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The 5th European DoE User Meeting, 10 July, 2014Cambridge, UKThomas Burns, Engineering PrincipalStarkey Hearing Technologies, Inc.Robust design of directional microphone arrays for hearing aidsStarkey Template v7 3.7.081Omni to Directional Mode: Left ear

Oblique ViewBirds Eye ViewA hearing aid in directional mode of operation suppresses sound energy from the rear while accentuating sound energy from the front. The idea is that a hearing aid user in a cocktail party will want to hear the person theyre speaking to in the front, while suppressing babble noise from the rear.Starkey Template v7 3.7.082Background Directional Microphone ArraysMost effective at improving speech intelligibility in noise.1dB of DI = 10% HINT improvement Dual Omni EndfireSimplest Tri Omni EndfireHigher DIDual Dipole OmniHigher DI, Most RobustRobustnessDesign of Experiments methods (Deming, Taguchi)Directional microphone arrays have been used in hearing aids since the 1970s and have been clinically proven to be the most effective way to improve speech intelligibility in noise; a one dB increase in the directivity index has yielded approximately 10% improvement in hearing in noise tests. The most common directional array in hearing aids utilizes two closely-spaced, omnidirectional microphones in a delay-and-sum configuration. A less common utilizes three closely-spaced, omnidirectional microphones in a delay-and-sum configuration. A third configuration, introduced here in this paper as a dual dipole omni (DDO) array utilizes two differential mics spaced closely and symmetrically around an omni microphone. Design of Experiments (DOE) methods are used to show how this third configuration is the most robust for directional performance when worn in situ.

Genichi Taguchi, together with W. Edwards Deming, pioneered the modern quality manufacturing movement following the Second World War. Taguchi and other prominent statisticians realized that although excessive variation was the root cause of poor manufacturing quality, chasing individual items in and out of specification was counterproductive. It was more cost effective to design a system whose performance (i.e., response) did not change with variations (i.e., levels) in the design inputs (i.e., factors). He called it robust design and published books describing the many case studies he performed using Design of Experiments (DOE) methods in various engineering disciplines. The 1953 case study involving the Ina Seito Tile manufacturer in Japan has become highly publicized in this effort to promote DOE methods.Starkey Template v7 3.7.083Taguchi Paradox?...Excessive variation is the root cause of poor manufactured quality.

Chasing individual items in/out of specification is counterproductive.

Robust Design1953: INA, a Japanese manufacturer of ordinary bathroom tile had built a brand new kiln at a cost of US $500k. It had such an uneven heating pattern that all fired tiles broke and crumbled without fail before they could be shipped. INA was on the verge of bankruptcy. In a paradigm shift, Taguchi changed the problem from one of rebuilding the kiln to one of making an improved slurry mixture (the tile paste) that could withstand a heavy dose of uneven heating and still transform itself into perfectly good bathroom tile.

Taguchi identified eight active ingredients used in the slurry mixture. Each ingredient could be added to the mixture in various strengths. The goal was to find the optimal combination of all eight strength levels (one level per ingredient) leading to durable bathroom tile.

Wait a minute, INA officials complained! There isnt enough money to carry out your test program of 28 trials or 256 batches of slurry in order to test all possible slurry combinations. Taguchi was able to conduct a successful test program using a fractional factorial design consisting of 16 individual trials (and a few extra trials thrown in for good measure). INA was saved. (from internet)Starkey Template v7 3.7.084Directional RobustnessFactorsSensitivity matching, Phase matching, In-situ placementLevelsSensitivity matching: +3dBPhase matching: +30sIn-situ: Directional Axis +10 re: horizonResponseDirectivity IndexUnidirectional IndexIn the case of directional hearing aids, the important factors for high performance include the sensitivity and phase matching of the microphones due to environmental drift, and also the in situ placement on the pinna as related to acoustical scattering from the head and torso. Over the average life (4 years) of a hearing aid, these factors can drift +3dB and +30microseconds, respectively. In addition, a dispensing audiologist can fit the hearing aid in situ on the pinna such that the directional angle of the microphone array is +10 referenced to the horizon, though in practice it is more common to see hearing aids fit with the directional axis 30 above the horizon. The responses that characterize the directional performance of the hearing aid includes the directivity index (DI), which is the ratio of the freefield on-axis (target) sound power to the isotropic noise, and the Unidirectional Index (UI) which is the ratio of the isotropic noise of the front hemisphere (target) to the rear hemisphere (noise). It should be noted that here are other important factors in the design of directional systems such as aperture distance and white noise gain; the white noise gain is improved by 6dB for every doubling of aperture distance. Unfortunately, we dont have the luxury of large apertures in hearing aids. The widest commercial aperture is typically 14mm, found in the largest standard devices fit behind the ear, and the smallest aperture is about 5mm, found in custom devices fit in the ear canal. For this study, an aperture distance of 8.5mm was chosen for the arrays, as dictated by the mechanical design constraints of stacking the three microphone array. It should be noted that all three arrays can be engineered to have commensurate white noise gain.Starkey Template v7 3.7.085Dual Omni (DO)

