VARIABLE STOPWRITE THRESHOLD USING KURTOSIS

BACKGROUND

The present invention relates to data storage systems, and more particularly, this invention relates to systems and methods for adjusting a stopwrite threshold based in part on kurtosis.

In magnetic storage systems, data is read from and written onto magnetic recording media utilizing magnetic transducers commonly. Data is written on the magnetic recording media by moving a magnetic recording transducer to a position over the media where the data is to be stored. The magnetic recording transducer then generates a magnetic field, which encodes the data into the magnetic media. Data is read from the media by similarly positioning the magnetic read transducer and then sensing the magnetic field of the magnetic media. Read and write operations may be independently synchronized with the movement of the media to ensure that the data can be read from and written to the desired location on the media.

An important and continuing goal in the data storage industry is that of increasing the density of data stored on a medium. For tape storage systems, that goal has led to increasing the track and linear bit density on recording tape, and decreasing the thickness of the magnetic tape medium. However, the development of small footprint, higher performance tape drive systems has created various problems in the design of a tape head assembly for use in such systems.

In a tape drive system, magnetic tape is moved over the surface of the tape head at high speed. Usually the tape head is designed to minimize the spacing between the head and the tape. The spacing between the magnetic head and the magnetic tape is crucial so that the recording gaps of the transducers, which are the source of the magnetic recording flux, are in near contact with the tape to effect writing sharp transitions, and so that the read element is in near contact with the tape to provide effective coupling of the magnetic field from the tape to the read element.

Tape drives have conventionally used a servo system to keep the write/read heads in the correct lateral location on the tape. The difference between the correct location and actual location of the heads is referred to as position error signal (PES).

However, it is difficult to pick the appropriate SW threshold due to the differences in distributions of PES data for different drives and/or different tapes. Another drawback is that when a particular predetermined SW threshold is used, the drive may write the data without any apparent error, when actually the adjacent tracks have been overwritten, rendering the data therein unreadable. This result is highly undesirable.

Current servo systems implement a fixed threshold such that if the PES is larger than the threshold, the writing of the heads will be stopped to prevent overwriting of adjacent tracks. This threshold is referred to as the stopwrite (SW) threshold.

BRIEF SUMMARY

A data storage system according to one embodiment includes a head; a drive mechanism for passing a medium over the head; and a controller electrically coupled to the head. logic encoded in or available to the controller for measuring a current position error signal. Logic is encoded in or available to the controller for various operations, including: calculating a standard deviation or a variance using the current position error signal sample; calculating a kurtosis value, using the current position error signal sample or derivative thereof; adjusting a threshold value using the kurtosis value; comparing the standard deviation or variance to the threshold value; enabling writing when the standard deviation or variance does not exceed the threshold value; determining a stopwrite threshold based on a standard deviation or a variance at a current position error signal sample when the standard deviation or variance exceeds the threshold value; determining whether the current position error signal sample exceeds the stopwrite threshold; disabling writing when the current position error signal sample exceeds the stopwrite threshold; and enabling writing when the current position error signal sample does not exceed the stopwrite threshold.

A method according to one embodiment includes measuring a current position error signal; calculating a standard deviation or a variance using the current position error signal sample; calculating a kurtosis value, using the current position error signal sample or derivative thereof; adjusting a threshold value using the kurtosis value; comparing the standard deviation or variance to the threshold value; enabling writing when the standard deviation or variance does not exceed the threshold value; determining a stopwrite threshold based on a standard deviation or a variance at a current position error signal sample when the standard deviation or variance exceeds the threshold value; determining whether the current position error signal sample exceeds the stopwrite threshold; disabling writing when the current position error signal sample exceeds the stopwrite threshold; and enabling writing when the current position error signal sample does not exceed the stopwrite threshold.

A computer program product according to one embodiment includes a computer readable storage medium having program code embodied therewith, the computer readable program code readable/executable by a controller to perform some or all operations of the foregoing method.

Other aspects and embodiments of the present invention will become apparent from the following detailed description, which, when taken in conjunction with the drawings, illustrate by way of example the principles of the invention.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1A is a schematic diagram of a simplified tape drive system according to one embodiment.

FIG. 1B is a schematic diagram of a tape cartridge according to one embodiment.

FIG. 2 illustrates a side view of a flat-lapped, bi-directional, two-module magnetic tape head according to one embodiment.

FIG. 2A is a tape bearing surface view taken from Line 2A of FIG. 2.

FIG. 2B is a detailed view taken from Circle 2B of FIG. 2A.

FIG. 2C is a detailed view of a partial tape bearing surface of a pair of modules.

FIG. 3 is a partial tape bearing surface view of a magnetic head having a write-read-write configuration.

FIG. 4 is a partial tape bearing surface view of a magnetic head having a read-write-read configuration.

FIG. 5 depicts a method according to one embodiment.

FIG. 6 is a flowchart of a method according to one embodiment.

FIG. 7 is a top down view of a data track according to one embodiment.

FIG. 8 is a graph according to one embodiment.

FIG. 9 is a graph according to one embodiment.

FIG. 10 is a flowchart of a method according to one embodiment.

FIG. 11A is a graph illustrating an exemplary set of PES data.

FIG. 11B is a graph illustrating an exemplary set of PES data.

FIG. 11C is a graph illustrating an exemplary set of PES data.

FIG. 12 is a graph exemplifying a normalized relationship between standard deviation and excess kurtosis according to one embodiment.

DETAILED DESCRIPTION

The following description is made for the purpose of illustrating the general principles of the present invention and is not meant to limit the inventive concepts claimed herein. Further, particular features described herein can be used in combination with other described features in each of the various possible combinations and permutations.

Unless otherwise specifically defined herein, all terms are to be given their broadest possible interpretation including meanings implied from the specification as well as meanings understood by those skilled in the art and/or as defined in dictionaries, treatises, etc.

It must also be noted that, as used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless otherwise specified.

The following description discloses several preferred embodiments of magnetic storage systems and/or related systems and methods.

