Other Acceptance Sampling Techniques

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Chapter 15

• Other Acceptance Sampling Techniques

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15-1. Acceptance Sampling by Variables

• 15-1.1 Advantages and Disadvantages of Variables
  Sampling
• Advantages
• Smaller sample sizes are required
• Measurement data usually provide more information
  about the manufacturing process
• When AQLs are very small, the sample sizes
  required by attributes sampling plans are very
  large.

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15-1. Acceptance Sampling by Variables

• 15-1.1 Advantages and Disadvantages of Variables
  Sampling
• Disadvantages
• The distribution of the quality characteristic
  must be known
• A separate sampling plan must be employed for
  each quality characteristic that is being
  inspected.
• It is possible that the use of a variables
  sampling plan will lead to rejection of a lot
  even though the actual sample inspected does not
  contain any defective items.

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15-1. Acceptance Sampling by Variables

• 15-1.2 Types of Sampling Plans Available
• Two types of variables sampling procedures
• Plans that control the lot or process fraction
  defective (or nonconforming). Procedure 1
• Plans that control a lot or process parameter
  (usually the mean). Procedure 2

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15-1. Acceptance Sampling by Variables

• 15-1.3 Caution in the Use of Variables Sampling
• The distribution of the quality characteristic
  must be known in order to use variables sampling
• The usual assumption is that the parameter of
  interest follows the normal distribution. This is
  a critical assumption.
• If the normality assumption is not satisfied,
  then estimates of the fraction defective based on
  the sample mean and standard deviation will not
  be the same as if the parameter were normally
  distributed.

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15-1. Acceptance Sampling by Variables

• 15-1.3 Caution in the Use of Variables Sampling
• It is possible to use variables sampling plans
  when the parameter of interest does not have a
  normal distribution.
• If the form of the distribution is known, it is
  possible to devise a procedure for applying a
  variables sampling plan.
• Not covered in this course.

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15-2 Procedure 1, the k method

• Two points on the OC curve
• (p1, 1 a) p1 is acceptable quality
• (p2, b) p2 is rejectable quality
• See Fig. 15-2
• n for s known
• n for s unknown

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Example 15-1 Procedure 1

• First line
• (p1 .01, 1 - a .95)
• Second line
• (p2 .06, b .10)
• At the intersection
• k 1.9, n 40 (s known)
• k 1.9, n 15 (s unknown)

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Example, cont.

• Take a sample of size n
• Compute Xbar and S, then
• ZLSL (Xbar LSL)/S
• Accept the lot if ZLSL gt k 1.9

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Procedure 2 M method

• Additional steps are needed
• Use Fig. 15-2 to obtain n and k as previous
• Use Fig 15-3 to get a value of M
• Note abscissa on Fig. 15-3
• Use Fig. 15-4 to convert ZLSL or ZUSL to a
  fraction defective

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Example 15-2

• Same data as in Example 15-1
• Abscissa value calculated as
• 1 1.9 SQRT(40)/39/2 .35
• Read M .030
• Suppose that a sample of n 40 is taken
• Suppose that Xbar 255 and S 15
• Then, ZLSL (Xbar LSL)/S (255-225)/15 2
• Read pest .020 from Fig. 15-4
• Since pest .020 lt M .030, accept the lot

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Procedure 2 (only) for 2 sided

• Get n and k as previous, and find M
• Find pest for LSL and USL from Fig. 15-4
• Add the two pest values
• If lt M accept, otherwise, reject

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15-3. MIL STD 414 (ANSI/ASQC Z1.9)

• 15-3.1 General Description of the Standard
• MIL STD 414 is a lot-by-lot acceptance-sampling
  plan for variables, introduced in 1957.
• Sample size code letters are used as in MIL STD
  105E, but the same code letter does not imply the
  same sample size in both standards.
• Sample sizes are a function of the lot size and
  the inspection level.
• All sampling plans assume the quality
  characteristic of interest is normally
  distributed.

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15-3. MIL STD 414 (ANSI/ASQC Z1.9)

• 15-3.1 General Description of the Standard
• MIL STD 414 is divided into four sections
• A General description of the sampling plans
  including definitions, sample size code letters,
  and OC curves for the plans.
• B Variables sampling plans based on the sample
  standard deviation for the case in which the
  process or lot variability is unknown.
• C Variables sampling plans based on the sample
  range method
• D Variables sampling plans for the case where
  the process standard deviation is known.

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Example 15-3

• Pg. 732

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15-3. MIL STD 414 (ANSI/ASQC Z1.9)

• 15-3.3 Discussion of MIL STD 414 and ANSI/ASQC
  Z1.9
• ANSI/ASQC Z1.9 is the civilian counterpart of MIL
  STD 414.
• Differences and revisions
• Lot size ranges were adjusted to correspond to
  MIL STD 105D
• Code letters assigned to the various lot size
  ranges were arranged to make protection equal to
  that of MIL STD 105E
• AQLs of 0.04, 0.065, and 15 were deleted
• Original inspection levels I, II, III, IV, and V
  were relabeled S3, S4, I, II, III, respectively.
• Original switching rules were replaced by those
  of MIL STD 105E, with slight revisions.

