TARGET VALUES

Target values are very important to the proper operation of the short-run charts . They can be determined in four different ways, depending on the available information. These four methods are discussed in order of preference.

Note that one should always use the nominal print specification for the target Xdouble bar value unless there is a sound engineering reason for not doing so.

METHOD 1: PRIOR CONTROL CHARTS FOR THIS PART NUMBER

Use this method in cases where separate traditional control charts have been kept for each part number. The target value is simply the center line from this previous chart. Make sure that the chart is in a good state of control before using any average values from the chart.

For variable-data short-run charts:

Target Xbar	=	Xbar
Target Rbar	=	Rbar
Target sbar	=	sbar

For attribute-data short-run charts:

Target pbar	=	pbar
Target npbar	=	npbar
Target cbar	=	cbar
Target ubar	=	ubar

Using prior control charts is the best method for obtaining target values, but most companies are just beginning their implementation of SPC and, as such, do not have any prior charts. If this is the case, try Method 2 for determining target values.

METHOD 2: OTHER HISTORICAL DATA FOR THIS PART NUMBER

If no control charts have been kept in the past, perhaps some data for this part number have been recorded from final inspection or audit results of prior runs (or at the customer's receiving inspection).

For variable-data charts, use these formulas where m is the number of measurements of historical data ( m should be at least 10). These measurements should be from the last shipment of this part number that was accepted for the characteristic being charted. Let X be the i th measurement of these m measurements (and be sure to eliminate all outliers before calculating target values):

The factor f ₂ is equal to d ₂ (for n, the subgroup size ) divided by c ₄ (for m, the number of measurements of historical data). Values of d ₂ and c ₄ can be found in Table 13.1. Values of f ₂ for commonly used n and m are found in Table 13.2. The sample standard deviations are calculated with the usual formula.

Table 13.1: Statistical Values Used for the Various Short-Run Charts

n	A 2	D 3	D 4	d 2	c 4	A 3	B 3	B 4
2	1.88		3.27	1.13	.798	2.66		3.27
3	1.02		2.57	1.69	.886	1.95		2.57
4	0.73		2.28	2.06	.921	1.63		2.27
5	0.58		2.12	2.33	.940	1.43		2.09
6	0.48		2.00	2.53	.952	1.29	0.03	1.97
7	0.42	0.08	1.92	2.70	.959	1.18	0.12	1.88
8	0.37	0.14	1.86	2.85	.965	1.10	0.18	1.82
9	0.34	0.18	1.82	2.97	.969	1.03	0.24	1.76
10	0.31	0.22	1.78	3.08	.973	0.98	0.28	1.72

Table 13.2: The f ₂ Factors for Calculating Target Rbar

	Desired Subgroup Size ( n ) for the Range
	m/n	2	3	4	5
Measurements (m) of historical data used to calculate s	5	1.20	1.80	2.19	2.47
	10	1.16	1.74	2.12	2.39
	15	1.15	1.72	2.10	2.37
	20	1.14	1.72	2.09	2.36
	25	1.14	1.71	2.08	2.35
	30	1.13	1.69	2.06	2.33

Target sbar and target ƒ are found from the following equations:

The c ₄ in the numerator is found for n, the subgroup size. The c ₄ in the denominator is for m, the number of measurements of historical data. Values of c ₄ can be found in Table 13.1.

For attribute-data charts, use the following formulas:

where m is the number of historical pieces examined, np is the number of nonconforming units found on the m units checked, n is the subgroup size for the selected part number (only needed for the short-run c or np charts), and c is the number of nonconformities found on the m historical pieces.

METHOD 3: PRIOR EXPERIENCE ON SIMILAR PART NUMBERS

Quite often, data collected for similar part numbers (surrogate data) run on the same process can be analyzed to estimate target values for a part number that has no historical data.

For variable-data charts, a scatter diagram displaying the history can be used. The process for such use is to

• Construct a scatter diagram.

• Draw the best fit line through the data.

• Read the values on the x-axis and the corresponding values on the y-axis. The reading on the y-axis becomes the estimate for the target Rbar.

For attribute-data charts, a similar method can be used. Suppose a target u bar is needed for the expected number of soldering nonconformities (shorts, solder balls, solder bridges, missed) on a new circuit board that has never previously been run.

From prior experience assembling similar circuit boards with this same soldering operation, an average of 3.2 soldering nonconformities per 100 solder joints is calculated. By counting the expected number of solder joints on the new board (179) from the engineering drawings, the target u bar can be determined as follows :

In addition, the experience, knowledge, and judgment of the personnel involved with this process may be used to help determine reasonable targets for part numbers without historical data.

METHOD 4: SPECIFICATION LIMITS

Sometimes a brand new part number will be run for which there is no prior data and no similarity to any other part number. Or perhaps a new machine is being used for the first time, having of course generated no prior data.

In these cases, target values may be determined from specification limits. This is not a preferred method to use, but quite often, with the limited information of short production runs, the most must be made of whatever is available. When data have been collected for this part number, they are used to revise the targets if necessary.

For variable-data charts, use these formulas:

Target Rbar (and sbar and ƒ ) is set to meet the capability requirements for this part number, so the C _PK number should reflect the capability goal for this characteristic. Usually, C _{PK (GOAL)} is set to 1.33, which means that the goal is to have the ±4 ƒ spread of the process within print specifications (use a C _PK = 1.00 for ±3 ƒ , a C _PK = 1.67 for ±5 ƒ , and a C _PK = 2.00 for +60).

In the case of a unilateral specification, choose a target Xdouble bar and then calculate the target variation value as follows (the "" lines mean absolute value):

Or, first choose a target Rbar (or sbar or ƒ ) and use this formula with a USL.

Target Xbar = USL - [3 C _PK / d ₂ ]Target Rbar

Target Xbar = USL - [3 C _PK / c ₄ ]Target sbar

Target Xbar = USL - 3 C _PK /Target ƒ

For a LSL use this formula:

Target Xbar = LSL + [3 C _PK / d ₂ ] Target Rbar

Target Xbar = LSL + [3 C _PK / c ₄ ] Target sbar

Target Xbar = LSL + 3 C _PK Target ƒ

For attribute-data charts, there are no specification limits, so engineering judgment can be applied instead. This fourth option is normally used when one is faced with a new plant (or equipment) start-up situation. Ideally, the expected number of nonconforming units (or nonconformities) will be 0, but this is unlikely to happen on the first day of production.

Some nonconforming units (or nonconformities) are likely to occur as the equipment is fine tuned and operators learn how to run the process properly. Any target values that are established should take this learning-curve effect into consideration by initially setting higher targets, then lowering them as time progresses. A good approach to measure this is to develop a negative exponential graph with the x axis as the weeks (1, 2, 3, ..., n ) and the y axis as the average nonconformities. The amount of nonconformities would be expected to decrease over time.