ISO 3951-4:2011 pdf free download – Sampling procedures for inspection by variables一 Part 4: Procedures for assessment of declared quality levels.
.3.4 Double specification limits under separate control
For double specification limits under separate control, there will be separate DQLs applying to each limit, say Du for the upper limit and DL for the lower limit. Denote the Form k plans for these DQLs by (nU, k11) and (‘IL’ kL) respectively. Denote the sample means arising from random samples of size nU and L by and L respectively. Calculate Qu = (U — u )I a and QL = (L — L)/ a. If Qu  and QL  k, the declared quality levels have not been contradicted; otherwise, at least one of the declared quality levels has been contradicted.
EXAMPLE Separate control of double specification limits is to be used with a Level II DQL of 0,65 % at the upper limit U= 3,125 and a Level Ill DQL of 0,25 % at the lower limit L = 3,100. The quality characteristic is normally distributed with a process standard deviation that is presumed to be known and equal to 0,003 10. From Table 1, it is seen that the appropriate Form k “ci’ method plans are fl1= 18, ku 2,021 for the upper limit and L = 34, k1 = 2,604 for the lower limit.
Suppose that the random sample of 18 items from the entity yields a sample mean = 3,117 3 and a sample standard
deviation sti = 0,002 91, and that a sample of size 34 from the same entity yields a sample mean = 3,116 9 and a standard deviation SL = 0,003 07. Neither of these standard deviations gives rise to doubt about the presumed value of o so we continue to use the “ci” method. The upper and lower quality statistics are calculated as = (3,125 —3,117 3)/0,003 10 = 2,484 and QL = (3,116 9 — 3,100)/0,003 10 = 5,452 respectively. As Q> kjLr and QL > kL, the declared quality levels are not contradicted.
7.3.5 Double specification limits under complex control
Complex control of double specification limits consists of combined control of both limits together with separate control of one of the limits. There will be a DQL for the combined fraction nonconforming at the two limits and a DQL for the fraction nonconforming at the limit that is under separate control. Suppose that the Form p* “a” method plan for the combined part of the complex requirement is ii, p. Suppose without loss of generality that the separately controlled limit is the upper limit, and that the appropriate plan for this limit is
‘1u’Pu
A random sample of size n is drawn, which yields a sample mean of L, and a sample standard deviation of s. A second random sample of size is drawn, which yields a sample mean of and a sample standard deviation of s. Provided that neither of the values s nor s casts doubt on the presumed value of a, we continue to use the “a” method as follows.
8.2 Tables indicating discriminatory ability
Tables 5 to 10 provide additional information about the probabilities of contradicting incorrect declared quality levels for different values of the quality ratio.
For each individual sampling plan, Tables 2 to 4 show the value of the limiting quality ratio (LQR) that corresponds to a risk of failing to contradict the declared quality level. This LQR together with the information presented in Tables 5 to 10 may be used to assess the discriminatory ability of each sampling plan.
Tables 2 to 4 also show the probability that the sample result will (falsely) contradict the declared quality level when the actual quality level is equal to the DQL.