1. Quality Control Chapter 6

2. Transformation Process Inputs Facilities Equipment Materials Energy Outputs Goods & Services Variation in inputs create variation in outputs Variations in the transformation process create variation in outputs

3. Variation All processes have variation. Common cause variation is random variation that is always present in a process. A ssignable cause variation results from changes in the inputs or the process. The cause can and should be identified. A process is in control if it has no assignable cause variation. The process is consistent

4. Statistical Process Control (SPC) Distinguishes between common cause and assignable cause variation Measure characteristics of goods or services that are important to customers Make a control chart for each characteristic The chart is used to determine whether the process is in control

5. Capability and Conformance Quality (1) A process is capable if It is in control and It consistently produces outputs that meet specifications. A capable process produces outputs that have conformance quality (outputs that meet specifications).

6. Capable Transformation Process Inputs Facilities Equipment Materials Energy Outputs Goods & Services that meet specifications

7. Capability and Conformance Quality (2) If the process is capable and the product specification is based on current customer requirements, outputs will meet customer expectations.

8. Customer Satisfaction Capable Transformation Process + Product specification that meets current customer requirements = Customer satisfaction

9. Objectives of SPC To determine if the process is in control (predictable) To determine if the process is capable (in control and meets specifications)

10. Variable Measures Continuous random variables Measure does not have to be a whole number. Examples: time, weight, miles per gallon, length, diameter

11. Attribute Measures Discrete random variables – finite number of possibilities Also called categorical variables Different types of control charts are used for variable and attribute measures

12. Examples of Attribute Measures Good/bad evaluations Good or defective Correct or incorrect Number of defects per unit Number of scratches on a table Opinion surveys of quality Customer satisfaction surveys Teacher evaluations

13. Descriptive Statistics Describe Results from a Random Sample The Mean- measure of central tendency The Range- difference between largest/smallest observations in a set of data Standard Deviation measures the amount of data dispersion around mean

14. Distribution of Data Normal distributions Skewed distribution

15. Random samples are taken from process output A process characteristic is measured Sample means are plotted Control limits are based on a confidence interval for the mean CL = center line (mean line) LCL = lower control limitUCL = upper control limit Control chart for the mean of a product characteristic

16. Percentage of values under normal curve  = population mean  = population standard deviation 95.4% of the population is within 2  of the mean 99.74% of the population is within 3  of the mean 99.74% of the population is within the interval from  3  to  3  We will compute 3  confidence intervals for sample means

17. X-bar Chart

18. R Chart

19. Interpreting Control Charts for Variables Use x-bar and R charts together x-bar chart monitors the mean R charts monitors dispersion

20. Specification Limits The target is the ideal value Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces Specification limits are the acceptable range of values for a variable Example: the amount of beverage in a bottle must be at least 15.8 ounces and no more than 16.2 ounces. Range is 15.8 – 16.2 ounces. Lower specification limit = 15.8 ounces or LSPEC = 15.8 ounces Upper specification limit = 16.2 ounces or USPEC = 16.2 ounces

21. Test for Process Capability (with respect to x ) The process is in control with respect to x AND The control limits (LCL and UCL) for x are within the specification limits Capability index, C pk is used to determine whether a process is capable

22. Process is Capable UCL LCL X Lower specification limit Upper specification limit

23. Process is Not Capable UCL LCL X Lower specification limit Upper specification limit UCL outside specification limits  not capable

24. C pk Index   = process mean (or estimated mean)  LSPEC = lower specification limit  USPEC = upper specification limit C pk = Smaller {(USPEC-  )/3  – LSPEC)/ 3  } If C pk >= 1, process meets customer requirements 99.74% of the time. To allow for changes in the mean, many firms set a requirement that C pk >= 1.33.

25. 3-Sigma Quality Uses 3  control limits for x  Corresponds to 3 defects per 1,000 units. If a product has 250 parts and each has 3  control limits, P[at least 1 bad part] = 0.528

26. 6-Sigma Quality Use 6-  control limits for x. Control limits are (X- 2A 2 R, X + 2A 2 R). Corresponds to 3.4 defects per million If a product has 250 parts and each has 6  control limits, P[at least 1 bad part] <0.001