Using MIL-STD-105 As a Process Control Procedure

In my previous article, I discussed the merits and cautions of the “acceptance number” equal zero (c=0) sampling plans contained within AS9138. A simple formula was provided to determine appropriate sample size, and it was illustrated that twice the inspection does not provide twice the consumer protection. Although there is an undeniable emotional appeal to implement sampling procedures that have an acceptance number of zero, readers must not jump to the conclusion that c=0 sampling procedures provide better consumer protection at the designed lot tolerance percent defective (LTPD) point.

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In this article the merits and limitations of MIL-STD-105 will be illustrated, and its link to process control will be demonstrated. Before discussing the technical merits of MIL-STD-105, its impressive evolution deserves some recognition.

Acceptance sampling and all its parameters were well developed before 1925 to support Bell Telephone Companies’ rapid growth.^{1, 2} The motivation was to establish an economic method to judge the quality of submitted lots during production or at final inspection. Considering the rapid growth of this industry, the old practice of 100-percent inspection was no longer an economic path forward. Harold Dodge, Harry Romig, Walter Shewhart, and several other notable pioneers worked side by side in the “inspection engineering” department to theorize, practice their ideas, and publish their methods. Through the 1930s additional advancements in control charting, acceptance sampling, and other statistical methods were developed, and as Dodge states, “All of these various techniques were interlocked to a greater or lesser degree in the various kinds of applications on telephone products”.²

As the United States prepared to enter World War II, there was great need to establish a government procurement standard that was efficient and effective due to the magnitude of the procurement activity. The original Dodge-Romig tables evolved and became the Army Services Forces Tables and slightly different Navy Tables.

After the war, the procedures merged to become nonmandatory joint Army-Navy JAN-STD-105, which the department of defense immediately rescinded and published in 1950 as MIL-STD-105A. After revision B of this standard in 1959, the American-British-Canadian working group developed ABC-STD-105, which after a few changes became MIL-STD-105D.³ In 1971 the procedure was adopted commercially and became ANSI/ASQ Z1.4, and in 1974, the International Standards Organization (ISO) adopted it as ISO2859.

The list of individuals engaged in conceiving, practicing, polishing, and writing MIL-STD-105 included: Dodge, Romig, and Shewhart, as well as George Edwards, Thornton Fry, Edward Molina, Paul Olmstead, Walther Bartky, Mary Torrey, Harold Freeman, Milton Friedman, Fredrick Mosteller, Leonard Savage, David Schwartz, W. Allen Wallis, Harold Bellinson, G. Rupert Gause, Lawrence Shaw, Leslie Simon, A. Stein, W. Edwards Deming, Joseph Juran, and others.

The more recent steps in the evolution of acceptance sampling, including aerospace recommended practice ARP9013 and AS9138 released in January 2018, are not aligned with the strategies of MIL-STD-105, and indicate that quality professionals have turned their backs on the idea of an “acceptable quality level” (AQL).

In the politically correct world of parts-per-million defective, MIL-STD-105 may be one of the most misunderstood and misapplied specifications ever. At this point, it would be purposeful to pause and question why these early pioneers would develop acceptance sampling procedures whereby nonconforming units are knowingly accepted when found in the sample. Was the idea of perfect quality beyond their comprehension? Are we smarter today with AS9138 than the early pioneers were nearly century ago, or are we missing a fundamental piece of the puzzle?

To find these answers, we should revisit the intention of the two procedures. While the focus of AS9138 is on isolated lot acceptance—particularly small lots, the focus of MIL-STD-105 is on acceptance of the process creating the product—particularly processes of infinite potential. This is a subtle but important distinction with philosophical and mathematical impact.

All processes have infinite potential, and the actual product they produce is only a sample, but for production processes, the duration is long enough to practice process control. To be more specific, the sampling plans of AS9138 focus on consumer risk, ignoring producer risk, and are based primarily on the hypergeometric distribution. The sampling procedures of MIL-STD-105 focus primarily on consumer risk but simultaneously recognize the existence of a process and are based on the binomial distribution for simple product, and the Poisson distribution for more complex product.

The difference in philosophy highlights the point that MIL-STD-105 is actually a “process control” specification that integrates process corrective action. But when should corrective action be sought? Care must be taken not to “tamper” with a process in its steady state for fear of actually increasing variation. Therefore a decision metric must be established for acceptance sampling so we know when to correct the process. If we explore the idea of AQL, we find the most current definition provided by AS9138 is: “The maximum percentage or proportion of nonconforming units in a lot or batch that, for the purposes of acceptance sampling, would be considered satisfactory as a process average.”

This is certainly a mouthful with many discussion points, but clearly the notion of process average and acceptance sampling are being tied together. Today we may believe that the idea of an “acceptable quality level” is outdated as we pursue zero defects or parts per million (PPM) quality levels. But, if PPM quality levels truly exist, then acceptance sampling is inappropriate because of the inability to detect this small proportion of nonconforming material. We must not speak of PPM quality levels on one hand, and practice acceptance sampling on the other.

