BACKGROUND OF THE INVENTION 
     This invention relates generally to estimation of cumulative wear on large industrial electric motors, and, more particularly, to a method and apparatus for determining a cumulative wear measure. 
     It has become increasingly clear that monitoring of selected parameters is an essential component of reliability prediction and insurance. The lifetime of a large industrial electrical motor, for example, is influenced by many factors including operating and environmental conditions. In their article “Basics of multi-stress aging tests: survey of actual operating conditions of large industrial motors,” published in the Conference Record of the 1990 IEEE International Symposium on Electrical Insulation, pp. 4-7, P. Paloniemi and A. Ristola suggest that in addition to the motor operating temperature, which in itself will be somewhat dependent on ambient temperature, design service considerations for evaluating stresses on large industrial motors should include such items as: 
     The number of electrical starts per year 
     Switchgear, as it is associated with impulses that can adversely impact insulation 
     Relative humidity 
     Dirt 
     E. L. Brancato, in the article “Estimation of Lifetime Expectancies of Motors,” published in the IEEE Electrical Insulation Magazine, Vol. 8, No. 3, 1992, on pp. 5-13 advises concerning motor insulation that in most motors, temperatures may vary during their lifetime due to operating and non-operating conditions in the plant. In order to predict the lifetimes of insulation, the duration of operation at these temperatures must be estimated. Brancato also states that the electrical endurance qualities of insulation are affected by both temperature and time, noting that relatively moderate temperatures will cause failure if maintained for very long periods of time. 
     Brancato also relates some illuminating history respecting thermal effects on insulation pointing out that in 1930, Montsinger introduced the concept of the 10° rule, which states that the thermal life of insulation is halved for each increase of 10° C. in the exposure temperature, while in 1948, Dakin postulated that the rate of thermal aging of insulation was another way of stating that the rate of temperature-induced changes (deterioration) obeyed the Arrhenius chemical rate equation. Using this basic concept, Brancato points out that the life of insulation aged at elevated temperatures was expressed as:        L   =     B                   exp        [     ϕ   kT     ]                                
     where L is the life in units of time (min, hr, etc.), B a constant (usually determined experimentally), φ the activation energy (eV), T the absolute temperature (° K), and k=0.8617×10 −4  (eV/K) the Boltzmann constant. 
     Taking the logarithm of both sides of this equation,          ln                 L     =       ln                 B     +     ϕ   kT                              
     Thus, if the logarithm of the life of the insulation is plotted against the reciprocal of the absolute temperature, a straight line results. 
     There are numerous reports concerning industrial experiences such as that of A. Helwig in the article “History and development of non-intrusive electrical testing and assessment of DC traction motor armature condition and reliability during overhaul,” published in the Seventh International Conference on Electrical Machines and Drives, 1995, pp. 111-115. Helwig notes that Queensland Rail (QR) uses its motive rollingstock, employing DC traction motors, in a highly variable climate—from a Southern Queensland Highland location at just below 0° Celsius for part of the year, to normal high humidity operation during the summer months, and from dry temperate operation in the winter months to tropical monsoonal conditions. Ambient trackside air temperatures in the tropics and on the coast can be as high as 50° C. These climatic variations, both seasonal and extreme, stress insulation systems. 
     Many crucial parameters of interest can be identified through consideration of the physics of wear and failure. Monitoring wear and failure is expected to be key to reducing the variance of lifetime estimators, which in turn should lead to a concomitant decrease in underwriting Long Term Service Agreement contracts. There is accordingly a need to equip electromechanical equipment, such as a motor and its control electronics, with inseparable sensors and recorders so as to be able to better assess the motor condition and better predict the time to failure. There are three important desiderata: 
     Identifying most important factors for predicting failure. 
     Estimating the sensitivity of the above-identified factors from empirical studies and physics. 
     Archiving the data collection on-board with only a nominal amount of data storage. 