Directional axisFR8.5 mm

TimeDelayInvert

Dipole0 sSupercardioid17 s

Cardioid29 sDual omnis are commonly used in delay-and-sum hearing aid configurations; the rear microphone output signal is inverted in polarity, delayed in time, and summed with the front output to produce any of the classic freefield polar patterns. Zero microseconds of delay produces a dipole pattern, sometimes referred to as a figure-eight or bidirectional. For a 1 cm spacing, ten microseconds produces a hypercardioid, seventeen microseconds produces a supercardioid, and twenty-nine microseconds a cardioid. It should be noted that although the angle of maximum sensitivity response (MRA) can flip along the directional axis, it cannot be steered to any other angle.Starkey Template v7 3.7.086OFAT degradation due to dual omni driftDegraded Pattern due to Mismatch250Hz500Hz1kHz2kHz4kHz0.3dB0.6dB1.1dB1.3dB2.4dB2 phase(22sec)4 phase(22sec)8 phase(22sec)16 phase(22sec)32 phase(22sec)

AmplitudePhase

DI=6dBHypercardioidIn the past, microphone drift mismatch was studied by varying One Factor At a Time (OFAT). For plane wave incidence, consider the freefield DI degradation for the case where the sensitivity mismatch due to drift occurs while the phase mismatch is constant, and vice versa. In order to degrade the DI by 2dB, the amount of sensitivity mismatch is dependent on frequency whereas the time-delay mismatch due to drift is constant. Nevertheless, it can be generally seen that sensitivity mismatch smudges the depth of the null while phase (time-delay) mismatch shifts the angle of the null, thereby causing the main lobe to implode on itself with only moderate values of time-delay mismatch.

In setting up the DOE for the DDO, sensitivity and time-delay mismatch was referenced to the central omni mic thus giving four mismatch quantities; namely, the Front-to-Omni mismatch and the Rear-to-Omni mismatch. Any Front-to-Rear mismatch would show up as an interaction in the ANOVA of the DOE. Taking ratios of input factors is a common method to simplify the problem, reduce the number of runs, and avoid the need for a transformation of the resulting response data.

Similarly, in setting up the DOE for the tri-omni, sensitivity and time-delay mismatch was referenced to the central omni mic thus giving four mismatch quantities; namely, the Front-to-Middle mismatch and the Rear-to-Middle mismatch for both sensitivity and time-delay (phase).

DOE is a more revealing process than OFAT for studying the physical system because all factors vary simultaneously over their respective levels. In addition, ANOVA is used on the output response to create, in most cases, a quadratic function that predicts the output response based on the input factors and their interactions. This is more useful than Monte-carlo analysis because ANOVA can also be used to prioritize which factors are the most important in predicting the output response, thereby providing the most effective strategy for design optimization.Starkey Template v7 3.7.087Tri Omni (TO)

MR8.5 mm

FInvert4s Time DelayDirectional axis8s Time Delay6dB

2kHzThree omnis can also be used in delay-and-sum hearing aid configurations; the middle microphone output signal is inverted in polarity, delayed in time, and summed with the front output and also summed with a delayed version of the rear output to produce a second order polar patterns of DI~9.5dB. It should be noted that although the angle of maximum sensitivity response (MRA) can flip along the directional axis, it cannot be steered to any other angle. The values shown here optimize the directional performance in freefield; when the device is placed in-situ, much different values are used to optimize directional performance. Well refer to in-situ optimized conditions as baseline.Starkey Template v7 3.7.088