In one general embodiment, a data storage system according to one embodiment includes a head; a drive mechanism for passing a medium over the head; and a controller electrically coupled to the head. logic encoded in or available to the controller for measuring a current position error signal. Logic is encoded in or available to the controller for various operations, including: calculating a standard deviation or a variance using the current position error signal sample; calculating a kurtosis value, using the current position error signal sample or derivative thereof; adjusting a threshold value using the kurtosis value; comparing the standard deviation or variance to the threshold value; enabling writing when the standard deviation or variance does not exceed the threshold value; determining a stopwrite threshold based on a standard deviation or a variance at a current position error signal sample when the standard deviation or variance exceeds the threshold value; determining whether the current position error signal sample exceeds the stopwrite threshold; disabling writing when the current position error signal sample exceeds the stopwrite threshold; and enabling writing when the current position error signal sample does not exceed the stopwrite threshold.

In another general embodiment, a method includes measuring a current position error signal; calculating a standard deviation or a variance using the current position error signal sample; calculating a kurtosis value, using the current position error signal sample or derivative thereof; adjusting a threshold value using the kurtosis value; comparing the standard deviation or variance to the threshold value; enabling writing when the standard deviation or variance does not exceed the threshold value; determining a stopwrite threshold based on a standard deviation or a variance at a current position error signal sample when the standard deviation or variance exceeds the threshold value; determining whether the current position error signal sample exceeds the stopwrite threshold; disabling writing when the current position error signal sample exceeds the stopwrite threshold; and enabling writing when the current position error signal sample does not exceed the stopwrite threshold.

In another general embodiment, a computer program product includes [a computer readable storage medium having program code embodied therewith, the computer readable program code readable/executable by a controller to perform some or all operations of the foregoing method.

FIG. 1A illustrates a simplified tape drive 100 of a tape-based data storage system, which may be employed in the context of the present invention. While one specific implementation of a tape drive is shown in FIG. 1A, it should be noted that the embodiments described herein may be implemented in the context of any type of tape drive system.

As shown, a tape supply cartridge 120 and a take-up reel 121 are provided to support a tape 122. One or more of the reels may form part of a removable cartridge and are not necessarily part of the system 100. The tape drive, such as that illustrated in FIG. 1A, may further include drive motor(s) to drive the tape supply cartridge 120 and the take-up reel 121 to move the tape 122 over a tape head 126 of any type. Such head may include an array of readers, writers, or both. Moreover, according to one approach, the head may be magnetic.

Guides 125 guide the tape 122 across the tape head 126. Such tape head 126 is in turn coupled to a controller 128 via a cable 130. The controller 128, may be or include a processor and/or any logic for controlling any subsystem of the drive 100. For example, the controller 128 typically controls head functions such as servo following, data writing, data reading, etc. The controller 128 may operate under logic known in the art, as well as any logic disclosed herein. The controller 128 may be coupled to a memory 136 of any known type, which may store instructions executable by the controller 128. Moreover, the controller 128 may be configured and/or programmable to perform or control some or all of the methodology presented herein. Thus, the controller may be considered configured to perform various operations by way of logic programmed into a chip; software, firmware, or other instructions being available to a processor; etc. and combinations thereof.

The cable 130 may include read/write circuits to transmit data to the head 126 to be recorded on the tape 122 and to receive data read by the head 126 from the tape 122. An actuator 132 controls position of the head 126 relative to the tape 122.

An interface 134 may also be provided for communication between the tape drive 100 and a host (integral or external) to send and receive the data and for controlling the operation of the tape drive 100 and communicating the status of the tape drive 100 to the host, all as will be understood by those of skill in the art.

FIG. 1B illustrates an exemplary tape cartridge 150 according to one embodiment. Such tape cartridge 150 may be used with a system such as that shown in FIG. 1A. As shown, the tape cartridge 150 includes a housing 152, a tape 122 in the housing 152, and a nonvolatile memory 156 coupled to the housing 152. In some approaches, the nonvolatile memory 156 may be embedded inside the housing 152, as shown in FIG. 1B. In more approaches, the nonvolatile memory 156 may be attached to the inside or outside of the housing 152 without modification of the housing 152. For example, the nonvolatile memory may be embedded in a self-adhesive label. In one preferred embodiment, the nonvolatile memory 156 may be a Flash memory device, ROM device, etc., embedded into or coupled to the inside or outside of the tape cartridge 150. The nonvolatile memory is accessible by the tape drive and the tape operating software (the driver software), and/or other device.

By way of example, FIG. 2 illustrates a side view of a flat-lapped, bi-directional, two-module magnetic tape head 200 which may be implemented in the context of the present invention. As shown, the head includes a pair of bases 202, each equipped with a module 204, and fixed at a small angle α with respect to each other. The bases may be “U-beams” that are adhesively coupled together. Each module 204 includes a substrate 204A and a closure 204B with a thin film portion, commonly referred to as a “gap” in which the readers and/or writers 206 are formed. In use, a tape 208 is moved over the modules 204 along a media (tape) bearing surface 209 in the manner shown for reading and writing data on the tape 208 using the readers and writers. The wrap angle θ of the tape 208 at edges going onto and exiting the flat media support surfaces 209 are usually between about 0.1 degree and about 5 degrees.

The substrates 204A are typically constructed of a wear resistant material, such as a ceramic. The closures 204B made of the same or similar ceramic as the substrates 204A.

The readers and writers may be arranged in a piggyback or merged configuration. An illustrative piggybacked configuration comprises a (magnetically inductive) writer transducer on top of (or below) a (magnetically shielded) reader transducer (e.g., a magnetoresistive reader, etc.), wherein the poles of the writer and the shields of the reader are generally separated. An illustrative merged configuration comprises one reader shield in the same physical layer as one writer pole (hence, “merged”). The readers and writers may also be arranged in an interleaved configuration. Alternatively, each array of channels may be readers or writers only. Any of these arrays may contain one or more servo track readers for reading servo data on the medium.

FIG. 2A illustrates the tape bearing surface 209 of one of the modules 204 taken from Line 2A of FIG. 2. A representative tape 208 is shown in dashed lines. The module 204 is preferably long enough to be able to support the tape as the head steps between data bands.

