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I first considered writing an article to discuss strictly MIL-STD 1916,  Department of Defense Test Method Standard: DOD Preferred Methods for Acceptance of Product (see PDF file attached to this article). That standard replaced MIL-STD 105 and it is often quoted when discussing statistical sampling, but often with unrealistic expectations. I know what you are thinking, another statistical sampling article? I just can’t seem to get away from the subject. Anyway, I started to dive into the standard in order to explain how it is most useful and when it is more appropriate to stick to general, and more basic, statistical methods when I found myself reading about reliability engineering.

Do reliability engineering concepts apply to inventory accuracy? Do they apply to any business process? It turns out that they can, and there are concepts such as Markov Decision Process (MDP) that are often applied to business. 

If we consider physical inventory control as our system, then we can see how that system exists in one state at a time that depends on a previous state (like a Markov chain). The system, most of the time, relies on transactions that themselves have a probabilistic outcome that would have an effect on the state of our inventory.  For instance, if 2% of receipts and issues posted are in error.

This brings back some memories. I once wrote a paper on how a logistics information system can impact operational readiness (Ao) and how optimizing the information system could have a more beneficial impact on operational readiness than increasing the reliability of individual weapons systems, because improving Mean Logistics Delay Time (MLDT) improves Ao for all associated weapons systems, even those that have not yet been invented.

It is the same concept with physical inventory controls. The system for managing the inventory, including transactions, policies, and procedures can have a more significant impact on inventory accuracy than any other physical attribute or strictly inventory-related activity.

What does that mean exactly? That there are other blocks in the chain that we need to consider. For example, procurement transactions, database maintenance actions, etc.

So what does that mean for MIL-STD 1916? Although it would not be wrong to apply MIL-STD 1916 to statistical physical inventory sampling to measure accuracy, one would still have to get their hands dirty (sort to speak) in order to analyze and extrapolate the results in a way that they provide us with a measure of our inventory accuracy for our entire population. In order to measure our results to see if we meet DoD guidance, we would still need to compute sample size, margin of error, and confidence intervals using basic statistical processes, even if relying on tables and methods from MIL-STD 1916. That military standard lends itself more to what engineers and reliability analysts refer to as “zero accept, one reject” methods (see this paper by Al-Refaie and Tsao (2011)). 

So,  to tie back to the MDP concept, MIL-STD 1916 absolutely has a place in physical inventory controls, but most especially in evaluating the reliability and acceptability of the transactional processes that are part of our inventory reliability chain.  In other words, testing each block in the chain of processes that affect inventory, such as receipt, issues, transfers, etc. is an excellent application for this type of statistical analysis.

Book recommendation of the month. Well, not really a recommendation, but a suitable reference to the above article: Modeling for Reliability Analysis: Markov Modeling for Reliability, Maintainability and Supportability by Jan Pukite & Paul Pukite. Buy a used copy for $10, the book is not worth the full sticker price.

Recently, I have noticed an increased interest in questioning the validity of conducting statistical sampling inventories. Many people do not understand the concepts or the value of statistical sampling and that may be driving these perceptions.

This post includes some excerpts from a paper that I wrote some years ago. It establishes the relationship from the CFO Act of 1990 down to DoD guidance on the conduct of statistical sampling inventories.

The Chief Financial Officer’s (CFO) Act of 1990 (Public Law 101-576) Established Statutory Reporting Requirements Regarding Inventory and Assets under the Authority of the Agency’s CFO

The CFO Act of 1990 provides the statutory requirements that:

• Establishes the authority of an agency’s CFO including “directing, managing, and providing policy guidance and oversight of agency financial management personnel, activities, and operations.”
• Requires the implementation of sound financial management practices under the CFO including “the implementation of agency asset management systems, including systems for cash management, credit management, debt collection, and property and inventory management and control.”
• Requires the CFO to submit “an annual report to the agency head and the Director of the Office of Management and Budget.”

The Federal Financial Management Improvement Act (FFMIA) of 1996 (Public Law 104-208) Established Specific Statutory Audit Requirements

• The FFMIA establishes the periodicity of auditing requirements to annual by stating that “no later than October 1, 1997, and October 1, of each year thereafter, the Comptroller General of the United States shall report to the appropriate committees of the Congress.”
• Section 805, subparagraph (b), in essence gives the Office of Federal Financial Management the authority to put any agency on report (i.e. DoD) by requiring “a listing of agencies whose financial management systems do not comply substantially with the requirements of Section 3(a) the Federal Financial Management Improvement Act of 1996, and a summary statement of the efforts underway to remedy the noncompliance.”

