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Chapter 6 - Part 1 Introduction to SPC

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**Proactive approaches to quality**

Design of Experiments Statistical Process Control

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Design of Experiments Tool for designing quality into a product or service at the design before production begins. Quality is designed into product or service by finding the levels of inputs that maximizes customer satisfaction. How should we design a laptop? What battery and processor speed? Longer battery life but slower speed? Faster speed but shorter battery life?

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Design of Experiments When is best room size and color when designing a hotel? In designing a new drink, what carbonation and sugar levels maximize taste? Carbonation and sugar levels that maximizes taste become the ???

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**Example of Designed Experiment**

Sugar and carbonation (factors) are each at two levels High Low Experiment is called a 2 x 2 factorial experiment, where there are two factors, each at two levels.

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**Example of Designed Experiment**

Potential customers rate all possible design combinations. Taste is rated on a scale of 1 to 10, with 10 being best. Are there significant differences between mean taste scores for all pairs of design combinations? Are changes in the mean taste score more sensitive to changes in sugar or carbonation?

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**Factorial Experiment Sugar Carbonation Focus Group 1 Focus Group 2**

Mean Taste Score L 4 6 5.0 H 9 2 5.5 8 8.5 1 4.5

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**Factorial Experiment - graph**

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Carbonation vs. Sugar

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Conclusion Best combination of inputs is Low Sugar High Carbonation At low level of carbonation, an increase in sugar does not appear to result in a statistically significant gain in the mean taste score. If carbonation is a the high level, a decrease in sugar results in a statistically significant gain in the mean taste score. This combination not only maximizes taste, but will lower cost of production if ????

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**Statistical Process Control (SPC)**

Tool for predicting future performance of a process. Main tools of SPC are control charts. Control charts make it possible to detect problems early enough to take corrective action on the process before too many defective units are produced. Control charts are proactive because action is taken on the process, and not on the output, to prevent defects from being produced.

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Control Charts Allow us to detect earlier shifts in the mean and/or variance of the quality characteristic of a product or service. Control charts have an upper control limit (UCL) and a lower control limit (LCL). Control limits are set at 3 standard deviations above and below the estimated mean of the quality characteristic, called the estimated process mean.

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SPC vs. DOE If design of experiments is used to determine target levels, then control charts can be used to determine if process is operating on target. If it is, control charts can be used to detect early shifts from target. If process is not on target, control charts can be used to determine if corrective action to adjust process mean to target is effective.

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Control Charts Control charts rely on sample inspection, not mass inspection. We may take a sample of 5 invoices every day to check for errors, or A sample of 5 bottles of a soft drink each hour to estimate the average number of ounces in a bottle. The samples are used to Estimate the process mean and to Compute the control limits The control limits, the estimated process mean and the means of all the sample means are plotted on the control chart.

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**Control Chart UCL Mean LCL Fraction Defective .50 .40 .30 .20 .10 1 2**

UCL Mean LCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Hour

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Control Charts In addition to detecting shifts in the process mean and/or variation, control charts allow us to determine what sources of variation are in the process. There are two sources of variation: Special causes Random variation (common causes) Random variation always exists in any process. Special causes of variation may or may not exits.

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**Random variation (Common Causes)**

Inherent in any process Due to many causes, each contribution a small amount to the total random variation Occurs within 3 standard deviations of mean (3-sigma limits)

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**Special Causes Not inherent in the process**

Occur when something unusual happens Unusual event can be good or bad If good, make it part of process If bad, eliminate it

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**What Sources of Variation are Present?**

If all the sample means fall randomly within the control limits, the variation between the sample means is due to random causes or variation. If at least one sample mean falls beyond the control limits, the variation is due to special or assignable causes of variation.

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Statistical Control If there are no special causes of variation in the process, the process is said to be in statistical control, or “in control.” Process mean (and/or variance) is stable and hence predictable. The sample means will vary randomly around the unknown process mean.

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**Statistical Control – Stable Process**

Sample number UCL LCL 1 2 3 4 .00135

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**Statistical Control – Stable Process**

Since all the sample means come the same stable distribution, each sample mean is an estimate of the process mean. Rather than using each sample mean as an estimate of the process mean, we can get a better estimate the mean of the process by ???

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Process Out of Control If one or more special causes of variation are present, the process is “out-of-control.” Process behaves erratically It is unstable and no longer predictable. It is therefore impossible to get a good estimate of the process mean.

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**Process in Control UCL Mean LCL**

Hour Sample mean Process in Control All the sample mean fall randomly within the control limits This variation is due to random causes.

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**Process that is Out of Control**

UCL LCL Mean Hour Sample mean Process that is Out of Control All the sample mean fall within the control limits, but pattern is not random. It is a predictable trend. Source of variation is due to a special cause.

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**Process that is Out of Control**

Hour Sample mean UCL LCL Mean Process that is Out of Control All the sample mean fall within the control limits, but pattern is not random. It is a predictable cyclical pattern. Source of variation is due to a special cause.

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Process out of Control UCL LCL Mean Hour One point beyond the control limit. Variation beyond control limits is due to unusual or special (assignable) causes

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**Responsibility for Corrective Action**

Knowing what sources of variation are present in the process allows us to determine who is responsible for taking corrective action to fix or improve the process. Removing or institutionalizing special causes— the worker Reducing random variation – management

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**An Offer You Can’t Refuse**

I claim I have a fair coin—50/50 chance of tossing a head or tail You’re willing to bet $1,000 that I don’t have a fair coin, but you want more data. I agree to toss the coin 100 times, count the number of heads, and repeat this experiment once a day over the next 10 days.

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**The Results Day # of heads 1 57 2 53 3 51 4 58 5 36 6 63 7 55 8 9 39**

10 44

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How Will You Bet? Based on these results, do you think I have a fair coin or a biased coin?

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**Control Chart for # of Heads**

Let P = probability of tossing a head = 0.50 Let n = number of tosses = 100 How many heads would you expect on each toss? What is the standard deviation of the number of heads tossed?

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**Control Chart for # of Heads**

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**Control Chart for # of Heads**

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**Control Charts Based on the control chart, what can you conclude?**

How would you bet? Coin is fair? Coin is not fair?

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Production Example Make up a production example that is analogous to coin tossing experiment by answering the following questions: What do the 100 tosses per day represent? What do the two outcomes, head and tail, represent?

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**Production Example What is the meaning of P = 0.5?**

How can zero defects be achieved?

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**Principle of Rational Subgrouping**

Principle states that we want to select samples to minimize variation within the samples but maximize the variation between. If something unusual is going on, we want it to occur between samples, not within. If it occurs within samples, we may miss it.

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**Violation of Rational Subgrouping**

Day Sample (Diameter) 1 2 3 Mean Monday 5 4 Tuesday 12 18 15 Wednesday 10

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**Conclusion Based on Control Chart**

Control Charts Errors Actual Condition of Process Conclusion Based on Control Chart Process In Control Process Not In Control In Control Correct Type I Error Out of Control Type II Error

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**Type I Error Type I Error-Thinking shift occurred when it didn’t—**

UCL Mean LCL 1 2 3 4 Sample number Type I Error-Thinking shift occurred when it didn’t— false alarm P(Type 1 Error)=2(.00135) =.0027

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**Type II Error Type II Error- Shift occurred but we failed to detect it**

UCL New Mean Mean LCL 1 2 3 4 Sample number Type II Error- Shift occurred but we failed to detect it

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