In this example, the tape 208 includes 4 to 22 data bands, e.g., with 16 data bands and 17 servo tracks 210, as shown in FIG. 2A on a one-half inch wide tape 208. The data bands are defined between servo tracks 210. Each data band may include a number of data tracks, for example 512 data tracks (not shown). During read/write operations, the readers and/or writers 206 are positioned to specific track positions within one of the data bands. Outer readers, sometimes called servo readers, read the servo tracks 210. The servo signals are in turn used to keep the readers and/or writers 206 aligned with a particular set of tracks during the read/write operations.

FIG. 2B depicts a plurality of readers and/or writers 206 formed in a gap 218 on the module 204 in Circle 2B of FIG. 2A. As shown, the array of readers and writers 206 includes, for example, 16 writers 214, 16 readers 216 and two servo readers 212, though the number of elements may vary. Illustrative embodiments include 8, 16, 32, 40, and 64 readers and/or writers 206 per array. A preferred embodiment includes 32 readers per array and/or 32 writers per array, where the actual number of transducing elements could be greater, e.g., 33, 34, etc. This allows the tape to travel more slowly, thereby reducing speed-induced tracking and mechanical difficulties and/or execute fewer “wraps” to fill or read the tape. While the readers and writers may be arranged in a piggyback configuration as shown in FIG. 2B, the readers 216 and writers 214 may also be arranged in an interleaved configuration. Alternatively, each array of readers and/or writers 206 may be readers or writers only, and the arrays may contain one or more servo readers 212. As noted by considering FIGS. 2 and 2A-B together, each module 204 may include a complementary set of readers and/or writers 206 for such things as bi-directional reading and writing, read-while-write capability, backward compatibility, etc.

FIG. 2C shows a partial tape bearing surface view of complimentary modules of a magnetic tape head 200 according to one embodiment. In this embodiment, each module has a plurality of read/write (R/W) pairs in a piggyback configuration formed on a common substrate 204A and an optional electrically insulative layer 236. The writers, exemplified by the write head 214 and the readers, exemplified by the read head 216, are aligned parallel to a direction of travel of a tape medium thereacross to form an R/W pair, exemplified by the R/W pair 222.

Several R/W pairs 222 may be present, such as 8, 16, 32 pairs, etc. The R/W pairs 222 as shown are linearly aligned in a direction generally perpendicular to a direction of tape travel thereacross. However, the pairs may also be aligned diagonally, etc. Servo readers 212 are positioned on the outside of the array of R/W pairs, the function of which is well known.

Generally, the magnetic tape medium moves in either a forward or reverse direction as indicated by arrow 220. The magnetic tape medium and head assembly 200 operate in a transducing relationship in the manner well-known in the art. The piggybacked MR head assembly 200 includes two thin-film modules 224 and 226 of generally identical construction.

Modules 224 and 226 are joined together with a space present between closures 204B thereof (partially shown) to form a single physical unit to provide read-while-write capability by activating the writer of the leading module and reader of the trailing module aligned with the writer of the leading module parallel to the direction of tape travel relative thereto. When a module 224, 226 of a piggyback head 200 is constructed, layers are formed in the gap 218 created above an electrically conductive substrate 204A (partially shown), e.g., of AlTiC, in generally the following order for the R/W pairs 222: an insulating layer 236, a first shield 232 typically of an iron alloy such as NiFe (permalloy), CZT or Al—Fe—Si (Sendust), a sensor 234 for sensing a data track on a magnetic medium, a second shield 238 typically of a nickel-iron alloy (e.g., 80/20 Permalloy), first and second writer pole tips 228, 230, and a coil (not shown).

The first and second writer poles 228, 230 may be fabricated from high magnetic moment materials such as 45/55 NiFe. Note that these materials are provided by way of example only, and other materials may be used. Additional layers such as insulation between the shields and/or pole tips and an insulation layer surrounding the sensor may be present. Illustrative materials for the insulation include alumina and other oxides, insulative polymers, etc.

The configuration of the tape head 126 according to one embodiment includes multiple modules, preferably three or more. In a write-read-write (W-R-W) head, outer modules for writing flank one or more inner modules for reading. Referring to FIG. 3, depicting a W-R-W configuration, the outer modules 402, 406 each include one or more arrays of writers 410. The inner module 404 of FIG. 3 includes one or more arrays of readers 408 in a similar configuration. Variations of a multi-module head include a R-W-R head (FIG. 4), a R-R-W head, a W-W-R head, etc. In yet other variations, one or more of the modules may have read/write pairs of transducers. Moreover, more than three modules may be present. In further approaches, two outer modules may flank two or more inner modules, e.g., in a W-R-R-W, a R-W-W-R arrangement, etc. For simplicity, a W-R-W head is used primarily herein to exemplify embodiments of the present invention. One skilled in the art apprised with the teachings herein will appreciate how permutations of the present invention would apply to configurations other than a W-R-W configuration.

The teachings herein may be applied to other types of data storage systems. For example, according to a general embodiment, a data storage system may include a head which may be magnetic, optical, etc. or any other type of head which would be apparent to one skilled in the art upon reading the present description. The system may additionally include a drive mechanism for passing an e.g., magnetic, optical, etc. medium over the head. The data storage system may further include a controller electrically coupled to the head.

The data storage system may also include logic according to any of the embodiments described and/or suggested herein. In one approach, the logic may be encoded in a controller and/or other hardware, stored in memory as software or firmware and available to the controller and/or other hardware, etc. and combinations thereof. Moreover, the logic may be for performing any of the process steps recited herein.

Conventional data storage systems include a predefined stopwrite threshold and can be inaccurate for any given period of writing. Depending on the situation, the stopwrite threshold can either be overly constraining by only permitting writing during a low PES, thereby minimizing the capacity of the tape; or it may be overly permissive by permitting writing during high PES samples, thus allowing adjacent tracks on the medium to be overwritten.

