Standard deviation target

The model building step deals with the development of mathematical models to relate the optimized set of descriptors with the target property. Two statistical measures indicate the quality of a model, the regression coefficient, r, or its square, r, and the standard deviation, a (see Chapter 9). 

When the target population is segregated, or stratified, equation 7.5 provides a poor estimate of the amount of sample needed to achieve a desired relative standard deviation for sampling. A more appropriate relationship, which can be applied to both segregated and nonsegregated samples, has been proposed. ... 

We now have a means of predieting the standard deviation multiplier z whieh ean be used in equation 3.2. However, z, the assembly toleranee standard deviation multiplier, must be estimated before this equation ean be satisfied. This is aehieved by setting a eapability requirement. The level of eapability required typieally by industry is Cp = 2 (Harry and Stewart, 1988 O Connor, 1991) whieh equates to 0.002 parts-per-million (ppm) (see Appendix II for a relationship between Cp, Cp and ppm). Note, this value is with no failure severity taken into aeeount, but is a blanket target value diffieult to realize in praetiee. It follows then for the overall assembly proeess eapability for a bilateral assembly toleranee ean be given from equation 3.7 as ... 

The variability or spread of the data does not always take the form of the true Normal distribution of course. There can be skewness in the shape of the distribution curve, this means the distribution is not symmetrical, leading to the distribution appearing lopsided . However, the approach is adequate for distributions which are fairly symmetrical about the tolerance limits. But what about when the distribution mean is not symmetrical about the tolerance limits A second index, Cp, is used to accommodate this shift or drift in the process. It has been estimated that over a very large number of lots produced, the mean could expect to drift about 1.5cr (standard deviations) from the target value or the centre of the tolerance limits and is caused by some problem in the process, for example tooling settings have been altered or a new supplier for the material being processed. 

Suppose rj i,/) is a sequence of random numbers produced by computer generation, which takes a Gaussian distribution of a known standard deviation cr, the target roughness heights z i,/) that obeys a given ACF can be written as... 

Table 1. Table of the computed abundances iron, and the two a elements calcium and nickel. All from the neutral-element lines. The standard deviation refers to the measurements in the different stars. In NGC 3680 we have only two targets, therefore instead of values a we put the difference between the two stellar abundances obtained. The average number of lines identified for each specie is also indicated. 

We do this by using the statistical ideas outlined above. First of all, the QC sample is measured a number of times (under a variety of conditions which represent normal day-to-day variation). The data produced are used to calculate an average or mean value for the QC sample, and the associated standard deviation. The mean value is frequently used as a target value on the Shewhart chart, i.e. the value to aim for . The standard deviation is used to set action and warning limits on the chart. 

The average/target value has already been established from previous data and is equal to 17 and the standard deviation is 1.5. 

---