DoD Financial Management Regulations (FMR)  implement Public Law 104-208 (FFMIA of 1996) and 101-576 (CFO Act of 1990)

• The DoD FMR, Chapter 4, paragraph 040305, establishes a clear relationship between inventory records and the general ledger by stating “activities must reconcile line item accountability records to balances recorded in the general ledger inventory accounts at least quarterly.”
• Additionally, the DoD FMR, Chapter 4, paragraph 040306, specifies physical count as the process used for reconciling inventories and general ledger: “Activities must take physical counts of inventories in accordance with the procedures prescribed in DoD 4140.1 R, “DoD Materiel Management Regulation.” Activities must adjust the general ledger for differences between the general ledger balances and the physical count.”

The DoD 4140.1-R Establishes Policies for Physical Counting and Gives Priority to Sampling Methodologies

• The DoD 4140.1-R, paragraph C5.7.5.1.4, directs DoD components to “devote resources and select items for physical inventory” as a means to comply with DoD FMR.  Paragraph C5.7.5.1.4.1 of DoD 4140.1-R gives number one priority to “annual random statistical samples that shall support the determination of logistics record accuracy and financial record accuracy.”

The DoD 4000.25-M Vol 2 Establishes Procedures for the Conduct of Statistical Sampling Inventories

• Paragraph C6.2.1.1 of DoD 4000.25-M reiterates that physical reconciliation is the material accountability method: “Ensure accurate property accountability records for the physical inventory are maintained in support of customer requirements and readiness by performing physical inventories and location surveys/reconciliations.”
• Paragraph C6.2.2.1 recognizes the impracticality and inefficiency of conducting complete inventories: “The dynamic nature of the physical inventory control function and the cost of counting and reconciling records require that the approach be more selective than the 100 percent wall-to-wall total item count concept.”
• Paragraph C6.2.10 of this instruction reiterates the policy in DoD 4140.1-R which gives top priority to sampling methodologies. Subparagraph C6.2.10.1 states “a stratified, hierarchical inventory sample shall be accomplished at least once annually for the purpose of validating the accuracy of the accountable record.”

 

References

• Chief Financial Officers (CFO) Act of 1990, (Public Law 101-76)
• Federal Financial Management Improvement Act (FFMIA) of 1996, (Public Law 104-208)
• Federal Managers Financial Integrity Act of 1982 (FMFIA) (Public Law. 97-255)
• Government Management Reform Act of 1994 (GMRA) (Public Law. 103-356)
• DLM 4000.25-2-M, “Military Standard Transaction Reporting and Accountability Procedures (MILSTRAP)”
• DoD 4140.1-R, “Material Management Regulation”
• DoD 7000.14-R, Department of Defense (DoD) Financial Management Regulation (FMR), Volume 4, Chapter 4, “Inventory and Related Property” (May 2009)

I have come to the conclusion that there are simply no good books on statistical sampling for novice practitioners. A lot of the literature begins by covering statistical principles, which is important, but statistics is such a large field that most people get turned off or lost. There is also a lot about the field of statistics that we don’t need to know, for our purposes. Which brings me to my latest book recommendation.

“Audit Sampling: An Introduction”, by Dan Guy, Douglas Carmichael, and Ray Whittington,  is perhaps the best book that I have been able to find. I have the Third Edition of this textbook and it is the most concise textbook that I have found on the subject. It is laid out precisely for auditors, meaning that there are not too many side-bars into statistical or mathematical theory. It is the closest thing that I have found to a step-by-step guide for audit sampling, although that is not what this book is. It is a textbook, in the traditional sense. It also includes some excellent appendices, such as the full text of Statement of Auditing Standards (SAS) No. 39: Audit Unit (AU) 350 – Audit Sampling.

I recently revisited this textbook while preparing for some discussions for an upcoming project. This inspired me to put together a presentation to try to condense the topic of statistical sampling of physical inventory down to its simplest tasks: Planning, Selection, and Evaluation.

In the Planning phase, we are concerned with establishing the statistical parameters, such as the confidence level and margin of error – which, in many cases, are given to us.  We use those parameters during this phase to calculate the sample size (see my previous post).

The Selection phase is concerned with randomly choosing the samples to be tested.

Finally, the Evaluation phase consists of testing the samples, computing the results, and reporting our findings.

I put together a slightly expanded version of the above in my own Sampling Guide, available for download from this link.