Embodiments of the present invention overcome the aforementioned drawback by providing a stopwrite system that is able to adjust the stopwrite threshold to accommodate varying write conditions. Preferably, such system and/or method is able to statistically calculate the PES standard deviation (or other derivative of a PES sample) and make changes to the stopwrite threshold accordingly, as explained in further detail below. Moreover, each system and/or method may ensure the appropriate stopwrite threshold to accommodate favorable conditions such that written data may be read back later.

Referring now to FIG. 5, a method 500 is depicted according to one embodiment. As an option, the present method 500 may be implemented in conjunction with features from any other embodiment listed herein, such as those described with reference to the other FIGS. Of course, however, such method 500 and others presented herein may be used in various applications and/or in permutations which may or may not be specifically described in the illustrative embodiments listed herein. Further, the method 500 presented herein may be used in any desired environment.

Referring to FIG. 5, a method 500 is depicted according to one illustrative embodiment of a simplified process for successfully recording data to a medium. The method 500 includes periodically determining a stopwrite threshold based on a standard deviation or a variance at a current position error signal sample. As discussed in more detail below, a smoothing factor applied to a subsequent calculation or calculations of the standard deviation (e.g., σ_raw) or variance (e.g., σ_k²) is altered based, at least in part, on a current magnitude of the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²). See operation 502. Alteration of the smoothing factor is explained in further detail below. It should be noted that the period may correspond to predetermined regular intervals; irregular intervals; periods calculated on the fly e.g., as a function of data rate, tape speed, etc.; etc.

With continued reference to FIG. 5, the method 500 also includes determining whether the current PES sample exceeds the stopwrite threshold. See operation 504.

In operation 506, writing is disabled when the current PES sample exceeds the stopwrite threshold.

The method 500 additionally includes enabling writing when the current PES sample does not exceed the stopwrite threshold. See operation 508.

According to various approaches the methods 500 and/or 600 (described below) may incorporate logic while conducting the aforementioned operations. In one approach, the logic may be encoded in a controller and/or other hardware, stored in memory as software or firmware and available to the controller and/or other hardware, etc. and combinations thereof.

In a preferred approach, the method 500 may be executed at intervals of less than about 1 second, more preferably less than about 0.01 seconds, still more preferably less than about 1 millisecond, but could be shorter or longer based on the desired embodiment. According to one illustrative embodiment which is by no means meant to limit the scope of the invention, the aforementioned logic may be executed at regular or irregular intervals of about 50 μs.

Referring now to FIG. 6 a method 600 is depicted according to one illustrative embodiment. As an option, the present method 600 may be implemented in conjunction with features from any other embodiment listed herein, such as those described with reference to the other FIGS. Of course, however, such method 600 and others presented herein may be used in various applications and/or in permutations which may or may not be specifically described in the illustrative embodiments listed herein. Further, the method 600 presented herein may be used in any desired environment.

In a preferred approach, the method 600 may be executed at regular or irregular intervals as the track is being written to.

Operation 602 includes measuring the current PES sample. In one approach, the previous PES samples may be measured to find the corresponding deviation. According to one approach, the PES may be measured by incorporating any method known in the art, e.g., using servos, etc.

Operation 604 includes updating the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²), based on PES samples, a current PES sample, etc. and the altered smoothing factor (B). See operation 502 of FIG. 5. According to various approaches, σ_rawmay be a standard deviation of PES samples, including prior PES samples, the current PES sample, etc. Moreover, σ_rawmay be calculated by incorporating any formula known in the art.

In a preferred illustrative embodiment, the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²) may be calculated using Equation 1, where σ_kis used as σ_raw.

σ_k²=B×σ_k-1²+(1−B)×x_k² Equation 1

According to the preferred embodiment, σ_k²represents the variance at the current PES sample, σ_k-1²represents the variance at the previous PES sample, and x_krepresents the current PES sample. By incorporating the variance of the previous PES samples, the accumulative distribution may be accurate, thereby preferably resulting in an accurate stopwrite threshold as well, without having to store all of the previous PES sample values. σ_rawcan be calculated by taking the square root of σ_k².

In one approach, if Equation 1 is incorporated for a first time, the value for σ_k-1²(variance of the previous PES sample) may implement stored data from the previous PES sample, an arbitrary value chosen by a user, etc. Without wishing to be bound by any theory, it is believed that the σ_k-1²value implemented for a first time Equation 1 is used, may not significantly affect the σ_rawvalue that is calculated and used to set the SW threshold during writing.

As noted above, the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²), in some approaches, is estimated with a smoothing factor, so that multiple PES samples are used to generate an accurate estimate of PES standard deviation. Depending on the embodiment, the value of the smoothing factor (B) may determine how much of an effect the previous PES sample has on the value of σ_rawbeing calculated, relative to the current PES sample.

It is desired that the smoothing factor generate a reasonable slowly changing PES standard deviation estimate. In some embodiments, the calculation of the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²) relies on a fixed smoothing factor. However, a fixed smoothing factor may be problematic. For example, if the PES standard deviation is over a specified limit, then a slowly changing standard deviation estimate can keep the stopwrite threshold low for too long. This results in unnecessary capacity loss.

For example, the drive may be exposed to different environments including normal tabletop operations, shock environments, high vibration environments, etc.; each of which having a different ideal smoothing factor. Moreover, drives may interact differently with different tapes. Use of a fixed smoothing factor in such environments may present disadvantages. According to an illustrative example, if a particular environment is suspected to be a high vibration environment (e.g., resulting in high PES), a fixed, small smoothing factor may be incorporated to quicken changes made to the standard deviation or the variance in the subsequent calculations thereof from the presently calculated value. Moreover, the small smoothing factor and resulting quick changes to the standard deviation or the variance may mirror the high PES values, and thereby cause a decreased stopwrite value. Preferably, a decreased stopwrite value may result in a high number of stopwrites to counteract the high PES. However, if the vibrations decrease (e.g., lower PES), the fixed, small smoothing factor may cause the stopwrite value to continue to rapidly change. Thus, although there may be a period of low PES, local high points may be misinterpreted as unfavorably high PES by the rapidly changing stopwrite value, thereby causing an unnecessary number of stopwrites during low vibration run time.

