IES 331 Quality Control Chapter 15 Acceptance Sampling by Variables Week 14 September 8-13, 2005

Acceptance Sampling by variables Advantages vs Disadvantages The same OC curve can be obtained with a smaller sample size than would be required by an attributes sampling plan Measurement data usually provide more information about manufacturing process than attributes data When acceptable quality level as are very small, sample sizes required by attributes sampling plans are very large DISADVANTAGES Distribution of OC curve must be known Most standard plans assume distribution of quality characteristic is normal A separate sampling plan must be employed for each quality characteristic that is being inspected Possible to reject a lot even though the actual sample inspected does not contain any defective items

Type of Sampling Plans for Variables Type 1: Plans to control the lot or process fraction defective (nonconforming) Type 2: Plans to control a lot or process parameter (process mean)

Basics of Variable Sampling Plan In case of one side specification

Caution in the use of Variable Sampling Usual assumption is that the parameter of interest follows the normal distribution If parameter of interest is not normally distributed, estimates of the fraction defective will not be the same as if normally distributed Difference between estimated fraction defectives may be large when dealing with very small fractions defective

Designing Variable Sampling Plan with a Specified OC Curve

Illustrated Example using Nomograph The density of a plastic part used in a cellular phone is required to be at least 0.70 g/cm3. The part supplied in large lots. It is desired to have p1 = 0.02, p2 = 0.10, alpha 0.10, and beta 0.05. Assume that the variability is unknown but will be estimated by the sample standard deviation a) Find the appropriate variable sampling plan b) Suppose that a sample of the appropriate size was taken, and sample average is 0.73, and sample standard deviation is 1.05 x 10-2. Should the lot be accepted or rejected?

Illustrated Example using Nomograph alpha 0.10, and beta 0.05.

Military Standard: MTL STD 414 MIL STD 414 is a lot-by-lot acceptance-sampling plan for variables Focal point is the AQL which ranges from 0.04% to 15% Five general inspection levels ___________________________________ Sample sizes are a function of the lot size and the inspection level Provision is made for normal, tightened, and reduced inspection Quality characteristic of interest is assumed to be normally distributed

Illustrated Example using MTL STD 414 An inspector for a military agency desires a variable sampling plan for use with an AQL of 1.5%, assuming that lots are of size 7000. If the standard deviation of the lot or process is unknown, derive a sampling plan using MIL STD 414