 

In DoD, the parameters for a statistical sampling inventory are usually dictated. For example, DLM 4000.25-2 lists the confidence level at 95% with a margin of error of +/- 2.5% for most inventories. That should be enough information to proceed with sampling.

However, I often get asked questions about statistical sampling as it relates to inventory. By far, the most common question that I get asked is how to determine the sample size.  There is no shortage of sources, including those in my previous article, that cover this subject and even provide reference tables.

Unfortunately, there is also no shortage of businesses and organizations that take advantage of the situation to try to make money.  If you are someone concerned with DoD Financial Improvement Audit Readiness (FIAR), and follow the trail from OMB Circular A-123 to Audit Unit (AU) Section 350, and search for guidance on statistical sampling, you will likely arrive at many for-sale products. The American Institute of Certified Public Accountants publication on audit sampling is one of many examples; at $99 a copy, I cannot recommend it, so please do not waste your money.

Some time ago, after helping someone with a question about sample size, the person asked me how I knew this and whether it was ok for the government to use “my” method. I proceeded to inform that person that statistics is mathematics and, despite what the AICPA wants to sell on their web site, it is not a proprietary method. Therefore, any statistics textbook is a perfectly good reference to validate any statistical method.

So I decided many years ago to develop a spreadsheet meant to illustrate and teach how sample size is calculated. Over the years, I have shared it and people keep asking me for it to this day.  If you would like to use it, here is the link: http://www.ncg-consulting.com/files/StatisticalSamplingInventory_v2.xlsx

 

As I discussed a while back, statistical sampling is one of the best methods to establish the validity of inventory without having to embark on lengthy and expensive wall-to-wall inventories.

However, there can be a lot of confusion as to how to actually perform statistical sampling inventories and what it all means.  So let me begin by recommending two publications that I believe offer excellent background.

The first one is Sampling Techniques (3rd ed.) by William G Cochran.  This is a textbook (meaning that it is expensive), but one can find used copies online for under $15. It is extremely comprehensive and perhaps too advanced for our needs. However, it is the best textbook on the subject available for the money, in my opinion.

The next book I will recommend is actually free. The best all around publication, in my opinion, on concepts and techniques for conducting statistical tests is GAO’s Using Statistical Sampling, publication PEMD-10.1.6, freely available online for download. Click on the image above to go to the site.

Now, after sending you reading, I should say that, in order to conduct a statistical sampling inventory we need to know very little statistics.  A lot of the confusion is driven by the terminology and interpretation, which is why it helps to understand the background.

 

To those unfamiliar with the field of military logistics, it might come as a surprise that the discipline they understand simply as “logistics”, in its full breadth and scope, is actually Logistics Engineering science.  Although my job has me spending a lot of time on the field in warehouses and labs, even members of my own family express surprise when they learn that my academic background is in computer science and mathematics. People who are familiar with concepts such as reliability engineering, forecasting, and data analytics, immediately understand the relationship between logistics and engineering.

After I retired from the Navy, I was fortunate to join the American Society of Naval Engineers (ASNE) and felt right at home. Even more so, after I read their code of ethics and recognized it as many of my own personal principles that I had been following throughout my career. Therefore, I would like to share those principles with the readers and hopefully they will be of use:

American Society of Naval Engineers (ASNE) Code of Ethics

1. We will only accept assignments we are qualified to perform, and we will perform at a high level of professional competence.

2. We will conduct ourselves in accordance with both the letter and the spirit of the applicable laws and regulations of jurisdictions where we perform engineering within our discipline.

3. We will be alert to the totality of our conduct so that a series of actions, each falling within the technical parameters of the law, when viewed together will not give the appearance of improper or unethical behavior.

4. We will not accept assignments that place us in conflicting roles that may bias our objectivity or judgment. Compensation will not be accepted from more than one party, even if permitted by law, without the full knowledge of all parties involved. Real or apparent conflicts of interest will be fully disclosed to the affected clients at the earliest opportunity.

5. We will not disclose sensitive information to third parties without specific authorization. Sensitive information obtained will be safeguarded from disclosure.

6. We shall neither discriminate against nor deny equal professional service to any person for reasons of age, race, creed, sex, or country of national origin.

7. We shall neither seek unfair advantage over other naval engineers nor publicly disparage the professional performance of another engineer and shall perform engineering within our discipline so as to avoid unnecessary controversy.

8. We shall conduct business and advertise in a restrained and highly professional manner avoiding exaggeration and misrepresentation.

9. We will work to the mutual benefit of the Society and the Naval Engineering profession by sharing the lessons of experience and professional study with fellow naval engineers.