Similar unfavorable results may be experienced when a fixed, high smoothing factor is selected for operation in a low vibration environment, and the environment transitions to a high vibration environment. This may result in an undesirably slow change in the stopwrite value to counteract the high vibrations, such that multiple errors may be made while writing on the tape.

Therefore, in a preferred embodiment, the value of the smoothing factor may vary, depending on the value of the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²).

According to one embodiment, the smoothing factor may switch between two values, depending on the standard deviation or the variance of the current position error signal in relation to a specified value. According to a preferred approach, the specified value may be σ_max(described in further detail below).

In one approach, if the standard deviation or the variance of the current position error signal sample is below a specified value (e.g., σ_maxor a value selected using the same or similar techniques as selection of σ_max), the smoothing factor is altered to slow a change in the standard deviation or the variance in the subsequent calculations thereof from the presently calculated value. In Equation 1, above, the value of the smoothing factor would thus be increased. The low standard deviation or variance of the current position error signal sample signifies desirable and consistent writing conditions. Therefore, the altered smoothing factor may allow for a decreased number of stopwrites to maximize the write capacity of the tape.

However, according to another approach, if the standard deviation or the variance at the current position error signal sample is above a specified value (e.g., σ_maxor a value selected using the same or similar techniques as selection of σ_max), the smoothing factor value may be altered to accelerate a change in the standard deviation or the variance in the subsequent calculations thereof from the presently calculated value. As explained above, high standard deviation or variance (e.g., high PES) signifies unfavorable write conditions. Therefore, the thus altered smoothing factor may result in a favorably increased number of stopwrites to ensure minimal and/or no errors are made while writing to the tape, thereby improving the readability of the tape.

According to various other embodiments, the smoothing factor may switch between at least two values, at least three values, several values, etc. with respect to at least one specified value, at least two specified values, several specified values, etc. Thus, the smoothing factor may incorporate multiple discreet values which may be determined by any number of parameters, depending on the desired embodiment. According to different approaches, the smoothing factor may be determined by incorporating different parameters including, but not limited to, kurtosis; vibration levels, e.g., measured with an accelerometer in the drive; etc.

According to various other embodiments, the smoothing factor may vary according to a mathematical function. In one approach, the function may preferably allow the smoothing factor value to continuously vary, thereby increasing accuracy and/or efficiency when writing to the tape. According to one example, the smoothing factor may be altered after each calculation of the standard deviation or the variance during run time (explained in further detail below). However, according to other approaches, the smoothing factor may be altered after every second, third, fourth, fifth, etc. iteration of calculating the standard deviation or the variance during run time.

In another embodiment, the smoothing factor may gradually change as the standard deviation or the variance of the current position error signal sample approaches a specified value. For example, the smoothing factor may gradually change rather than jump abruptly when the specified limits are reached. This may preferably result in a more accurate response to external conditions, and ensure more efficient writing of data to the tape.

According to one approach, the value of the smoothing factor may be linearly interpolated between the specified high and low values thereof. In yet another approach, the smoothing factor may follow a nonlinear but prespecified curve between high and low values thereof.

Without wishing to be bound by any theory, it is believed that a value for smoothing factor B between about 0.95 and about 0.999 results in an optimal effect for most embodiments, but B may be any value. According to various embodiments, the value of the smoothing factor may be determined by the operating conditions, a predetermined value, selected from a lookup table, specified by a user, etc. Due to the highly adaptive nature of the embodiments described and/or suggested herein, in various approaches, the value of B may be outside the optimal range listed above, while maintaining desirable results. In yet another approach, B may be allowed to vary preferentially within the foregoing range, and allowed to exit the range when desirable for faster or slower change in the standard deviation or variance.

With continued reference to FIG. 6, operation 606 includes determining whether the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²) exceeds a predetermined threshold (e.g., σ_max).

According to various approaches, a predetermined threshold (e.g., σ_max) may be calculated using any method known in the art; however an illustrative example, which is in no way meant to limit the invention, is provided.

In the following example, assume a data storage system includes a magnetic tape head writing data to shingled data tracks on the tape of the magnetic tape head as shown in FIG. 7.

Referring now to FIG. 7, the shingled track width w₁defines the width of the first written track between the first written edge 702 and the second written edge 704. According to one approach, the second written edge 704 may be a first written edge of a second written track overlapping part of the first written track.

Moreover, the reader width w₂defines the distance between the reader's outer edges 706, while the shingled reader guard bands w_3Aand w_3Bdefine the distance between the reader's outer edges 706 and the written edges 702 and 704 respectively. According to various approaches, the values of the shingled reader guard bands w_3A, w_3Bmay be the same or different, depending on the position of the reader. The relative position of the reader with respect to a given written track may vary with time for a given magnetic tape head due to various factors (e.g., temperature, humidity, mechanical imperfections, movement of the reader, etc.).

According to one illustrative example, which is by no means meant to limit the scope of the invention, the shingled track width w₁may be 4.75 μm (microns). Furthermore, the reader width w₂may be 2.3 μm, while both the shingled reader guard bands w_3Aand w_3Bmay be 1.23 μm (e.g., the reader is centered between the first and second written edges in a direction perpendicular thereto).

In some approaches, if too much of the reader is positioned over an adjacent written track rather than the track of interest, the reader may not be able to read the data written on the track of interest. It is preferred that a shingled reader guard band ensures that 100% of the reader width is within the first and second written edges of a given shingled track of interest. However, in one approach, a reader may be able to successfully read the data stored in a given written track of interest when approximately 10% of the reader width is outside the plane of the first and/or second written edges of the given written track of interest. Therefore, a shingled reader guard band may include 10% of the reader width as shown in Equation 2; but could be more or less depending on the desired embodiment.

Shingled reader guard band=1.23 μm+0.10(2.3 μm) Equation 2

Thus, with continued reference to the present illustrative example, the shingled reader guard bands may each be 1.46 μm.