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15-5 Chain sampling

• Plans with c 0 are undesirable
• OC curves are convex throughout
• Pa drops rapidly
• Unfair to the producer
• Rectifying inspection can require screening of a
  very large number of lots that may be of
  acceptable quality

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ChSP-1

• Chain sampling uses the cumulative results
• 1. For each lot, select a sample of size n and
  observe d
• 2. If d 0, accept the lot
• If d gt 2, reject the lot
• If d 1, accept the lot provided there have
  been no defectives in the previous i lots

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ChSP-1

• So, if n 5 and i 3, lots would be accepted
  if d 0 in the sample of n 5, or, if d 1 in
  the sample of n 5 and no defectives in the
  previous i 3 lots

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ChSP-1

• See Fig. 15-6 that shows OC curves for ChSP-1
  plans with n 5, c 0, and i 1,
  2, 3, 5

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ChSP-1

• Pa P(0,n) P(1,n)P(0,n)i
• Example Computation of Pa
• With n 5, c 0, and i 3
• For p .10
• See pg. 737

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Conditions for chain sampling

• Lots should be one of a series in a continuing
  stream of lots
• Lots should come from a process in which
  production is repetitive under the same
  conditions
• Lots should be offered for acceptance in
  substantially the order of production

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Conditions for chain sampling

• Lots should usually be expected to be of
  essentially the same quality
• There should be no reason to believe that the
  current lot is of any poorer quality than those
  preceding
• There should be a good record of quality
  performance on the part of the vendor

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Conditions for chain sampling

• There must be confidence that the vendor will not
  take advantage of its good record and
  occasionally send a bad lot when such a lot would
  have the best chance of acceptance

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15-6 Continuous sampling

• Previously, we have been describing lot-by-lot
  plans
• Many manufacturing operations are continuous
• Personal computers

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Continuous sampling plans

• Alternating sequences of sampling inspection and
  screening (100 inspection)
• Begins with 100 inspection
• When i units (the clearance number) is found to
  be free of defects, sampling inspection (at
  fraction f) is instituted

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Start
CSP-1
!00 of the items are inspected
Have i consecutive units been defect free?
No
Yes
Inspect a fraction f of the units selected in a
random manner
Has a defect been found?
No
Yes
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CSP-1

• Has an overall AOQL
• Depends on i and f
• Many possible combinations can produce the same
  AOQL
• See Table 15-3 on pg. 739
• For an AOQL 0.79, among many others
• i 59, f 1/3
• i 76, f 1/4

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Choosing i and f

• Workload of the inspectors and operators
• QA people do the sampling inspection
• Manufacturing does the 100 inspection

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CSP-1

• Average number of units inspected in a 100
  screening sequence following the occurrence of a
  defect
• u (1 qi)/(pqi)
• where q 1 p and p is the fraction defective
  when the process is operating in control

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CSP-1

• Average number of units passed under the sampling
  inspection procedure before a defective unit is
  found
• v 1/(fp)

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CSP-1

• Average fraction inspected in the long run
• AFI (u fv)/(u v)
• Average fraction of manufactured units passed
  under the sampling inspection procedure
• Pa v/(u v)

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CSP-1

• OC curve gives the percentage of units passed
  under sampling inspection
• OC curves for several combinations are shown in
  Fig. 15-8
• Many variations of CSP-1
• CSP-2, CSP-F, CSP-V, CSP-T

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Example

• Suppose that p .02, f .08, and i 100
• q 1 .02 .98
• The average number of pieces inspected in a 100
  screening sequence following the finding of a
  nonconforming item
• u (1 - .98100)/.02(.98)100 327.02

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Example

• The average number of pieces inspected in a
  period of sampling inspection
• v 1/.08(.02) 625

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Example

• With u and v, the AFI can be found
• AFI 327.02 .08(625)/(327.02 625) .396
• Also
• AOQ .02(1 - .396) .012

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Example

• The average fraction of units passed under the
  sampling inspection procedure
• Pa 625/(327.02 625) .656
• Can also find this in Fig. 15-8

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Skip-lot sampling plans

• Lot-by-lot inspection plan in which only a
  fraction of the lots are inspected
• Used only when the vendor has a good history of
  quality production

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SkSP-2

• Begins with normal inspection with every lot
  inspected under the reference plan
• When i consecutive lots are accepted under normal
  inspection, switch to inspecting a fraction f of
  the lots
• When a lot is rejected under skipping inspection,
  return to normal inspection

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SkSP-2

• Let P be the probability of acceptance of a lot
  under the reference plan
• Pa(f, i) is the probability of acceptance for
  SkSP-2
• Pa(f, i) fP (1 f)Pi/ f (1 f)Pi

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SkSP-2

• Let P be the probability of acceptance of a lot
  under the reference plan
• F is the average fraction of submitted lots that
  are sampled
• F f/(1 f)Pi f

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SkSP-2

• See Fig. 15-9
• OC curves for SkSP-2 plans
• Holding f ¼, showing OC curves for i 4, i
  10, and the reference plan n 20, c 1
• See Fig. 15-10
• OC curves for SkSP-2 plans
• Holding i 8, showing OC curves for f 1/3, f
  ½ and the reference plan n 20, c 1

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SkSP-2

• See Fig. 15-11
• ASN curves for four different plans using
  reference plan n 20, c 1
• The reductions in ASN are substantial for small
  values of p

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Assignment

• Odd numbered exercises

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End