Contents
- Index
Variables Single For Defective Units
This type of sampling is applicable only for measurable characteristics that are normally distributed.
Characteristic:
Defective units
Assumptions:
(1) Physical measurements are required and these measurements must be normally distributed. This type of sampling plan is sensitive to departures from normality so a formal test for normality should be performed.
(2) For the known standard deviation option, the process standard deviation must be consistent from lot-to-lot. A control chart of the range or standard deviation should be maintained to demonstrate that this assumption is met. When setting up the plan, historical data must be used to estimate the process standard deviation.
(3) Representative sample
Parameters:
Standard Deviation: Known or Unknown
Specification Limits: 1 or 2
Form: 1 (k-method) or 2 (M-method)
These addition parameters depend on the form selected:
Form 1:
n = sample size, integer satisfying n³1 if standard deviation known and n³2 if standard deviation is unknown
k = accept constant, real number.
MSD = maximum standard deviation. Calculated from n and k. Only used for standard deviation unknown - 2 specs.
Form 2:
n = sample size, integer satisfying n³2 if standard deviation known and n³3 if standard deviation is unknown
M = maximum percent defective, real satisfying 0<M<100.
v = calculated from n (only used when standard deviation is known). v = 
Form 1 is simpler to use and generally preferred. Form 2 has been included because it is used in ANSI Z1.9.
Procedure Standard Deviation Known:
Form 1:
(1) Take a representative sample of n units from the lot to be inspected.
(2) Measure each unit and calculate the average of the samples, denoted 
.
(3) For a lower spec limit (LSL), accept if ³ LSL + k S.
For an upper spec limit (USL), accept if £ USL - k S.
For two spec limits, accept if LSL + k S £ £ USL - k S.
Otherwise reject the lot.
Form 2:
Using Form 2 requires a table of the normal distribution. The symbol F below represents the normal distribution function that must be looked up using this table. The procedure for executing a Form 2 plan is as follows:
(1) Take a representative sample of n units from the lot to be inspected.
(2) Measure each unit and calculate the average of the samples, denoted .
Procedure Standard Deviation Unknown:
Form 1:
(1) Take a representative sample of n units from the lot to be inspected.
(2) Measure each unit and calculate the average and standard deviation of the samples, denoted and S respectively.
(3) For a lower spec limit, accept if ³ LSL + k S.
For an upper spec limit, accept if £ USL - k S.
For two spec limits, accept if LSL + k S £ £ USL - k S and S £ MSD (USL - LSL) / 100.
Otherwise reject the lot.
Form 2:
Using Form 2 requires a table of the incomplete Beta distribution. The symbol Ix(a,b) below represents the incomplete beta distribution function that must be looked up using this table. Such a table can be found in ANSI Z1.9. The procedure for executing a Form 2 plan is as follows:
(1) Take a representative sample of n units from the lot to be inspected.
(2) Measure each unit and calculate the average and standard deviation of the samples, denoted and S respectively.