Depending on the dimensions and/or conditions for a given magnetic tape head, a threshold deviation value (e.g., σ_max) may be calculated from the magnetic tape drive design. In a preferred approach, the threshold deviation value may incorporate an appropriate stopwrite to filter the data such that written data may be successfully read back later (explained in further detail below). According to a preferred approach, the threshold deviation value (e.g., σ_max) may vary as to preferably accommodate any possible PES distribution (explained in further detail below). Thus, when analyzing a given data set of a given data storage system, the data may be evaluated as a distribution (e.g., a normal distribution).

According to various other approaches, the deviation value σ may incorporate, but is not limited to a factor “N” which may have a value of 1, 2, 3, 4.5, etc. or any other value which would be obvious to one skilled in the art upon reading the present description. In one illustrative example, the factor N may have a value of 3 such that the deviation value may be represented by 3σ (3σ_total) for a distribution of a given data set's PES. In one approach, the corresponding deviation value may be within the shingled reader guard band value calculated above, as shown in Equation 3.

3σ_total=1.46 μm Equation 3

Once the equation is simplified and both sides are divided by 3, the resulting σ_totalvalue (e.g., standard deviation) is 0.49 μm.

However, the value σ_totalincludes a combination of the deviations of both the written edge (σ_w) and the reader edge (σ_r) of the magnetic tape head. Equation 4 shows the relationship between σ_totaland the deviation values (σ_wand σ_r) of the two signals combined to form σ_total.

σ_total=(σ_w²+σ_r²)^1/2 Equation 4

However, because the tape path and/or the actuator of the magnetic tape head may not able to distinguish the difference between when the head is reading and when the head is writing in some embodiments, σ_wmay be considered the same value as σ_r. Therefore, Equation 4 allows for either the maximum deviation of the written edge or the deviation of the reader edge to be calculated at any time. In one approach, the σ_wvalue may be calculated by simplifying Equation 4 as is shown in Equation 5.

0.49 μm=(σ_w²+σ_w²)^1/2 Equation 5

Once simplified, Equation 5 results in the value for σ_was 0.35 μm. Therefore, according to the present illustrative example, a deviation of 0.35 μm may be incorporated in various embodiments as a threshold deviation value (e.g., σ_max), including any of the embodiments described and/or suggested herein.

As noted above, the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²) is compared to the predetermined threshold (e.g., σ_max) in operation 606. With continued reference to FIG. 6, operation 608 includes determining a stopwrite threshold based on the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²), when the standard deviation or the variance exceeds the predetermined threshold (e.g., σ_max).

In one approach, the stopwrite threshold may be determined by selecting a stopwrite value preassociated with the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²). In a preferred approach, the stopwrite value may be listed in a look up table (LUT) having stopwrite values calculated for various σ_rawvalues, a plot as depicted in FIG. 8, etc. In another approach, the stopwrite values may be calculated in real-time and then implemented, as the current PES samples are measured.

Referring to FIG. 8, stopwrite values may be calculated for various possible σ_rawvalues using a variance formula known in the art. These σ_rawvalues (along the x-axis) and their corresponding stopwrite values (along the y-axis) may be stored in a plot as is shown in FIG. 8 for future use. As discussed above, the maximum desired σ_rawvalue may preferably be 0.35 μm which corresponds to that which is depicted in the graph.

With continued reference to FIG. 6, operation 610 includes determining if the current PES sample exceeds the stopwrite threshold acquired in operation 608. In the case that the current PES sample in fact exceeds the stopwrite threshold, operation 612 of the method 600 disables writing.

In a preferred approach, if writing is enabled or disabled during an interval, it is enabled or disabled only for the current interval. It is preferred that, at the start of each new interval, the logic may be run to determine if the writing should be enabled or disabled for that given interval. In another approach, if writing is enabled or disabled during an interval, it may remain enabled or disabled for at least one, at least two intervals, multiple, etc. intervals, regardless of the logic.

With continued reference to FIG. 6, operation 614 includes not updating a truncated value (e.g., σ_truncated). According to a preferred approach, the truncated value is not updated when writing is disabled. More information about σ_truncatedis provided below, including operations when σ_truncatedis updated.

Referring back to operation 606, if it is determined that the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²) does not exceed the predetermined threshold (e.g., σ_max), the method 600 proceeds to operation 618 which enables writing.

Similarly, referring back to operation 610, if the current PES sample is determined to not exceed the stopwrite threshold, then the method 600 proceeds to operation 618, thereby enabling writing as described above.

With continued reference to FIG. 6, once writing has been enabled in operation 618, the method 600 proceeds to update a truncated value (e.g., σ_truncated) and verify that the truncated value is less than σ_max. See operation 620.

According to a preferred approach, a method may include updating a truncated value (e.g., σ_truncated) by incorporating the current PES sample when writing is enabled. In one approach, the truncated value may be a standard deviation or variance of PES samples.

In some approaches, the truncated value may be compared to the predetermined threshold (e.g., σ_max). If the truncated value maintains a value at, or below the predetermined threshold, then it may be expected that, when reading back the written data on the track, no errors will occur.

According to one approach, if the σ_rawis greater than the σ_max, then the method of truncated normal distributions (e.g., σ_truncated) may be incorporated to determine the truncation value such that the correct number of samples may be eliminated, but the PES values written to tape have the same standard distribution of σ_max. Thus, the σ_rawof the data which may be written to the tape will preferably be less than the value σ_max. This may be accomplished by obtaining the correct truncation value from a formula, a look up table, a predetermined value, a chart, etc. For example, the SW Threshold line in FIG. 8 may be used. The foregoing feature is an important feature implemented in some embodiments because it guarantees that data will be written to tape with no more u than the σ_max, no matter how high the actual σ really is. Although in some embodiments this design may sacrifice capacity by increasing stopwrite frequency, it will preferably ensure that no errors will occur during reading.

For example, if the σ_truncatedvalue for the data actually written to the aforementioned track remains less than σ_max, there should be no errors when reading back that same portion of the track. However, if the σ_truncatedvalue for the data being written to the aforementioned track rises above the σ_maxvalue, errors may be expected to occur when later reading the data written to that same segment of the track. According to one approach, such errors may be caused by not having enough of the intended data successfully written to the track; as suggested by the high deviation. Therefore, it may be desirable to perform some additional evaluations in the even that σ_truncatedis a not less than σ_max.

