ControlChart

Statistical techniques can be helpful throughout the product cycle, including development activities prior to manufacturing, in quantifying process variability, in analyzing this variability relative to product requirements or specifications, and in assisting development and in eliminating or greatly reducing this variability. This general activity is called process capability analysis. We have studied the histogram for variation distribution. If sufficient number of data are collected, the distribution will follow certain smooth curve. Most of manufacturing parameters follow normal distribution or can be approximated as normal distribution. As indicated in the following figure, the range from ì - 3ó to ì + 3ó covers 99.73% of the process. In other words, if everything remains the same, the output of process will have 99.73% of chance to fall into this range. The total range is 6ó, which indicates the potential output value of the process. The 6ó is governed by and is an indication of the process.

Areas under the normal distribution

The smaller 6ó is in relation to the specification range, the more capable is the process. In order to deal with the relationship between the process variability (6ó) and specifications, a process capability index, C_p, is defined as:

C_p = (USL - LSL) / 6ó

where USL and LSL are upper specification limit and lower specification limit. These specification limits are defined by the engineering group.

Process capability index is a measure of the ability of the process to manufacture product that meets specification. If the C_p is less than 1, the specification range is smaller than 6ó of the process. The process is said not capable. There will be certain amount of scraps producing with usual process. If the C_p is larger than 1, the specification range is larger than 6ó of the process. There will be no scraps because everything produced in the process (within 6ó range) will be in the specification limits. This process is said capable. For a usual process, a minimum value for C_p of 1.33 has been suggested. The following table presents the recommendation on the process capability index for different situations.

Recommended minimum process capability index, C_p

	Two-sided specification	One-sided specification
Exixting process New process Safety, strength, or critical parameter, existing process Safety, strength, or critical parameter, new process	1.33 1.50 1.50 1.67	1.25 1.45 1.45 1.60

WORKING EXAMPLE

The diameter of one end of a gyro drive shaft is subject to statistical control using and R charts. After 30 subgroups of 5 shafts each have been examined, it is calculated that the standard deviation of the process ó is 4.73. The specifications on the shaft are 1,140 " 10.

1. Calculate the process capability index, C_p, for the process.

2. Is the process capable? Or is there any scraps produced in the process?

Process Capability Analysis at John Deere

John Deere, a major manufacturer of farm equipment, uses SPC to assess the capability of machine tools that it purchases. At Deere Harvester Works, almost all machine tool purchases have been subjected to SPC analysis since the late 1970s. Deere had decided to acquire a vertical column handsaw that could make angle as well as straight cuts. A Marvei 81A PC handsaw produced by Armstrong-Blum Manufacturing Company was selected. Before it was shipped, however, Deere studied its ability to meet performance criteria.

Figure 16.28 shows the basic analysis. Process capability is measured by testing the machine with the materials and tooling that will be used in its intended application. The natural variation must be less than two-thirds of the tolerance to be acceptable. Deere engineers begin testing at the supplier's plant if possible. The Deere quality or engineering staff observes the test and records the data for analysis. They prefer to send the operator who will use the machine at the supplier's plant to perform the tests. In addition to testing for process capability, reliability is demonstrated by operating the machine for 8 hours continuously without a failure.

Deere's capability study sets up very specific guidelines. The key elements are:
• No change in operators during the test.
• No change in raw material batches.
• No change in measuring devices. The devices must be calibrated at the beginning and end of the test and may a!so be checked periodically during the test. Repeatability is also verified.
• No change in inspectors.
• No change in temperature of equipment, material, or coolant,
• No change in coolant level.

Deere has developed a patented software package for collecting, storing, and analyzing me data collected. This system, called CA1R (Computer-aided Inspection and Reporting System), generates reports to analyze variability and control. Control charts from tests on the Marvel saw to check cut length on an S^S-mm rectangular steel tube are shown in Figure 16.29. Figure 16.30 shows the results of the process capability analysis.

One of Deere's managers noticed that suppliers often learn more about their machine's capabilities during the testing. In one case, a CNC punch press supplier's chief engineer discovered that the machine's capability deteriorated as steel shafts of heavier weight were used. By reprogramming the machine control, the vendor was able to improve the machine's capability on heavy sheets. The tests also showed that the flatness of the sheet was crucial and could be correlated with process capability.

'While this process consumes time, Deere believes that the long-term benefits far outweigh the costs As one manager stated. "Usually we end up with a better supplier and a better machine than we would have gotten otherwise."

Key Issues for Discussion:

1. From the control chart data in Figure 16.29, verify the control limits and estimate of the standard deviation using the formulas in this chapter.
2. Discuss the data found in Figure 16.30- What is the process capability index? What conclusions do you reach about the machine tool?
3. Discuss the guidelines set for Deere's capability test. Why are such guidelines strictly adhered to?

Figure 1. Quality Control at John Deere

Default select range used: 1 to 15

Number of pieces per sample: 3

Upper limit on x-bar: 875.400208

Average of x-bars: 875.275800

Lower limit on x-bar: 875.151917

R-bar/D2 estimate: 0.071666

Upper limit on R: 0312424

Average if R's: 0.121330

Lower limit on R: 0.000000

Figure 2. CAIR System Control Analysis

Normal probabilities

Nominal: 875.0000

+ TOL: 1.0000

- TOL: 1.0000

Sample size: 45

Probability predictions: Process as is

% in spec: 100.00

% under: 0.00

% over: 0.00

Six sigma: 0.4758

Total tolerance: 2.0000

Capability ratio: 23.7900

Avg+3S: 875.5138

Avg-3S: 875.0379

Target: 875.0000

Average: 875.2758

Adjustment needed: -0.2758

Process after adjustment

% in spec: 100.00

% under: 0.00

% over 0.00

Figure 3. CAIR System Capability Analysis

Class Resources

School of Technology
College of Business & Applied Sciences
Eastern Illinois University