Dual Dipole Omni (DDO)OmniFront DipoleRear DipoleDirectional axisFRONTREAR8.5 mm-47dB

2kHz250 sec Delay256 sec DelayThe dual dipole omni (DDO) array is constructed by arranging two dipoles symmetrically about a central omni such that all five inlets are collinear along a directional axis. Given the typical dimensions of hearing aid microphones, the three microphones can be stacked for an outer aperture distance (inlets 1 and 5) of 8.5mm and an inner aperture distance (inlets 2 and 4) of 2mm. Though the DDO array has five inlets, there are only three microphone output signals. In order to achieve a freefield DI~9.5dB, the omni is delayed by 250sec, reduced in gain by 47dB, and summed with a 256sec delayed version of the rear dipole output. For those skilled in the art, all other first-order and second-order freefield polar patterns can be realized by mixing these three mics and delaying them to various degrees.

The values shown here optimize the directional performance in freefield; when the device is placed in-situ, much different values are used to optimize directional performance. Well refer to in-situ optimized conditions as baseline.

Starkey Template v7 3.7.089Responses:

Hypercardioid = Max DIFreefieldIn-situ

MRA

For planar wavefronts impinging on a directional endfire array, the maximum response angle is aligned along the directional axis and can point to either 0 or 180 - nothing else. The time delay mismatch can steer the null angle and adjust the relative strengths of the main and rear lobes as they implode in on one another like a water balloon, but the MRA can only flip between 0 and 180. When this array is placed in situ on one side, the MRA shifts to approximately 40 and 220 in azimuth, depending on the frequency, due to acoustical scattering from the head and torso. If an identical array is placed in situ on the other side, the perceptual sum for isotropic noise is 0, i.e., on the forehead. If, however, the endfire array is improved to produce a narrower main lobe, the Directivity Index at the MRA will get higher, but the Directivity Index on axis will get smaller simply because the on-axis sensitivity is reduced and higher-order arrays would consequently be penalized if theyre benchmarked with the DI on axis. For this reason, the DI at the MRA is used in this study as the DOE response rather than the on-axis DI.

The binaural sum can be computed by taking the magnitude of the L/R complex sum or by taking sum of the L/R magnitudes these are the mathematical options. Depending on frequency, the former produces a few tenths increase in the DI whereas the latter produces a 3dB increase, as compared to one-sided data. Although it is not known which mathematical approach correlates to the perceived SNR for a hearing aid user in isotropic noise, improving the DI at the MRA equally in both the L/R devices presumably will produce a binaural sum with improved SNR for targets on axis. Thus, we will focus in this study on the directional performance of one hearing aid placed in situ.

Starkey Template v7 3.7.0810Data Acquisition Process:Pinna placementKEMAR at 10 resolution + 10 @ 10 increments (614 locations)

Directional axisDI (and UI) was measured as per ANSI S3.35, Appendix B.11The microphone arrays were integrated into a standard behind the ear hearing aid, and the aid was positioned in a fixture located behind the pinna. The acrylic fixture was constructed through stereo lithography and was keyed to tilt the directional axis of the microphone array to any of the angles relative to the horizon. Each of the three aids was measured at 1 resolution along the azimuthal plane in freefield. At 2kHz, the relative sensitivity and time-delays were computed to produce a hypercardioid (DI=6dB) for both the dual omni endfire and Blumlein arrays, and an approximate second order cardioid (DI=7.3dB) for the DDO array. These sensitivities and time-delays were used as the baseline values for the DOE, i.e., the drift mismatch in the twenty DOE runs was applied in addition to these values. The idea is that the device is optimized in freefield, placed in situ, and then the effect of drift is studied in the context of acoustical scattering from the head and torso.

The data were acquired by placing the hearing aids in situ on a measurement manikin and measuring the impulse responses of each microphone, which includes the head and torso related transfer functions. The KEMAR manikin wore a sweater, and a single ring was used to adjust its neck length. A loudspeaker was incrementally positioned at 10 resolution along the surface of a 1 meter radius sphere circumscribing the (center of the) measurement manikins head. Although ANSI S3.35 requires 48 loudspeaker locations for measuring the directivity index, 614 were used here. The process was automated and the higher resolution allows us to visualize polar patterns in very fine spatial resolution. For the dual omni and Blumlein arrays containing two mics each, 7,368 impulse responses were acquired for all three positions on the pinna and for replicates. For the DDO array, 11,052 impulse responses were measured.