Referring now to FIG. 9, a graph displays results from implementation of one illustrative embodiment, which in no way is meant to limit the invention. The graph of FIG. 9 depicts the outcome of incorporating a method similar to and/or the same as that described in method 600, to a given set of data. As shown, the σ_rawand stopwrite threshold (SW Threshold) values change as the PES is evaluated at predetermined intervals. Moreover, the σ_truncatedvalue remains at or below the σ_maxvalue of 0.35 μm for this illustrative example, thereby ensuring that the data being written will be able to be successfully read back.

According to various approaches, the geometry of the data storage system (e.g., track width, reader width, etc.), may contribute in determining the allowable distribution during writing for various embodiments.

Moreover, further embodiments may incorporate kurtosis, preferably to gain a more detailed understanding of the written data deviations, as well as the standard deviation of a given embodiment. Gaining a more detailed understanding of the standard deviation may allow for more efficient writing of data in preferred approaches than if a normal distribution (e.g., Gaussian distribution) is assumed for the deviations. Assuming normal distribution for a given embodiment may result in an inaccurate representation of the deviations, which may ultimately cause unnecessary stopwrites. For example, data may entail kurtosis risk in which data points may be spread much wider than the normal distribution may entail. Thus, fewer data points may be clustered near the average, and more data points may populate the extremes above and/or below the average.

According to various embodiments, different deviations of the written data, e.g., infrequent, large deviations, frequent moderately sized deviations over a given period of time, etc. may produce the same standard deviation when calculated. Referring to FIGS. 11A-11C, although each of the graphs display a different distribution of PES samples, with the y-axis representing the number of samples that have the specified PES value in the x-axis, the standard deviation of the data corresponding to each of the graphs is calculated as being approximately the same value. Therefore, as stated above, it is preferable to gain an understanding of the deviations that correspond to, and form the standard deviation of a given embodiment. One way to gain such understanding is by using a kurtosis value, which is intended to include raw kurtosis, excess kurtosis, and any derivative thereof. In the example presented in FIGS. 11A-11C, the excess kurtosis value of the distribution in FIG. 11A is −1.5, the excess kurtosis value thereof in FIG. 11B is 0, and the excess kurtosis value thereof in FIG. 11C is +1.5. By observing kurtosis, one can determine when to stopwrite for each of the different distributions, as opposed to a one-size-fits-all approach, as occurs when a normal distribution is assumed for all cases.

As stated above, gaining a more detailed understanding of deviations may result in writing data more efficiently to the tape. For example, the PES corresponding to a given embodiment may be desirable (e.g., low deviations), resulting in a low threshold value. Moreover, a low threshold value may thereby limit the acceptable PES values for writing, to much lower than what may actually result in successful writing to the tape. However, by incorporating kurtosis, preferably a maximum amount of data may be written to the magnetic medium, while retaining the ability to be successfully read back, thereby increasing the capacity of the tape (explained in further detail below).

According to an illustrative example, a flowchart illustrates a method 1000 in FIG. 10. As an option, the present method 1000 may be implemented in conjunction with features from any other embodiment listed herein, such as those described with reference to the other FIGS. Of course, however, such method 1000 and others presented herein may be used in various applications and/or in permutations which may or may not be specifically described in the illustrative embodiments listed herein. Further, the method 1000 presented herein may be used in any desired environment.

Operation 1002 of method 1000 includes measuring a current position error signal. According to one approach, the PES may be measured by incorporating any method known in the art, e.g., using servos, etc.

Operation 1004 includes calculating a standard deviation (e.g., σ_raw), or equivalently, a variance (e.g., σ_k²) using the current position error signal sample. In an exemplary approach, the standard deviation or the variance may be updated based on the current position error signal sample.

According to various approaches, calculating a standard deviation (e.g., σ_raw) or a variance (e.g., σ_k²) may incorporate prior PES samples, the current PES sample, etc. Moreover, the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²) may be calculated by incorporating any formula known in the art and/or described herein. In a preferred approach, calculating the standard deviation (e.g., σ_raw) or the variance (e.g., σ_k²), may incorporate an altered smoothing factor “B” (see operation 502 of FIG. 5).

With continued reference to FIG. 10, operation 1006 includes calculating a kurtosis value, using the current position error signal sample or derivative thereof. According to various approaches, a kurtosis value may be calculated by incorporating any of the equations described and/or suggested herein, a low-pass filter, an algorithm, etc. or any other method which would be apparent to one skilled in the art upon reading the present description.

According to one approach, the current PES sample derivative may incorporate the standard deviation or a variance calculated from the current PES sample, depending on the desired embodiment. Moreover, in yet another approach, the kurtosis may be derived by incorporating the standard deviation or variance, either of which may preferably be calculated using the current PES. In a preferred approach, the kurtosis may be used to understand and/or characterize the distribution shape of the deviations, thereby allowing for much more efficient stopwrites and increased tape capacity.

In a preferred illustrative embodiment, a raw kurtosis value may be calculated by preferably first calculating the variance (σ_k²) by incorporating Equation 1 as explained above, or any other method which would be apparent to one skilled in the art upon reading the present description. Additionally, Equation 6 may be incorporated as to calculate the fourth moment (M₄).

M
₄=(B×M_4-1)+(1−B)×x_k⁴ Equation 6

Accordingly, M_4-1represents the fourth moment at the previous PES sample, B represents the smoothing factor as explained above, and x_k⁴represents the current PES sample to the fourth power.

