sigma limits 35

Process Capability Range of natural variability in process Measured with control charts Process cannot meet specifications if natural variability exceeds tolerances 3-sigma quality specifications equal the process control limits. 6-sigma quality specifications twice as large as control limits

Process Capability Natural Natural control Design control limits specs Process can meet specifications Process cannot meet specifications Natural control limits Design specs PROCESS Process capability exceeds specifications

Process Capability If the R chart shows control, estimate the standard deviation of items as If the R chart does not show control, remove the ones that showed lack of control, calculate a revised and new control limits for R. Repeat the process as long as it is needed. Estimate standard deviation of items as shown above. Process capability

Process Capability By computing we can conclude whether the mean has shifted towards upper/lower specification limit and if it has shifted at all. If both the numbers are equal, the mean is at the center. If the first number is smaller, the mean has shifted towards LSLx. If the second number is smaller, the mean has shifted towards USLx. If then the process is capable of producing 99.74% items within the specification limits. Else, either the process needs improvement or the specification limits must be widened.

Text Exercise 2.2: Is the following process capable?:

Reading and Exercises Chapter 1: pp. 3-24 Chapter 2: pp. 37-54 Problems 2.5, 2.6, 2.10