010-10p3p2p1Directional axisIn-situ placementThe microphone arrays were integrated into a standard behind the ear hearing aid, and the aid was positioned in a fixture located behind the pinna. The acrylic fixture was constructed through stereo lithography and was keyed to tilt the directional axis of the microphone array to any of the angles relative to the horizon with excellent reproducibility.Starkey Template v7 3.7.0812

Measured in-situ results

FRBaseline(SII)Dotted: Measured Replicate Data. Parentheses: SII weighted data. p1 means position 1 which is -10 degrees. p2 is 0 degrees, and p3 is +10 degrees. The (proprietary) baseline weights (not shown here) were computed to produce the results shown in this graph.Starkey Template v7 3.7.0813

Measured in-situ results

FMRBaseline(SII)Dotted: Measured Replicate Data. Parentheses: SII weighted data. p1 means position 1 which is -10 degrees. p2 is 0 degrees, and p3 is +10 degrees. The (proprietary) baseline weights (not shown here) were computed to produce the results shown in this graph. The SII DI was computed with weights from 160Hz to 8kHz.

Starkey Template v7 3.7.0814

Measured in-situ results

OFRBaseline(SII)Dotted: Measured Replicate Data. Parentheses: SII weighted data. p1 means position 1 which is -10 degrees. p2 is 0 degrees, and p3 is +10 degrees. The (proprietary) baseline weights (not shown here) were computed to produce the results shown in this graph. The SII DI was computed with weights from 160Hz to 8kHz.

Starkey Template v7 3.7.0815

Measured in-situ results

FRBaseline(SII)Dotted: Measured Replicate Data. Parentheses: SII weighted data. p1 means position 1 which is -10 degrees. p2 is 0 degrees, and p3 is +10 degrees. The (proprietary) baseline weights (not shown here) were computed to maximize the DI at each frequency. The resulting UI is shown in this graph. The SII UI was computed with weights from 160Hz to 8kHz.

Starkey Template v7 3.7.0816

Measured in-situ results

FMRBaseline(SII)Dotted: Measured Replicate Data. Parentheses: SII weighted data. p1 means position 1 which is -10 degrees. p2 is 0 degrees, and p3 is +10 degrees. The (proprietary) baseline weights (not shown here) were computed to maximize the DI at each frequency. The resulting UI is shown in this graph. The SII UI was computed with weights from 160Hz to 8kHz.

Starkey Template v7 3.7.0817

Measured in-situ results

OFRBaseline(SII)Dotted: Measured Replicate Data. Parentheses: SII weighted data. p1 means position 1 which is -10 degrees. p2 is 0 degrees, and p3 is +10 degrees. The (proprietary) baseline weights (not shown here) were computed to maximize the DI at each frequency. The resulting UI is shown in this graph. The SII UI was computed with weights from 160Hz to 8kHz.

Starkey Template v7 3.7.0818Experimental Setup:10-1030s-30s-3dB3dBdtdAdBaselineConditionsOptimal Response Surface5 Factors:

F/R Sensitivity Mismatch(13 levels)

F/R Time Mismatch(7 levels)

Directional Angle on Ear(3 levels)

Proprietery Baseline conditionswere calculated from in-situdata.

FRThe DOE setup was based on a simple central composite design (CCD) using three factors; center points were chosen to detect curvature in the response surface and lack of fit in the predicted estimates within the design space.Starkey Template v7 3.7.0819Summary:Prescribed Factors and their Levels:1. Front/Rear Magnitude Mismatch:+3dB in 0.5dB increments.2. Front/Rear Phase Mismatch: +30sec in 10sec increments.3. Directional Axis Angle: +10 in 10 increments.

