Fault detection and diagnosis of gear transmission systems have attracted considerable attention in recent years, due to the need to decrease the downtime on production machinery and to reduce the extent of the secondary damage caused by failures. However, little research has been done to develop gear shaft and planetary gear crack detection methods based on vibration signal analysis. In this thesis, an approach to gear shaft and planetary gear fault detection based on the application of the wavelet transform to both the time synchronously averaged (TSA) signal and residual signal is presented. Wavelet approaches themselves are sometimes inefficient for picking up the fault signal characteristic under the presence of strong noise. In this thesis, the autocovariance of maximal energy wavelet coefficients is first proposed to evaluate the gear shaft and planetary gear fault advancement quantitatively. For a comparison, the advantages and disadvantages of some approaches such as using variance, kurtosis, the application of the Kolmogorov-Smirnov test (K-S test), root mean square (RMS) , and crest factor as fault indicators with continuous wavelet transform (CWT) and discrete wavelet transform (DWT) for residual signal, are discussed. It is demonstrated using real vibration data that the early faults in gear shafts and planetary gear can be detected and identified successfully using wavelet transforms combined with the approaches mentioned above. In the second part of the thesis, the planetary gear deterioration process from the new condition to failure is modeled as a continuous time homogeneous Markov process with three states: good, warning, and breakdown. The observation process is represented by two characteristics: variance and RMS based on the analysis of autocovariance of DWT applied to the TSA signal obtained from planetary gear vibration data. The hidden Markov model parameters are estimated by maximizing the pseudo likelihood function using the EM iterative algorithm. Then, a multivariate Bayesian control chart is applied for fault detection. It can be seen from the numerical results that the Bayesian chart performs better than the traditional Chi-square chart.

Fault detection and diagnosis of gear transmission systems have attracted considerable attention in recent years, due to the need to decrease the downtime on production machinery and to reduce the extent of the secondary damage caused by failures. However, little research has been done to develop gear shaft and planetary gear crack detection methods based on vibration signal analysis. In this thesis, an approach to gear shaft and planetary gear fault detection based on the application of the wavelet transform to both the time synchronously averaged (TSA) signal and residual signal is presented. Wavelet approaches themselves are sometimes inefficient for picking up the fault signal characteristic under the presence of strong noise. In this thesis, the autocovariance of maximal energy wavelet coefficients is first proposed to evaluate the gear shaft and planetary gear fault advancement quantitatively. For a comparison, the advantages and disadvantages of some approaches such as using variance, kurtosis, the application of the Kolmogorov-Smirnov test (K-S test), root mean square (RMS) , and crest factor as fault indicators with continuous wavelet transform (CWT) and discrete wavelet transform (DWT) for residual signal, are discussed. It is demonstrated using real vibration data that the early faults in gear shafts and planetary gear can be detected and identified successfully using wavelet transforms combined with the approaches mentioned above. In the second part of the thesis, the planetary gear deterioration process from the new condition to failure is modeled as a continuous time homogeneous Markov process with three states: good, warning, and breakdown. The observation process is represented by two characteristics: variance and RMS based on the analysis of autocovariance of DWT applied to the TSA signal obtained from planetary gear vibration data. The hidden Markov model parameters are estimated by maximizing the pseudo likelihood function using the EM iterative algorithm. Then, a multivariate Bayesian control chart is applied for fault detection. It can be seen from the numerical results that the Bayesian chart performs better than the traditional Chi-square chart.

Avoidable rework constitutes a large part of development projects, i.e. 20-80 percent depending on the maturity of the organization and the complexity of the products. High amounts of avoidable rework commonly occur when having many faults left to correct in late stages of a project. In fact, research studies indicate that the cost of rework could be decreased by up to 30-50 percent by finding more faults earlier. However, since larger software systems have an almost infinite number of usage scenarios, trying to find most faults early through for example formal specifications and extensive inspections is very time-consuming. Therefore, such an approach is not cost-effective in products that do not have extremely high quality requirements. For example, in market-driven development, time-to-market is at least as important as quality. Further, some areas such as hardware dependent aspects of a product might not be possible to verify early through for example code reviews or unit tests. Therefore, in such environments, rework reduction is primarily about finding faults earlier to the extent it is cost-effective, i.e. find the right faults in the right phase. Through a set of case studies at a department at Ericsson AB, this thesis investigates how to achieve early and cost-effective fault detection through improvements in the test process. The case studies include investigations on how to identify which improvements that are most beneficial to implement, possible solutions to the identified improvement areas, and approaches for how to follow-up implemented improvements. The contributions of the thesis include a framework for component-level test automation and test-driven development. Additionally, the thesis provides methods for how to use fault statistics for identifying and monitoring test process improvements. In particular, we present results from applying methods that can quantify unnecessary fault costs and pinpointing which phases and activities to focus improvements on in order to achieve earlier and more cost-effective fault detection. The goal of the methods is to make organizations strive towards finding the right fault in the right test phase, which commonly is in early test phases. The developed methods were also used for evaluating the results of implementing the above-mentioned test framework at Ericsson AB. Finally, the thesis demonstrates how the implementation of such improvements can be continuously monitored to obtain rapid feedback on the status of defined goals. This was achieved through enhancements of previously applied fault analysis methods. / Avhandlingen handlar om hur en mjukvaruutvecklingsorganisation kan hitta fel tidigare i utvecklingsprocessen. Fokus ligger på att hitta rätt fel i rätt fas, d.v.s. när det är som mest kostnadseffektivt. Avhandlingen presenterar en samling fallstudier utförda inom detta området på Ericsson AB. Nyckelord: processförbättring, felanalys, tidig feldetektering