Quality control tool afor process capabilities

Control charts and its uses

1. STATISTICAL QUALITY CONTROL PROBLEMS

2. X-bar chart: The mean or average change in process over time from subgroup values. The control limits on the X-Bar brings the sample’s mean and center into consideration. R-chart: The range of the process over the time from subgroups values. This monitors the spread of the process over the time.

3. Use X Bar R Control Charts When: Even very stable process may have some minor variations, which will cause the process instability. X bar R chart will help to identify the process variation over the time When the data is assumed to be  normally distributed. X bar R chart is for subgroup size more than one (for  I-MR chart  the subgroup size is one only) and generally it is used when rationally collect measurements in subgroup size is between two and 10 observations. The X Bar S Control chart  are to be consider when the subgroup size is more than 10. When the collected data is in continuous ( ie Length, Weight) etc. and captures in time order

4. Control chart constants

5. Control chart

6. Procedure Calculate the average R value, or R-bar, and plot this value as the centerline on the R chart. Based on the subgroup size, select the appropriate constant, called D4, and multiply by R-bar to determine the Upper Control Limit for the Range Chart. All constants are available from the reference table. UCL (R) = R-bar x D4

7. Procedure If the subgroup size is between 7 and 10, select the appropriate constant, called D3, and multiply by R-bar to determine the Lower Control Limit for the Range Chart. There is no Lower Control Limit for the Range Chart if the subgroup size is 6 or less. LCL(R) = R-bar x D3

8. Procedure Using the X-bar values for each subgroup, compute the average of all Xbars , or X-bar-bar (also called the Grand Average). Plot the X-bar-bar value as the centerline on the X Chart Calculate the X-bar Chart Upper Control Limit, or upper natural process limit, by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and adding that value to the average (X-bar-bar). UCL (X-bar) = X-bar-bar + (A2 x R-bar)

9. Procedure Calculate the X-bar Chart Lower Control Limit, or lower natural process limit, for the X-bar chart by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and subtracting that value from the average (X- barbar ). LCL(X-bar) = X-bar-bar - (A2 x R-bar) Plot the Lower Control Limit on the X-bar chart.

10. Problem 1 Calculate the 3ϭ control limits for X-bar and R charts based on the first 12 samples reflecting the process before any problems were denounced.

11. Solution

12. Solution

13. Problem 1 -Continue Plot X-bar and R charts labeling the data points, upper and lower control limits, and center lines on both charts. Plot the means/ranges of all 18 samples, but use the control limits and center lines calculated for the first 12 samples

14. Problem 1 -Continue Do you feel that the screw production process is in control? Is there something suspicious? The graphs confirm that the customers complaints are justified – it really seems as if the variation in the screw diameters has increased significantly. The R-chart suggests significant differences even within single samples! Clearly some corrective measures have to be taken to bring this process back under control!

15. Problem 2 Calculate the 3ϭ control limits for the supplier’s manufacturing process based on the first 15 weeks (i.e. weeks 1-15, when the quality of the alloy did not seem to be an issue).

16. Problem 2

17. Problem 2 -Continue Create the SPC chart including the weekly data, control limits, and the center line. Plot the defective fractions of all 20 weeks, but use the control limits and the center line of the first 15 weeks!! Interpret the chart – what does it suggest?

18. Solution

19. Inference from chart Clearly there is an upward tendency in the fraction of defective packages of alloy. Even though the problem was not noticed before week 15, it seems as if this process started already in week 9. The magnitude of the fluctuations is not as alarming as is the steady upward tendency. Even though only the very last weeks reveal defective fractions outside the control limits, the graph gives the impression that the fractions will keep on increasing in future. Whatever the reasons for this increase might be, it leads to severe quality problems of Screwed’s final products and cannot be accepted. Definitely this problem should be looked into more carefully …

20. Problem 3 Calculate UCLr , LCLr , UCLx , and LCLx using the following expressions:

21. Solution

22. Solution The process is not in control because the sample mean for sample 4 (in the X-bar graph) falls outside the control limits.

23. np chart is one of the quality control charts is used to assess trends and patterns in counts of binary events (e.g., pass, fail) over time . np chart requires that the sample size of the each subgroup be the same and compute control limits based on the  binomial distribution.

24. Control charts for attribute data u chart  is for the number of defects per unit   c chart  is for the number of defects . p chart plots the proportion of defective items. The np chart reflects integer numbers rather than proportions. The applications of np chart are basically the same as the applications for the p chart .

25. Control chart for attributes

26. Assumptions of Attribute charts: np chart The probability of non-conformance is the same for each item There should be two events (pass or fail), and they are mutually exclusive Each unit is independent of the other The testing procedure should be the same for each lot

27. np chart

28. Problem 4 Smartbulbs Inc is a famous LED bulb manufacturer. Supervisor drawn randomly constant sample size of 200 bulbs every hour and reported the number of defective bulbs for each lot. Based on the given data, prepare the control chart for the number of defectives and determine process is in statistical control?

29. Problem 4

30. Solution no of lots k = 20 Σnp = 105 Σn = 4000 Compute p̅ = total number of defectives / total number of samples = Σnp / Σn =105/4000= 0.0263 1- p̅ = 0.9738 Calculate centreline np ̅ = total number of defectives/no of lots = Σnp /k =105/20 = 5.3

31. Solution

32. C Chart c chart is also known as the control chart for defects (counting of the number of defects). It is generally used to monitor the number of defects in constant size units. There may be a single type of defect or several different types, but the c chart tracks the total number of defects in each unit and it assumes the underlying data approximate the Poisson distribution . The unit may be a single item or a specified section of items—for example, scratches on plated metal, number of insufficient soldering in a printed circuit board.

33. C Chart

34. C Chart

35. How do you Create a C Chart Determine the  subgroup size . The subgroup size must be large enough for the c chart; otherwise, control limits may not be accurate when estimated from the data.   Count the number of defects in each sample Compute centreline c̅ = total number of defects / number of samples = Σc /k Calculate upper control limit (UCL) and low control limit (LCL). If LCL is negative, then consider it as 0. Plot the graph with number of defects on the y-axis, lots on the x-axis: Draw centerline , UCL and LCL. Use these limits to monitor the number of defects going forward. Finally, interpret the data to determine whether the process is in control.

36. Problem Mobile charger supplier drawn randomly constant sample size of 500 chargers every day for quality control test. Defects in each charger are recorded during testing. Based on the given data, draw the appropriate control chart and comment on the state of control.