These are applied to the optimized (baseline) conditions.RunR/F (dB)R/F (usec)Dir Angle (deg)SII DI (dB)SII UI (dB)133010-4.11-4.452-0.5-2003.108.343-330-10-1.25-1.224-1.5-30-102.426.0051-10102.545.436-1.5-30-102.355.947-3-30101.254.1483-20100.732.669310-100.09-0.09100.5300-4.52-8.4311310-100.03-0.11121-10-102.916.26131-10-102.856.2214-3002.024.26153-3000.792.9616-1.50102.976.1217-33010-1.56-1.7018-110-103.172.9319-3001.984.24200.5300-4.45-8.45

FRThe type of CCD chosen in this study was an Optimal Response Surface in which twenty runs were determined by allowing the sensitivity mismatch to vary over thirteen levels, i.e., +3dB in 0.5dB increments. The time-delay mismatch varied over seven levels, i.e., +30microseconds in 10microsecond increments, and the directional axis angle varied over three levels, i.e., +10 referenced to the horizon, in 10 increments. In the twenty individual runs, there were replicates, which is to say, the directional data were acquired twice at each position on the pinna; when a repeated run was specified, the second data set was used, thereby allowing systematic measurement error to enter into the ANOVA computations for experimental noise.

Dual Omni = 5 replicates; Blumlein = 6 replicates; Starkey Template v7 3.7.0820Experimental Setup:10-1030s-30s-3dB3dBdtdAdBaselineConditionsOptimal Response Surface5 Factors:

F/M Sensitivity MismatchR/M Sensitivity Mismatch(13 levels)

F/M Time MismatchR/M Time Mismatch(7 levels)

Directional Angle on Ear(3 levels)

Proprietary Baseline conditionswere calculated from in-situdata.

FMRThe DOE setup was based on a simple central composite design (CCD) using three factors; center points were chosen to detect curvature in the response surface and lack of fit in the predicted estimates within the design space.Starkey Template v7 3.7.0821Summary:

Prescribed Factors and their Levels:1. F/M, R/M Magnitude Mismatch:+3dB in 0.5dB increments.2. F/M, R/M Phase Mismatch: +30sec in 10sec increments.3. Directional Axis Angle: +10 in 10 increments.

These are applied to the optimized (baseline) conditions.

FMR

ReplicatesTriplicatesThe type of CCD chosen in this study was an Optimal Response Surface in which 31 runs were determined by allowing the sensitivity mismatch to vary over thirteen levels, i.e., +3dB in 0.5dB increments. The time-delay mismatch varied over seven levels, i.e., +30microseconds in 10microsecond increments, and the directional axis angle varied over three levels, i.e., +10 referenced to the horizon, in 10 increments. In the 31 individual runs, there were 4 replicates and 1 triplicate, which is to say, the directional data were acquired twice at each position on the pinna; when a repeated run was specified, the second data set was used, thereby allowing systematic measurement error to enter into the ANOVA computations for experimental noise.

Dual Omni = 5 replicates; Blumlein = 6 replicates; Starkey Template v7 3.7.0822Experimental Setup:10-1030s-30s-3dB3dBdtdAdBaselineConditionsOptimal Response Surface5 Factors:

F/O Sensitivity MismatchR/O Sensitivity Mismatch(13 levels)

F/O Time MismatchR/O Time Mismatch(7 levels)

Directional Angle on Ear(3 levels)

Baseline conditions (proprietary)were calculated from in-situdata.

OFRThe DOE setup was based on a simple central composite design (CCD) using three factors; center points were chosen to detect curvature in the response surface and lack of fit in the predicted estimates within the design space.Starkey Template v7 3.7.0823Summary:

Prescribed Factors and their Levels:1. F/O, R/O Magnitude Mismatch:+3dB in 0.5dB increments.2. F/O, R/O Phase Mismatch: +30sec in 10sec increments.3. Directional Axis Angle: +10 in 10 increments.

These are applied to the optimized (baseline) conditions.

OFR

ReplicatesTriplicatesThe type of CCD chosen in this study was an Optimal Response Surface in which 31 runs were determined by allowing the sensitivity mismatch to vary over thirteen levels, i.e., +3dB in 0.5dB increments. The time-delay mismatch varied over seven levels, i.e., +30microseconds in 10microsecond increments, and the directional axis angle varied over three levels, i.e., +10 referenced to the horizon, in 10 increments. In the 31 individual runs, there were 4 replicates and 1 triplicate, which is to say, the directional data were acquired twice at each position on the pinna; when a repeated run was specified, the second data set was used, thereby allowing systematic measurement error to enter into the ANOVA computations for experimental noise.

