An adaptive acceptance test design for an RMS parameter

Abstract

One of the most difficult problem areas encountered in advanced avionic is the verification by testing that the delivered product meets the agreed-to and specified design requirements. In a majority of cases, the details and the criteria, by which seller will assure buyer that the product meets the design commitments, are left to be defined after contract award. This invariably leads to disagreements between buyer and seller, which are settled only after long, costly negotiations. In recent System developments, the is to be question has been properly addressed by including a Verification Cross Reference Index in the back of the specification. This matrix and proper description in the Quality Assurance section of the procurement specification will identify which design requirements must be tested and the type of test required (i. e., qualification testing, acceptance testing, analysis, etc). What has often been overlooked in the past is a clear definition of buyer/seller risk, sample size requirements for critical parameters, and the general question of . . . What test design is adequate on a critical parameter to demonstrate specification compliance? This paper proposes a solution to that question for those parameters, critical to the accuracy of the system, which have performance specified by RMS values. The concept presented could, with proper mathematical changes, be extended to any set of other parameters. The key idea is to specify, in the procurement specification, the criteria by which critical parameters will be verified. This paper presents a statistical technique, the results of which may be placed in a procurement specification, to establish an equitable buyer/seller risk on parameters critical to system performance. The technique is designed to adapt the acceptance requirement to the actual manufacturing process in a manner which allows the seller maximum flexibility without affecting the buyer's risk. Procedures and example curves for implementation are presented. A technique is presented in this paper which uses ensemble test data to refine initial assumptions and has as its primary goal that the real buyer and seller risks be as equal as possible at the conclusion of the production contract. In this paper, the real buyer's risk is . . . Given that with true performance in excess of the contractual specification are manufactured, what is the cumulative probability of these being accepted? In a like manner, the real seller's risk is . . . Given that with performance equal to or better than the contractual specification are manufactured, what is the cumulative probability of these being rejected? As will be shown later in this paper, the proposed test is fair to the seller, since, in the long run, he is guaranteed of selling a system for every system he builds (tests) which has performance as good as or better than contractual requirements. The technique is also fair to the buyer since the ensemble of he actually buys will perform better than the specification requirement. The technique presented could also allow the control of other criteria. One of the most prominent of these other criteria would be assurance that at the completion of the production program, the RMS performance capability of the ensemble of delivered is at least as good as the RMS performance requirement in the procurement specification. Indeed, there are many other such concepts. However, the writer believes that the concept of true, equal buyer/seller risk has the most appeal, since it tends to suppress the buyer's fear of dog systems while retaining a fairness in yield ratio for the seller. Accordingly, this paper will address itself only to the concept of equality of buyer and seller's risk as defined above. In the pursuit of this or any other concept involving the design of an acceptance test, it must be noted that the procurement specification requires performance over the time and environmental conditions. The acceptance test is conducted, in almost all cases, on new equipment and in a relatively benign environment. Accordingly, the test design must transform the RMS value in the procurement specification to a smaller RMS value which is appropriate to the environment and the newness of the equipment at time of test. This may be done by detailed analysis, or simply by reduction by an arbitrary percentage. It is suggested that, if the principles presented in this paper were incorporated into the verification or quality assurance section of the procurement specification at the time of contract bidding, the numerous and bitter arguments concerning acceptance test requirements which usually arise after contract award would be avoided. In addition, contracts could be bid with reasonable knowledge of yield factors; and contracts could be awarded with reasonably firm knowledge of what will end up in the field.