#sequential testing processing

[conceptsjust]

Sequential testing processing

#Sequential testing processing Patch#

#Sequential testing processing software#

The test was terminated after 15 cumulative samples were taken. Table 3 lists an ASN of 23 for this test at the desired standard deviation level of 12.5. The Excel spreadsheet outputs are illustrated in Table 2, Figure 1 and Table 3. The sequential sampling parameters s0=12.5, s1=24.3, a=0.001 and b=0.001 are chosen for the study. The cloth manufacturer accepts the customer’s specification based on a standard deviation comparison of New Machine A with the historical results obtained for older equipment. The specification range (USL-LSL) in this case is 100 pounds and the maximum allowable process standard deviation calculates as 100/(6 x 1.33) = 12.5 pounds.

#Sequential testing processing Patch#

A Process Capability Application Example 1Ī textile customer specifies an average burst strength and tolerance of 120 pounds +/- 50 pounds for each patch of manufactured cloth and further requires a minimum C p of 1.33. The ASN estimates the average number of samples required for a decision at a specified standard deviation s since the exact number is not known beforehand. The expansion of inequality (2) results in expression (4) below: The test is continued when (2) b/(1-a) = (1-b)/a. For each value of N, the probability ratio P1N/PON is calculated. The test is continued when inequality ratio (2) applies and discontinued at the first occurrence of the ratios (1) or (3) resulting in the acceptance of hypotheses H0 or H1 respectively.Īs an example of test principle usage, consider the sequence of observations X1…XN from a normally distributed process with a known mean m and unknown standard deviation s, where the test hypothesis is s = s1. Where P0N, P1N are the probability density functions corresponding to the test H0 and alternate H1 hypothesis for the sequential set of observations X1…XN, and a, b are the selected Type I (producer’s risk) and Type II (consumer’s risk) errors. The basis for Wald’s sequential test are the probability inequality ratios: Examples of the mentioned 50 percent sampling economy can be found in the document. Numerous examples of the theory’s practical applications and sampling saving economies were later published1 by the Statistical Research Group of Columbia University. Historically, sequential testing results from the theory of sequential analysis that was created by WALD 2 in 1943 for war time military equipment development and inspections. Sequential test or inspection plan sample sizes are dependent on the outcome of the observations and require three decisions: 1) accept the test hypothesis, 2) take another observation and 3) reject the test hypothesis. With the exception of double sampling, most accept/reject inspection decisions assume that the observational numbers are independent of the results and require a predetermined sample size. Hence, for a selected USL-LSL specification range, any sampling decision on whether a process is capable is dependent upon the process standard deviations s0 ( C p > 1 ) s1 ( C p = 1.33). Applying Wald’s Sequential Test Method to Process Capability DecisionsĪ process is defined as capable when the determined statistical control limits are at least equal to or within the specification limits and deemed incapable whenever the control limits lie outside of the specification limits.

#Sequential testing processing software#

It is also both computer user and spreadsheet software friendly. The sequential test method for process capability decisions described below will often result in a 50 percent sampling saving when compared with the most powerful classical tests. Our rapid pace and highly competitive industrial environments often require expeditious decisions/actions in the above areas and an automated statistical method which minimizes sampling during these studies would be highly desirable. Process changes and/or improvements need to be evaluated.The capability of a process to meet customer specifications needs to be determined or.Engineering tolerances are reviewed against the observed variability of the process and/or new equipment is evaluated,.Process capability ( C p) studies are usually performed whenever:

[tonkieye]

Sequential testing processing

#Sequential testing processing install#

#Sequential testing processing serial#

Alpha and/or beta spent at each stage is reported. Corresponding P-Value boundaries are given for each boundary statistic. Futility boundaries can be binding or non-binding. Boundaries can be computed based on popular alpha- and beta-spending functions (O’Brien-Fleming Analog, Pocock Analog, Hwang-Shih-DeCani Gamma family, linear) or custom spending functions, or boundaries may be input directly, if desired. The spacing of the stages can be equal or custom specified. For one- and two-sided tests, efficacy and/or futility boundaries can be generated. Superiority by a Margin Tests for One Poisson Rate (Simulation)Įach of these procedures can be used to determine power, sample size and/or boundaries for the corresponding group-sequential test.Non-Inferiority Tests for One Poisson Rate (Simulation).Tests for One Poisson Rate (Simulation).Superiority by a Margin Tests for Two Poisson Rates (Simulation).Non-Inferiority Tests for Two Poisson Rates (Simulation).Tests for Two Poisson Rates (Simulation).Superiority by a Margin Tests for One Hazard Rate (Simulation).Non-Inferiority Tests for One Hazard Rate (Simulation).Superiority by a Margin Tests for Two Hazard Rates (Simulation).Non-Inferiority Tests for Two Hazard Rates (Simulation).Tests for Two Hazard Rates (Simulation).Logrank Tests of Two Survival Curves assuming Proportional Hazards.Logrank Tests of Two Survival Curves assuming Exponential Survival.Superiority by a Margin Tests for Two Proportions using Odds Ratios (Simulation).Superiority by a Margin Tests for Two Proportions using Ratios (Simulation).Superiority by a Margin Tests for Two Proportions using Differences (Simulation).Superiority by a Margin Tests for Two Proportions (Simulation).Non-Inferiority Tests for Two Proportions using Odds Ratios (Simulation).Non-Inferiority Tests for Two Proportions using Ratios (Simulation).Non-Inferiority Tests for Two Proportions using Differences (Simulation).Non-Inferiority Tests for Two Proportions (Simulation).Tests for Two Proportions using Odds Ratios (Simulation).Tests for Two Proportions using Ratios (Simulation).Tests for Two Proportions using Differences (Simulation).Tests for Two Proportions – Unequal n’s.Superiority by a Margin T-Tests for Two Means (Simulation).Non-Inferiority T-Tests for Two Means (Simulation).Superiority by a Margin Tests for Two Means with Known Variances (Simulation).Non-Inferiority Tests for Two Means with Known Variances (Simulation).Non-Inferiority Tests for Two Means – Mann-Whitney Test.Tests for Two Means (Simulation) General Assumptions – Mann-Whitney Test.Tests for Two Means (Simulation) General Assumptions.Tests for Two Means (Simulation) Assuming Normality.Tests for Two Means with Known Variances (Simulation).Tests for One Mean with Known Variance (Simulation).The various group-sequential sample size calculation procedures in PASS allow you to study the power and sample size for an expanding list of scenarios: For more details about group-sequential analysis and sample size re-estimation in NCSS, you can click here.