Starkey Template v7 3.7.0824DOE response: DI (20 runs)

FRBaselineAt position 1 (-10 degrees) the baseline proved to give the highest DI for all frequencies.Starkey Template v7 3.7.0825DOE response: DI (31 runs)

FMRBaselineAt position 1 (-10 degrees) the baseline proved to give the highest DI for all frequencies.Starkey Template v7 3.7.0826DOE response: DI (31 runs)

OFRBaselineAt position 1 (-10 degrees) the baseline proved to give the highest DI for all frequencies, except below (300Hz). There may be a little tweaking that could occur below 300Hz.

Starkey Template v7 3.7.0827DOE response: UI (31 runs)

FRBaselineAt position 1 (-10 degrees) note that the baseline was optimized to produce the highest DI. This plot shows that there are some conditions where the UI can be increased, relative to the baseline.

Starkey Template v7 3.7.0828DOE response: UI

FMRBaselineAt position 1 (-10 degrees) note that the baseline was optimized to produce the highest DI. This plot shows that there are some conditions where the UI can be increased, relative to the baseline.Starkey Template v7 3.7.0829DOE response: UI

Baseline

OFRNote, the baseline weights were optimized to produce the highest DI. This plot shows that there are some conditions where the UI can be increased, relative to the baseline.Starkey Template v7 3.7.0830SII DI Coded Response Factor Equation SII DI = + 4.29- 0.059 * F/O Sensitivity Mismatch+ 0.12 * R/O Sensitivity Mismatch+ 0.69 * F/O Time Delay Mismatch+ 0.54 * R/O Time Delay Mismatch - 0.31 * F/O Sensitivity Mismatch*R/O Sensitivity Mismatch+ 0.77 * F/O Time Delay Mismatch*R/O Time Delay Mismatch+ 1.06 * F/O Sensitivity Mismatch 2 - 1.36 * R/O Sensitivity Mismatch 2+ 0.97 * F/O Time Delay Mismatch 2 - 1.57 * R/O Time Delay Mismatch 2Main FactorsInteractionsSecond Order terms

OFRThese are coded factor coefficients with actual labels. High coefficients high importance.Note that the DI response surface equation shows that sensitivity mismatch was not a relatively significant factor in predicting the DI within the design space.Starkey Template v7 3.7.0831SII UI Coded Response Factor Equation SII UI = + 5.87- 0.45 * F/O Sensitivity Mismatch- 0. 20 * R/O Sensitivity Mismatch+ 0.57 * F/O Time Delay Mismatch- 0.005 * R/O Time Delay Mismatch- 0.95 * Directional Axis+ 0.94 * F/O Sensitivity Mismatch * R/O Sensitivity Mismatch- 0.31 * F/O Sensitivity Mismatch * R/O Time Delay Mismatch+ 1.14 * F/O Time Delay Mismatch * R/O Time Delay Mismatch- 1.48 * R/O Sensitivity Mismatch 2- 0.93 * R/O Time Delay Mismatch 2Main FactorsInteractionsSecond Order terms

OFRThese are coded factor coefficients with actual labels. High coefficients high importance.Note that the UI response surface equation shows that sensitivity mismatch was not a relatively significant factor in predicting the UI within the design space.Starkey Template v7 3.7.0832SII DI Coded Response Factor Equation SII DI = + 1.07- 0.27 * F/M Sensitivity Mismatch- 1.09 * R/M Sensitivity Mismatch+ 0.52 * F/M Time Delay Mismatch- 0.78 * R/M Time Delay Mismatch- 0.92 * Directional Axis Angle+ 0.76 * F/M Sensitivity Mismatch*R/M Time Delay Mismatch- 2.79 * F/M Time Delay Mismatch 2- 1.77 * R/M Time Delay Mismatch 2+ 1.80 * Directional Axis Angle 2Main FactorsInteractionsSecond Order terms