Moreover, the raw kurtosis value of a given sample may be calculated by preferably incorporating Equation 7.

kurtosis=M₄/(σ_k²)² Equation 7

Mathematically, the kurtosis value for a normal distribution is 3. However, according to one approach, raw kurtosis values may preferably be shifted by −3, thereby producing excess kurtosis (EK) values. Thus, EK values may be calculated by simply subtracting 3 from the raw kurtosis values data as illustrated in Equation 8,

EK=kurtosis−3 Equation 8

With continued reference to FIG. 10, method 1000 also includes adjusting a threshold value (e.g., σ_max) using the kurtosis value. See operation 1008. According to different approaches, the kurtosis value may incorporate a raw kurtosis value and/or an excess kurtosis value. However, according to various other approaches, a threshold value (e.g., σ_max) may be calculated using any method known in the art.

In a preferred approach, specific EK values may correspond to calculated threshold values which result in preferred writing conditions to the tape. Thus, σ_maxmay be adjusted to the calculated threshold values which correspond to the EK values for a given tape. However, if σ_maxis less than a calculated threshold corresponding from a given EK value, σ_maxmay not be adjusted, depending on the desired embodiment. Moreover, if σ_maxis at, or greater than, a calculated threshold corresponding to a given EK value, σ_maxmay preferably be adjusted to a value at or below the calculated threshold.

According to an illustrative approach, combinations of threshold values and kurtosis values may be precalculated as to preferably ensure the data will be read back successfully. Referring to FIG. 12, a graph illustrates a preferred relationship between EK values and calculated threshold values (σ_max) according to an exemplary embodiment, which is in no way intended to limit the invention. The curve represents the critical threshold (σ_max) for a particular EK value. The critical threshold (σ_max) has been normalized such that if EK=0, then the critical threshold (σ_max)=1. Depending on a given EK value, a corresponding threshold value may be acquired graphically, e.g., using a graph of normalized values like that depicted in FIG. 12, and used to evaluate at least a portion of the tape.

According to various other approaches, the calculated threshold values may be stored in a lookup table, a database, calculated in real time, etc.

As the deviations of a given embodiment begin to stray away from the normal distribution of the data, this causes the value of EK to increase to larger positive numbers. As depicted in FIG. 12, as the EK values increase to larger positive numbers, σ_maxdecreases to compensate for the widening deviations, thereby maintaining a maximized tape capacity for the given embodiment, while also ensuring successful readback of the data written thereto.

Moreover, according to preferred approaches, incorporating calculated threshold values results in a more detailed understanding of the deviations may be achieved, thereby providing improved settings for writing to the tape. In a preferred approach, the threshold (e.g., σ_max) may be influenced by a raw or excess kurtosis value, thereby representing the standard deviation more closely, and improving the tape capacity by more efficiently applying stopwrites.

With continued reference to FIG. 10, operation 1010 includes comparing the standard deviation (e.g., σ_raw) or variance (e.g., σ_k²) to the threshold value (e.g., σ_max), as adjusted using the kurtosis in operation 1008.

Furthermore, method 1000 includes enabling writing when the standard deviation or variance does not exceed the threshold value (e.g., σ_max) as seen in operation 1012. According to a preferred approach, if the standard deviation or variance is less than the threshold, then the standard deviation or variance should have sufficiently small variation that it will later be able to be successfully read back.

Referring to operation 1014, method 1000 additionally includes determining a stopwrite threshold based on a standard deviation or a variance at a current position error signal sample when the standard deviation or variance exceeds the threshold value.

With continued reference to FIG. 10, operation 1016 includes determining whether the current position error signal sample exceeds the stopwrite threshold acquired in operation 1014. In the case that the current position error signal sample in fact exceeds the stopwrite threshold, operation 1018 of the method 1000 disables writing.

Similarly, referring back to operation 1016, if the current position error signal sample does not exceed the stopwrite threshold, then the method 1000 proceeds to operation 1012, thereby enabling writing as described above.

In a preferred approach, if writing is enabled or disabled during an interval, it is enabled or disabled only for the current interval. It is preferred that, at the start of each new interval, the logic may be run to determine if the writing should be enabled or disabled for that given interval. In various other approaches, if writing is enabled or disabled during an interval, it may remain enabled or disabled for at least one, at least two intervals, multiple, etc. intervals, regardless of the logic.

In a preferred approach, the method 1000 may be executed at regular or irregular intervals as the track is being written to. Moreover, the method 1000 may be executed at intervals of less than about 1 second, more preferably less than about 0.01 seconds, still more preferably less than about 1 millisecond, but could be shorter or longer based on the desired embodiment. According to one illustrative embodiment which is by no means meant to limit the scope of the invention, the aforementioned method may be executed at regular or irregular intervals of about 50 μs.

According to an illustrative approach, as mentioned above, a smoothing factor may be applied to a subsequent calculation of the standard deviation or variance. In one approach, the smoothing factor may be altered based at least in part on a current magnitude of the standard deviation or the variance.

In one approach, if the standard deviation or the variance at the current position error signal sample is below a specified value (e.g., σ_maxor a value selected using the same or similar techniques as selection of σ_max), the smoothing factor may preferably be altered to slow a change in the standard deviation or the variance in the subsequent calculations thereof from the presently calculated value. Refer to Equation 1, as described above.

Moreover, according to an exemplary embodiment determining the stopwrite threshold may include updating the standard deviation or the variance based on the current position error signal sample and/or the altered smoothing factor. Furthermore, in one approach, it may be determined whether the standard deviation or the variance exceeds a predetermined threshold. Moreover, the stopwrite threshold may be based on the standard deviation or the variance when the standard deviation or the variance exceeds the predetermined threshold according to an illustrative approach.

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as “logic,” a “circuit,” “module,” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a non-transitory computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the non-transitory computer readable storage medium include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a portable compact disc read-only memory (e.g., CD-ROM), a Blu-ray disc read-only memory (BD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a non-transitory computer readable storage medium may be any tangible medium that is capable of containing, or storing a program or application for use by or in connection with an instruction execution system, apparatus, or device.

A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a non-transitory computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device, such as an electrical connection having one or more wires, an optical fibre, etc.

Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fibre cable, RF, etc., or any suitable combination of the foregoing.

Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer, for example through the Internet using an Internet Service Provider (ISP).

Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of an embodiment of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

VARIABLE STOPWRITE THRESHOLD USING KURTOSIS

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