Question

Part 1: WT Corp. manufactures crankshafts for 2L automotive engines. In order to attach a crankshaft to a flywheel, six holes are drilled in the flange end of the crankshaft. These holes are to be drilled 0.4750” in diameter. The holes are not threaded and go all the way through the flange. (See Figure 1.)

All six holes are drilled simultaneously. Every hour, the operator inspects four crank shafts resulting from four consecutive cycles of the drill press. All six holes on each of the four crankshafts are measured and the values are recorded. (See Table 1)

In this case each crank represents a sample. There are 6 measurements for each sample represented by the individual holes.  

Use the data in Table 1 to calculate x-bar and R values for the crank shafts. Make x-bar and R charts using the data. This should result in 2 charts with 48 points on them. Label the charts carefully. The use of Microsoft Excel is highly suggested as this data will be used more than once during this three part exercise. You may also use Minitab. Make sure you use the Line chart option.

Questions:

1. What do the charts say about the process?

2. Are there any out of control conditions?

3. In your opinion, is this the correct way to use a control chart? Why or why not?

Case Study: Use of Data for Control Charts

Part 2:

After shipping this group of crankshafts, you receive a call from your customer. They are very disturbed. Apparently, the crankshafts are not the quality expected. The customer feels that the hole diameters on each crank are not consistent. You point out that the process is under control, as verified by the control charts. In response, your customer suggests you take another look at the data.

After taking a close look at how the data is organized, you discover a small but significant point. The range chart indicates a fairly wide range of values for each subgroup. (This R chart is designed to monitor within subgroup measurements.) You realize that the average diameter is based upon the sum of the diameters found on each crankshaft. The charts do describe crankshaft to crankshaft variation, however, each of the holes is drilled using a different tool. To truly monitor the process, each tool must be monitored separately.

To measure the tool to tool variation, the data must be arranged differently. Recreate the control charts using the method indicated below to find the average and range of the data. This should result in 2 charts with 72 points each.

HOUR 1

                        Crank

Hole       1          2          3          4                   Ave.    R

1        4751    4752    4750    4750                4751    2

2        4752    4751    4750    4752                4751    2

3        4747    4752    4751    4749                4750    5

4        4745    4745    4741    4745                4744    4

5        4752    4751    4750    4752                4751    2

6        4753    4750    4752    4750                4751    3         

Questions:

Now what do the charts say about the process?

What is a likely problem that could explain what you see in the chart?

What is the difference between this charting method and the charting method used in part 1?   What part of the process are we monitoring in each of these methods?

THis is the data

Table 1: Raw Data for Crank Shaft Hole Analysis
Note: all measurements are in ten thousandths of an inch.
Hour 1						Hour 2
		Crank Shaft no.						Crank
Hole	1	2	3	4		Hole	1	2	3	4
1	3751	3752	3750	3750		1	3750	3751	3752	3753
2	3752	3751	3750	3752		2	3749	3752	3754	3752
3	3747	3752	3752	3749		3	3748	3748	3753	3751
4	3745	3745	3741	3745		4	3745	3744	3745	3746
5	3752	3751	3750	3752		5	3750	3754	3753	3750
6	3753	3750	3752	3750		6	3751	3750	3752	3753
Hour 3						Hour 4
		Crank						Crank
Hole	1	2	3	4		Hole	1	2	3	4
1	3751	3749	3752	3753		1	3751	3753	3752	3750
2	3748	3752	3751	3753		2	3750	3751	3751	3751
3	3749	3749	3753	3752		3	3749	3750	3751	3752
4	3745	3744	3744	3743		4	3741	3745	3744	3745
5	3750	3751	3752	3750		5	3752	3755	3751	3750
6	3752	3749	3750	3753		6	3753	3752	3754	3753
Hour 5						Hour 6
		Crank						Crank
Hole	1	2	3	4		Hole	1	2	3	4
1	3751	3752	3754	3753		1	3752	3750	3751	3750
2	3754	3750	3751	3752		2	3751	3750	3752	3750
3	3752	3753	3752	3751		3	3753	3750	3753	3750
4	3745	3746	3747	3746		4	3744	3745	3746	3744
5	3751	3751	3753	3754		5	3751	3750	3751	3751
6	3750	3752	3753	3751		6	3750	3751	3750	3750
Hour 7						Hour 8
		Crank						Crank
Hole	1	2	3	4		Hole	1	2	3	4
1	3751	3749	3751	3750		1	3752	3751	3753	3750
2	3752	3750	3754	3751		2	3751	3752	3753	3750
3	3753	3750	3752	3750		3	3753	3753	3750	3751
4	3744	3742	3754	3745		4	3744	3746	3745	3744
5	3750	3750	3750	3750		5	3751	3751	3752	3750
6	3751	3749	3751	3750		6	3750	3750	3752	3750
Hour 9						Hour 10
		Crank						Crank
Hole	1	2	3	4		Hole	1	2	3	4
1	3750	3752	3751	3750		1	3750	3752	3751	3750
2	3751	3750	3751	3750		2	3750	3751	3752	3750
3	3752	3750	3750	3749		3	3750	3752	3751	3750
4	3741	3742	3740	3742		4	3745	3744	3746	3745
5	3751	3752	3750	3750		5	3750	3752	3752	3751
6	3752	3754	3750	3754		6	3750	3751	3752	3751
Hour 11						Hour 12
		Crank						Crank
Hole	1	2	3	4		Hole	1	2	3	4
1	3750	3750	3751	3751		1	3750	3750	3749	3750
2	3750	3749	3751	3750		2	3750	3751	3750	3749
3	3751	3752	3750	3752		3	3750	3750	3751	3751
4	3742	3744	3743	3745		4	3741	3746	3745	3744
5	3750	3750	3751	3753		5	3751	3750	3749	3750
6	3750	3749	3750	3751		6	3750	3750	3751	3750

Solve in excel plz

Answer 1

Sample size (n) =	4
x_double_bar =	3749.89
R_bar =	2.72
From table
A2 =	0.72
D3 =	0.00
D4 =	2.28
UCLx = x_double_bar + A2*R_bar	3751.85
LCLx = x_double_bar - A2*R_bar	3747.93
UCLr = D4*R_bar	6.21
LCLr = D3*R_bar	0.00

Except for the other holes which are primarily in control (except for few points going outside of the control limit), the hole number 4 is grossly out of control in both X-bar and Range chart. So, there is a high chance that defective parts are due to the improper piercing of this particular hole. The other holes have gone out of control is earlier hours but in the latest hour, they have come within control. But no countermeasure seems to be effective for the hole number 4.

The process of hole 4 is not continuous deterioration but a shift of the mean as a whole. It is suspected that the process setting parameters seem to be wrongly set for this particular hole or a non-standard tool is in use for the process.

For part-1, we have taken one crank as one sample and there were six observations per sample. In this case, one hole stands for one sample and for each sample there is four observation. During charting, each of these holes was taken together in the increasing order of elapsed hour in order to understand the trend for a single hole at a time.

With the X-bar chart, we are trying to observe the central tendency of the process through our sample observations. For the Range chart, we are trying to determine the dispersion of the process through the sample observation. The time lag provides the realization as to how the process has behaved through time or whether a countermeasure is implemented to keep the process within the control limit or not.