#Sequential testing processing install#

For more details about group-sequential tests in PASS, we recommend you download and install the free trial of the software. The group-sequential tools in PASS are easy-to-use and validated for accuracy. PASS includes procedures for power analysis and sample size calculations for many different one-sample and two-sample group-sequential cases. We show that a key benefit of modular product architecture lies in the reduction of testing cost.Sample Size for Group-Sequential Tests in PASS Finally, we analyze the relationship between testing strategies and the structure of design hierarchy. Using information theory to measure the test efficiency, we further show that in the case of imperfect testing (due to noise or simulated test conditions), the attractiveness of parallel strategies decreases. We derive the optimal testing strategy as a function of testing cost, prior knowledge, and testing lead time.

#Sequential testing processing serial#

We model this trade-off in the form of a dynamic program and derive the optimal testing strategy (or mix of parallel and serial testing) that minimizes both the total cost and time of testing. Parallel testing has the advantage of proceeding more rapidly than serial testing but does not take advantage of the potential for learning between tests, thus resulting in a larger number of tests. An important managerial problem in product design in the extent to which testing activities are carried out in parallel or in series.

[longstand]

Sequential testing processing

Array methods such as frequency-wavenumber analysis can be applied to this set of correlation traces to help guarantee the validity of detections and lower the detection threshold. The basic procedure is to perform correlation on the individual channels, and then stack the correlation traces using zero-delay beam forming. A primary focus of this project has been the application of waveform correlation techniques to seismic arrays. A periodic analyst review will then be applied to verify the performance and, if necessary, adjust and consolidate the master event set. These additional master events are generated by an independent, conventional detection system. By this we mean that the detector is initiated using a basic set of reference ('master') events to be used in the correlation process, and then an automatic algorithm is applied successively to provide improved performance by extending the set of master events selectively and strategically. The principal goal is to develop an adaptive processing algorithm. The overall objective has more » been to develop and test a new advanced, automatic approach to seismic detection using waveform correlation. This final report summarizes the results of a three-year cooperative project undertaken by NORSAR and Lawrence Livermore National Laboratory. These algorithms are therefore effective at detecting repeating events, such as explosions and aftershocks at a specific location. matched filter) that is correlated against a continuous, possibly multichannel, data stream to detect new occurrences of that same signal. The basic concept is that a representative event waveform is used as a template (i.e. « lessĬorrelation detection is a relatively new approach in seismology that offers significant advantages in increased sensitivity and event screening over standard energy detection algorithms. Questions still to be answered are pointed out. This paper presents an overview of the current technology. Current criteria may require periodic statements with respect to materials loss the analysis procedures must be structured to provide such information. Significant work has been done on loss estimators, but their role in the materials accounting decision process has only begun to be examined. Control of the overall false-alarm rate is an important requisite of the composite procedure. For example, we must more » select the most appropriate combinations, which implies some consideration of possible diversion scenarios, such as abrupt or protracted. These questions lead to considering combinations of materials balances, which exposes a whole new set of concerns. The emphasis on accounting in which balances may be drawn on a daily or weekly basis, raises anew questions in these two areas: (1) what is the most effective means of extracting the maximum amount of information and (2) how should safeguards decision-makers use the results, and what impact does the decision process have on the analysis techniques. With materials balances taken at intervals, methods for treating materials balance data and their use by safeguards decision-making are relatively straightforward. Using examples, the implications for managerial practice are discussed and suggestions for further research undertakings are provided.= , If sequential tests are increasing refinements of one another, managers should invest their budgets in a few high-fidelity tests, whereas if the tests identify problems independently of one another it may be more effective if developers carry out a higher number of lower-fidelity tests. Third, the relationship between sequential tests can have an impact on optimal testing strategies. Second, a simple form of our model results in an EOQ-like result: The optimal number of tests (called the Economic Testing Frequency or ETF) is the square root of the ratio of avoidable cost and the cost of a test. First, optimal testing strategies need to balance the tension between several variables, including the increasing cost of redesign, the cost of a test as function of fidelity, and the correlation between sequential tests. An analysis of the model results in several important findings. In this paper, we develop a mathematical model that treats testing as an activity that generates information about technical and customer-need related problems. A fundamental problem in managing product development is the optimal timing, frequency, and fidelity of sequential testing activities that are carried out to evaluate novel product concepts and designs.