An approach to reliability growth planning based on failure mode discovery and correction using AMSAA projection methodology

Abstract

Exact expressions for the expected number of surfaced failure modes and system failure intensity as functions of test time are presented under the assumption that the surfaced modes are mitigated through corrective actions. These exact expressions depend on a large number of parameters. Functional forms are derived to approximate these quantities that depend on only a few parameters. Such parsimonious approximations are suitable for developing reliability growth plans and portraying the associated planned growth path. Simulation results indicate that the functional form of the derived parsimonious approximations can adequately represent the expected reliability growth associated with a variety of patterns for the failure mode initial rates of occurrence. A sequence of increasing MTBF target values can be constructed from the parsimonious MTBF projection approximation based on the following:(1) planning parameters that determine the parsimonious approximation; (2) corrective action mean lag time with respect to implementation and; (3) test schedule that gives the number of planned Reliability, Availability, and Maintainability (RAM) test hours per month and specifies corrective action implementation periods.

Reliability growth by failure mode removal

“…Following [7], assume μ k is a realization of independent identically distributed random variables with distribution function…”

“…We assume all FMs are present initially; the times between activations of a single FM are independent identically distributed having distribution (7). Focus on inferring status of an FM type k at the end of testing occurring at time D þ T using information from test results during D. Apply Bayes' formula to remove the condition on μ k , given experience during D to obtain these explicit forms:…”

“…Failure mode removal from any system, both hardware and software, is a dynamic uncertain process; see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] for various discussions of problem approaches. In [5,6,8,9,16] an unknown number of FMs are supposed present in the system initially, and the subsequent random times until FM activations are independent and identically distributed; in [8,9] the unknown number of failure modes is assumed deterministic and asymptotic arguments are used for its estimation; in [5,6] the unknown number of FMs has a Poisson distribution, and estimation of the Poisson mean is discussed; [13] includes a Bayesian treatment of the general model; [16] considers a dynamic statistical model for mean number of FMs remaining.…”

“…In [18,19] a neural network approach is discussed. In [7,9] reliability growth models are suggested for the management of system testing. In [10] a series system of subsystems with resulting FM masking is considered.…”

Reliability growth planning for discrete-use systems

“…Whilst all of these RG planning models are for continuous-use systems and have proven to be useful over the years there are notable technical shortcomings of methods based on the Duane Postulate. These technical issues, outlined in ATEC IPG 09-1 [15], have not only been observed from decades of lessons learned in RG planning but also constitute the impetus for advancing second generation models like PM2-continuous [16,17] and its discrete analogue presented herein.…”