FMRThese are coded factor coefficients with actual labels. High coefficients high importance.Note that the DI response surface equation shows that sensitivity and time-delay mismatch, together with directional angle, each contributed relatively significantly in predicting the DI within the design space.Starkey Template v7 3.7.0833SII UI Coded Response Factor Equation SII UI = + 3.26- 0.29 * F/M Sensitivity Mismatch- 0.80 * R/M Sensitivity Mismatch+ 0.62 * F/M Time Delay Mismatch- 0.78 * R/M Time Delay Mismatch- 0.94 * Directional Axis Angle- 1.39 * F/M Sensitivity Mismatch 2- 1.61 * R/M Sensitivity Mismatch 2- 3.10 * F/M Time Delay Mismatch 2+ 2.91 * Directional Axis Angle 2

Main FactorsInteractions (none)Second Order terms

FMRThese are coded factor coefficients with actual labels. High coefficients high importance.Same story for UI: sensitivity and time-delay mismatch, together with directional angle, each contributed relatively significantly in predicting the UI within the design space.

Starkey Template v7 3.7.0834SII DI Coded Response Factor Equation SII DI = + 1.89- 0.99 * R/F Sensitivity Mismatch- 2.36 * R/F Time Delay Mismatch- 1.93 * Directional Axis Angle- 0.55 * R/F Sensitivity Mismatch * R/F Time Delay Mismatch- 3.00 * R/F Time Delay Mismatch 2+ 2.11 * Directional Axis Angle 2Main FactorsInteractionsSecond Order terms

FRThese are coded factor coefficients with actual labels. High coefficients high importance.Note that the DI response surface equation shows that time-delay mismatch and directional angle both contributed relatively significantly in predicting the DI within the design space.Starkey Template v7 3.7.0835SII UI Coded Response Factor Equation SII UI = + 3.56- 1.75 * R/F Sensitivity Mismatch- 4.89 * R/F Time Delay Mismatch- 2.72 * Directional Axis Angle- 4.46 * R/F Time Delay Mismatch 2+ 3.78 * Directional Axis Angle 2Main FactorsInteractions (none)Second Order terms

FRThese are coded factor coefficients with actual labels. High coefficients high importance.Same story for UI: sensitivity and time-delay mismatch, together with directional angle, each contributed relatively significantly in predicting the UI within the design space.Starkey Template v7 3.7.0836Dual Omni Endfire

FRCorrelation GridStarkey Template v7 3.7.0837Tri Omni Endfire

FMRCorrelation GridDual Dipole Omni

OFRCorrelation GridOverlay PlotsThe following plots depict the directional performance across the factors and their levels.Yellow shows:DISII>4dB and UISII>6dB.Propagation of Error (POE) 4dB and SIIUI > 6dB).Starkey Template v7 3.7.0841Dual Dipole Omni

OFRDesired Operating Conditions:POE less than 0.75dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB).

Starkey Template v7 3.7.0842Dual Dipole Omni

OFRDesired Operating Conditions:POE less than 0.75dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB).Starkey Template v7 3.7.0843Dual Dipole Omni

OFRDesired Operating Conditions:POE less than 0.75dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB).

Starkey Template v7 3.7.0844Dual Dipole Omni

OFRDesired Operating Conditions:POE less than 0.75dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB).

Starkey Template v7 3.7.0845Overlay PlotsThe following plots depict the directional performance across the factors and their levels.Yellow shows:DISII>2dB and UISII>3dB*.Propagation of Error (POE) 4dB and SIIUI > 6dB). POE is higher than than DDO array, and yellow space is smaller.

Starkey Template v7 3.7.0847Tri Omni

FMRDesired Operating Conditions:POE = 2.4dB.POE = 3.1dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB). POE is higher than than DDO array, and yellow space is smaller.

Starkey Template v7 3.7.0848Tri Omni

FMRDesired Operating Conditions:POE = 2.4dB.POE = 3.1dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB). POE is higher than than DDO array, and yellow space is smaller.

Starkey Template v7 3.7.0849Tri Omni

FMRDesired Operating Conditions:POE = 2.4dB.POE = 3.1dB.Under these operating conditions, prediction is that a device has 95% chance of operating in the yellow (SIIDI > 4dB and SIIUI > 6dB). POE is higher than than DDO array, and yellow space is smaller.

Starkey Template v7 3.7.0850Overlay PlotsThe following plots depict the directional performance across the factors and their levels.Yellow shows:DISII>4dB and UISII>6dB.Propagation of Error (POE)