LAB 8 - Purdue University



LAB 8 INSTRUCTIONS FOR EXCEL 2003

XBAR AND RANGE CONTROL CHARTS

FOR PROCESS WITH SIGMA UNKNOWN

NAME_____________________LAB TIME________LAB BLDG_______________

1. Xbar and Range control charts are used in many process control applications.

2. In this lab we will start with data on a process where the customer’s desired dimension is 140-146 mm, and therefore the target dimension is 143mm.

3. For each sample, three parts are selected from recent production. The diameter of each part is measured and recorded.

4. Open the Lab8Data file. You will see data for 30 samples of size = 3.

CALCULATE MEAN AND RANGE FOR EACH SAMPLE

5. In F2 calculate the sample mean for the first sample. Copy this calculation down to obtain the sample means for all 30 samples.

6. In G2 calculate the sample range for the first sample. Enter =MAX(B2:D2)-MIN(B2:D2). Copy this calculation down for all 30 samples.

7. In F33 calculate the overall mean of the sample means. XBARBAR = _________

8. In G33 calculate the overall mean of the sample ranges. RBAR = _________

CALCULATE CONTROL LIMITS FOR XBAR CHART

9. The UCL = TARGET + A2 * RBAR. When n=3, A2 = 1.023 UCL = _________

The CL = TARGET CL = _________

The LCL = TARGET - A2 * RBAR LCL = _________

10. In I2, enter = 143 + 1.023 * G33

In J2, enter = 143

In K2, enter = 143 – 1.023 * G33

11. Copy the VALUES in I2:K2 (Not the formulas) down through line 31 using:

Copy>Paste Special>Values. The values should be the same on every row.

CALCULATE CONTROL LIMITS FOR RANGE CHART

12. The UCL = D4 * RBAR When n=3, D4 = 2.574 UCL = _________

The CL = RBAR CL = _________

The LCL = D3 * RBAR When n=3, D3 = 0 LCL = _________

13. In M2 enter = 2.574 * G33

In N2 enter = G33

In O2 enter = 0

14. Copy the VALUES in M2:O2 (Not the formulas) down through line 31 using:

Copy>Paste Special>Values. The values should be the same on every row.

CONSTRUCT THE XBAR CHART

15. Hold the Ctrl key down and highlight A1:A31, F1:F31, I1:I31, J1:J31, K1:K31

16. Go to the Chart Wizard, select XY (Scatter), select the type with the points connected by straight lines, next, next, enter title “XBAR CHART FOR DIAMETER”, enter label for X axis “ SAMPLE NUMBER”, enter label for Y axis “SAMPLE MEAN”, next, and put the chart in the worksheet.

CONSTRUCT THE RANGE CHART

17. Hold the Ctrl key down and highlight columns A, G, M, N, O from row1 through row 31.

18. Go the Chart Wizard, select XY(Scatter), select the type with the points connected by straight lines, next, next, enter title “RANGE CHART FOR DIAMETER”, enter label for X axis “SAMPLE NUMBER”, enter label for Y axis “SAMPLE RANGE”, next, and put the chart in the worksheet.

19. Print the XBAR and RANGE charts to turn in with this instruction/question sheet.

20. Save your file.

INTERPRET THE CONTROL CHARTS

21. Rule 1: Any point on either chart which is outside the control limits is evidence that the process is affected by Special Cause variation, and is “out of control”.

22. Rule 2: A ”run” of 9 consecutive points on the same side of the centerline on any chart is evidence that the process is affected by Special Cause variation and is “out of control”.

23. Rule 3: A “trend” of 7 consecutive points either ascending or descending on any chart is evidence that the process is affected by Special Cause variation and is “out of control”.

24. List the “out of control” signals on the lines below:

|Sample Number |Chart Type |Rule Violated |

| | | |

| | | |

| | | |

| | | |

| | | |

| | | |

PROCESS CAPABILITY, CALCULATION OF Cp AND Cpk

25. Estimate process standard deviation σ from formula σ = RBAR / d2. For a sample size = 3, d2 = 1.693. Technically, we should have an RBAR which does not include any out-of-control values. If we recalculate RBAR for samples 13 through 30 we get RBAR = 1.4211. Use this value for the estimate of σ.

Estimate of σ = _________________

26. The customer’s tolerance for the diameter = 140 – 146.

27. Calculate Cp using the formula: Cp = (cust max – cust min) / 6σ

Cp = ______________________________

28. Cpk cannot be calculated because there has not been a long run (at least 20 samples) under stable conditions. However, lets pretend that the manufacturer has no more out-of-control conditions and that the XBARBAR since the last out-of-control signal = 142.5. Calculate the value of Cpk using this value of XBARBAR.

Cpk = (The distance between XBARBAR and nearest specification limit) / 3 σ.

The numerator should be a positive number so that Cpk comes out +.

Cpk = ___________________

Will this value of Cpk satisfy the customer?________________

29. What would Cpk be if the process mean, XBARBAR, is raised to 143.0?

______________________

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