ASTM E2555-07(2018)

4.1 The procedure and tables presented in this practice are based on the use of the Weibull distribution in acceptance sampling inspection. Details of this work, together with tables of sampling plans of other forms, have been published previously. See Refs 4.2 The procedure to be used is essentially the same as the one normally used for attribute sampling inspection. The only difference is that sample items are tested for life or survival instead of for some other property. For single sampling, the following are the required steps:

4.3 Both the sample sizes and the acceptance numbers used are those specified by Practice E2234 plans. It will be assumed in the section on examples that single sampling plans will be used. However, the matching double sampling and multiple sampling plans provided in MIL-STD-105 can be used if desired. The corresponding sample sizes and acceptance and rejection numbers are used in the usual way. The specified test truncation time, 4.4 The probability of acceptance for a lot under this procedure depends only on the probability of a sample item failing before the end of the test truncation time, 4.5 The underlying life distribution assumed in this standard is the Weibull distribution (note that the exponential distribution is a special case of the Weibull). The Weibull model has three parameters. One parameter is a scale or characteristic life parameter. For these plans and procedures, the value for this parameter need not be known; the techniques used are independent of its magnitude. A second parameter is a location or “guaranteed life” parameter. In these plans and procedures, it is assumed that this parameter has a value of zero and that there is some risk of item failure right from the start of life. If this is not the case for some applications, a simple modification in procedure is available. The third parameter, and the one of importance, is the shape parameter, β.5 The magnitude of the conversion factors used in the procedures described in this report depends directly on the value for this parameter. For this reason, the magnitude of the parameter shall be known through experience with the product or shall be estimated from past research, engineering, or inspection data. Estimation procedures are available and are outlined in Ref (1).

4.6 For the common case of random chance failures with the failure rate constant over time, rather than failures as a result of “infant mortality” or wearout, a value of 1 for the shape parameter shall be assumed. With this parameter value, the Weibull distribution reduces to the exponential. Tables of conversion factors are provided in Annex A1 for 15 selected shape parameter values ranging from ¹/₂ to 10, the range commonly encountered in industrial and technical practice. The value 1, used for the exponential case, is included. Factors for other required shape parameter values within this range may be obtained approximately by interpolation. A more complete discussion of the relationship between failure patterns and the Weibull parameters can be found in Refs 4.7 One possible acceptance criterion is the mean life for items making up the lot (μ). Mean life conversion factors or values for the dimensionless ratio 100t/μ have been determined to correspond to or replace all the p' or percent defective values associated with Practice E2234 plans. In this factor, 4.8 Annex Table 1A lists, for each selected shape parameter value, 100t/μ ratios for each of the Practice E2234 AQL [p'(%)] values. With acceptance inspection plans selected in terms of these ratios, the probability of acceptance will be high for lots whose mean life meets the specified requirement. The actual probability of acceptance will vary from plan to plan and may be read from the associated operating characteristic curves supplied in MIL-STD-105. The curves are entered by using the corresponding p'(%) value. Annex Table 1B lists 1004.8.1 These ratios are to be used directly for the usual case for which the value for the Weibull location or threshold parameter (γ) can be assumed as zero. If γ is not zero but has some other known value, all that shall be done is to subtract the value for γ from t to get t₀ and from m to get m₀. These transformed values, 1.1 This practice presents a procedure and related tables of factors for adapting Practice E2234 (equivalent to MIL-STD-105) sampling plans to acceptance sampling inspection when the item quality of interest is life length or reliability. Factors are provided for three alternative criteria for lot evaluation: mean life, hazard rate, and reliable life. Inspection of the sample is by attributes with testing truncated at the end of some prearranged period of time. The Weibull distribution, together with the exponential distribution as a special case, is used as the underlying statistical model.

1.2 A system of units is not specified by this practice.

1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.

1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.