More likely, the reality is that an organization employs many professionals who handle nonconforming material at various points in the process. For short run processes, perhaps through a roll of the dice, 100-percent conformity has been achieved, but most process will produce at least a small rate of nonconforming material. This steady-state nonconforming material rate can be considered the process AQL.³

Figure 1: From H.F. Dodge, H.G. Romig, “Relationship between consumer’s risk and producer’s risk,” from “Single Sampling and Double Sampling Inspection Tables,” The Bell System Technical Journal, January 1941

In figure 1, Dodge and Romig developed a sampling plan with the primary goal of protecting the consumer with 10-percent risk of accepting material, which is 3-percent nonconforming.⁴ Secondarily, they recognized a process that has a process-average proportion nonconforming of 0.0045 (0.45%). Their resulting acceptance sampling plan chooses the acceptance number that minimizes total inspection costs when considering screening. The point here is that Dodge and Romig are clearly recognizing the existence of a process having a process average. In fact, it was written into the early versions of MIL-STD-105 that the process average was to be estimated from the previous 20 cumulative lots submitted for inspection.³ In other words, there is a characteristic of “process control” to be considered in acceptance sampling plans.

To further illustrate the property of process control, the example of figure 2 is chosen from MIL-STD-105 for a lot size of 600 units under General Inspection Level II, Single Sampling, Normal Inspection, AQL = 1.0. This corresponds to Code Letter J, and sample size n=80. The decision criterion for process acceptance are accept on Ac=2 and reject on Re=3. The operating characteristic curve can easily be calculated using the binomial distribution (figure 2 left). Readers should take special note that when the lot presented for inspection is the same quality level as the process average (p=0.01), the probability of acceptance is 0.954 (0.046 producer risk). This decision criterion is clearly not set at 3σ (0.997) as would be standard control charting convention. In fact, using the standard normal distribution of Z values corresponding to 0.954, we see that the “decision limit” is set at 1.685σ.

Validating the Ac and Re numbers can be done in similar fashion to the ‘np’ control limit calculation appearing in figure 2 (right). Substituting 1.685σ instead of the conventional 3σ used for “control limits” yields a “decision limit” of 2.3. Therefore, when using “decision limits” on an ‘np’ chart for a process whose process average is 1 percent nonconforming, and the sample subgroup size of 80 units, we should accept the lot on two and reject on three nonconforming units.

Dodge would actually fix the AQL point as the process average, calculate the 3σ limit using the AQL value as if it were the process average, and switch to tightened inspection if the cumulative average of the past 20 lots exceeded this limit.⁵ Dodge further makes note that control charts were a part of standard procedure for the lot-by-lot sampling results for thousands of inspection layouts used in the shop process and final inspection.² We can actually plot on an np chart, with two sets of limits: decision limits for lot rejection and corrective action; and control limits for determining when to additionally switch to “tightened inspection.” The examples here serve to illustrate the link between “process control” and MIL-STD-105.

Figure 2: Single sampling plan n=80, Ac=2, Re=3 (left); and corresponding ‘np’ chart upper control limit (right)

MIL-STD-105 has its roots in process control, but it does have some practical shortcomings. First, the moral dilemma of knowingly accepting product when nonconformities are found in the sample. Second, large sample sizes are required in order to simultaneously protect the consumer and provide process control features. These difficulties are the core issues that have given appeal to the c=0 sampling plans of AS9138.

Readers should be aware that AS9138, paragraph E.2.1, does not provide an accurate accounting of the origin of AQL and furthermore provides a misleading inference that most product required during World War II were not critical. In fact, AQL was established to ensure equity between small suppliers and large suppliers providing exactly the same item, because c=0 plans favor the large supplier.^{1, 6} Second, it must be clear that any acceptance sampling procedure must never be applied to critical items, not MIL-STD-105 and not AS9138. It is misleading to imply that AS9138 is an appropriate solution.

In summary, AS9138 and MIL-STD-105 have fundamentally different objectives, and a direct comparison is inappropriate. AS9138 focuses on the judgment of isolated lots, and MIL-STD-105 focuses on process control. MIL-STD-105 has been largely misunderstood and has been misapplied by many organizations because of acceptance numbers greater than zero. There are some companies that have attempted to follow the sample sizes of MIL-STD-105 but force the acceptance number to zero, thereby invalidating the operating characteristic curves and destroying the consistency of the procedure. Dodge refers to the few c=0 sampling plans within MIL-STD-105D as “maverick” plans, not in harmony with the balance of the standard.³

But what if there was a third option? An option that is easily administered, offers the characteristics of process control, does not allow nonconforming units in the sample, and provides better consumer protection than the other choices? In my next article, I will introduce the notion of imaginary limit sampling procedures.

Sources cited
1. H.F. Dodge, H.G Romig, “A Method of Sampling Inspection,” The Bell System Technical Journal, pp. 613–631, October 1929.
2. H.F. Dodge, “Notes on the Evolution of Acceptance Sampling Plans, Part I,” Journal of Quality Technology vol. 1, No. 2, pp. 77–88, April 1969.
3. H.F. Dodge, “Notes on the Evolution of Acceptance Sampling Plans, Part III,” Journal of Quality Technology, vol 1, No. 4, pp. 225–232, October 1969.
4. H.F. Dodge and H.G. Romig, “Single Sampling and Double Sampling Inspection Tables,” The Bell System Technical Journal, pp. 1–61, January 1941.
5. H.F. Dodge, “Notes on the Evolution of Acceptance Sampling Plans, Part II,” Journal of Quality Technology, vol 1, No. 3, pp. 155–157, July 1969.
6. American Statistical Association, Journaled 105th annual meeting, Cleveland, Ohio, January 27, 1946. Special topic, “Acceptance Sampling,” pp. 45–51, pp. 48–50, published by ASA Washington D.C., 1950.

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