1. Quality Control Ross L. Fink

2. Quality Control n Quality control involves controlling the delivery processes to adhere to the specifications (or product design).

3. Quality Control Approaches n 100 % Inspection n Acceptance Sampling n Statistical Process Control (SPC) or Control-Chart Method

4. Acceptance Sampling Accept or Reject Entire Lot Based Upon Quality of Sample

5. Statistical Process Control n Basic Approach – Take one sample of size 5 each hour – Measure quality characteristic – Plot measurement over time (sample number)

6. Run Chart

7. Distribution of Measurement on Control Chart n Since we are taking a mean, the Central Limit Theorem of the Sample Mean applies n Therefore, mean follows a normal distribution. n Three Sigma Limits

8. Plot of Mean

9. Theory of Control Charts n Purpose of control charts is to separate natural variability (common cause) from nonrandom variability (assignable cause). n In-control (common cause) versus out-of- control (assignable cause).

10. Types of Variability

11. X-bar Chart

12. Control Chart Rules n Simple Rules – One point above UCL – One point below LCL n Most organizations use more complex rules – e.g., seven consecutive points increasing

13. Constructing a Control Chart n Obs. 1 2 3 4 5 n Sample n 111.6314.4414.5217.5812.71 n 213.3016.2115.0416.0914.19 n 312.6011.4914.7315.5817.41 n 413.6813.4913.2416.9816.23 n 515.1215.2111.6914.9116.36 n 615.7016.0916.7815.4814.56 n 713.4614.2817.0913.8415.85 n 814.2213.9014.4715.1819.31 n 912.4415.1216.0014.6216.05 n 1014.0414.8819.2614.3716.35 n 1112.4213.2515.5615.1814.13 n 1215.6512.9416.1615.9818.67 n 1315.7113.7814.1916.0213.78 n 1414.8012.1716.0012.9312.34 n 1515.6312.1414.9816.6114.21 n 1610.1315.4317.0917.7218.72 n 1713.7315.2613.5314.4315.22 n 1811.4417.0013.7213.1113.80 n 1910.7210.1215.8019.7211.72 n 2015.4315.0015.5814.9915.40

14. Find Sample Means and Ranges n Obs. 1 2 3 4 5 Mean Range n Sample n 111.6314.4414.5217.5812.7114.185.95 n 213.3016.2115.0416.0914.1914.962.93 n 312.6011.4914.7315.5817.4114.365.92 n 413.6813.4913.2416.9816.2314.723.75 n 515.1215.2111.6914.9116.3614.664.67 n 615.7016.0916.7815.4814.5615.722.22 n 713.4614.2817.0913.8415.8514.903.63 n 814.2213.9014.4715.1819.3115.425.39 n 912.4415.1216.0014.6216.0514.853.62 n 1014.0414.8819.2614.3716.3515.785.22 n 1112.4213.2515.5615.1814.1314.113.14 n 1215.6512.9416.1615.9818.6715.885.72 n 1315.7113.7814.1916.0213.7814.702.23 n 1414.8012.1716.0012.9312.3413.653.83 n 1515.6312.1414.9816.6114.2114.714.47 n 1610.1315.4317.0917.7218.7215.828.59 n 1713.7315.2613.5314.4315.2214.431.73 n 1811.4417.0013.7213.1113.8013.815.56 n 1910.7210.1215.8019.7211.7213.619.60 n 2015.4315.0015.5814.9915.4015.280.59

15. Calculate Grand Mean and Grand Range

16. Control Limits

17. Table n Factors for Computing Control Chart Limits n Sample SizeMean FactorUpper RangeLower Range – N A2D4D3 – 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

18. Control Limits

19. X-bar Chart

20. R Chart

21. In-Control v. Out-Of-Control n What are the implications of being in- control? n What are the implications of being out-of- control?