For an unknown mean, the sample size is increased by one and the saving’s percentage is reduced to 50 percent. The ASN required for a sequential test decision at a standard deviation level of s0=12.5 is 23 according to Table 3, resulting in an average sampling economy of 52 percent. The substitution of the textile process parameters, s0=12.5, s1=24.3, a=0.001, b=0.001, in the discriminating test equation (6) yields s12/s02=3.78=X.9992(f)/X.0012(f) at about 47 degrees of freedom, which translates into a required sample size of 48 for the classical test. The test’s sample size can be estimated from the power of the discriminating test 3 needed to distinguish between the population variances s12 and s02 at f degrees of freedom: Thus, a rejection of the test hypothesis H0 occurs at some chosen significance level a such that If H0 is correct, then X2/f is the distribution for s2/s02 for f degrees of freedom. The test hypothesis H0 specifies the population variance as H0: s2 = s02 and the alternate hypothesis H1: s12 > s02. When a classical test of significance is applied to question of whether the sample variance s2 differs significantly from the desired population variance s0, a Chi-square test X2 is usually applied. Table 2: Sequential Sampling Process Capability Determination Figure 1: Sequential Sampling Process Capability Plot, New Machine A Table 3: New Machine A Variance Sampling Economy The test is continued when (2) b/(1-a) = 1.33) since the older equipment is not capable. Hence, for a selected USL-LSL specification range, any sampling decision on whether a process is capable is dependent upon the process standard deviations s0 ( C p > 1 ) s1 ( C p = (1-b)/a. Where the upper specification limit (USL) and lower specification limit (LSL) represent the upper and lower specification limits and s the population standard deviation (STD), is a handy measure of process capability.īy convention, if C p 1, the process is considered marginally or definitively capable (e.g., C p >= 1.33). Applying Wald’s Sequential Test Method to Process Capability DecisionsĪ process is defined as capable when the determined statistical control limits are at least equal to or within the specification limits and deemed incapable whenever the control limits lie outside of the specification limits. It is also both computer user and spreadsheet software friendly. The sequential test method for process capability decisions described below will often result in a 50 percent sampling saving when compared with the most powerful classical tests. Our rapid pace and highly competitive industrial environments often require expeditious decisions/actions in the above areas and an automated statistical method which minimizes sampling during these studies would be highly desirable. Process changes and/or improvements need to be evaluated.The capability of a process to meet customer specifications needs to be determined or.Engineering tolerances are reviewed against the observed variability of the process and/or new equipment is evaluated,.Process capability ( C p) studies are usually performed whenever:
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