     BRIEF SUMMARY OF THE INVENTION 
     In accordance with a preferred embodiment of the invention, a statistical monitoring method and apparatus is employed to compute and store the history of a function of one or more monitored environmental variables that is useful for estimation, with suitable precision, of the time to failure of a particular electromechanical system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic illustration of an acceleration factor estimator using tailored quantizers, in accordance with a preferred embodiment of the invention. 
     FIG. 2 is a flowchart describing a preferred method for constructing the acceleration factor estimator using tailored quantizers of FIG.  1 . 
     FIG. 3 is a flowchart illustrating the function of the acceleration factor estimator using tailored quantizers of FIG.  1 . 
     FIG. 4 is an example of an acceleration factor estimator in accordance with FIG. 1, using two sensors with different numbers of quantization levels. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 illustrates a preferred embodiment 100 of the acceleration factor estimator using tailored quantizers composed of one or more sensors, such as sensors  110 - 1 ,  110 - 2 , . . . ,  110 -N, that generate continuous electrical output signals relating to the value of the environmental quantities or variables that they are measuring. These continuous output signals are sent to samplers, such as samplers  120 - 1 ,  120 - 2 , . . . ,  120 -N, that, under control of a clock,  160 , sample the continuous output signals at a sampling rate of S samples per second, or S samples-Hz. The samples are sent to respective quantizers, such as quantizers  130 - 1 ,  130 - 2 , . . . ,  130 -N, each quantizer having been designed such that the quantization error introduced into the acceleration factor estimator by the quantizer is approximately constant over the range of the measured variable. The output signals of the quantizers are combined in an address calculator  140  that performs a one-to-one mapping of the quantizer output signals to a memory unit address which is provided to a memory  150  which increments the content of the address calculator specified address by unity. 
     The invention produces a relatively small data set that may be used to produce an acceleration factor for more accurate failure prediction. The output signals of sensors appropriate to monitoring the most important failure environmental factors are sampled. Each sensor output signal is quantized with a respective quantizer specifically tailored to sensitivity of the individual sensor in the reliability acceleration factor. The quantized output signals constitute a product or Kronecker address and the content of a memory location corresponding to that address is incremented by unity. This technique satisfies the third of the three desiderata above, as is apparent if the sensors are considered to be sampled at a rate of S samples-Hz and sensor i  is considered to produce  B     i    bits per quantized sample. By using a memory that has        2       Σ   i          B   i                              
     memory locations, where each location has the capability of storing a W-bit word where W=┌log 2 (T·S)┐ and T is the maximum time in seconds between reading and resetting the memory, only          2       Σ   i          B   i         ·   W                          
     bits of storage are required as contrasted, say, with a “brute force” approach of storing the output signal of each sensor at each sampling instant, which would require a memory of        S   ·   T   ·       ∑   i          B   i                              
     bits. 
     It is expected that there will be long strings of the same Kronecker address, and in another embodiment a compression coding is applied to the sequence of Kronecker addresses. Suitable compression would be provided by a run-length encoding scheme that would create and store a histogram of run length encodings. Many run-length encoding schemes are known in the art, such as described, for example, in “Optimization of Facsimile Data Compression” by R. Ohnishi, Y. Ueno and F. Ono, published in the National Telecommunications Conference Record, 1977, pp. 49.1.1-49.1.6. As statistics are accumulated, it is expected that the appropriate encoding tables will be created so that the compressed storage technique can be finely tuned. 
     FIG. 2 illustrates the functioning of the acceleration factor estimator using tailored quantizers via an operational flowchart  200 . The key variables affecting accelerated time to failure are identified at the first step  210 . This may be done by experimentation on a particular system or by physical modeling. At the next step  220 , the form of the acceleration factor estimator involving the key variables identified in block  210  is determined. This step may also be accomplished by experimentation on a particular system or by physical modeling. At the next step  230 , the ranges of the key variables to be monitored are set. This is done by considering the environmental and operating extremes of the equipment to be monitored. At the next step  240 , the quantizers to be used to quantize the key variables are designed and tailored. This is accomplished by determining the resolutions and quantizer relationship required to represent the output signals of the individual sensors measuring the key variables over the ranges determined at step  230 . In a preferred mode for selecting the quantizer relationship, the quantization error introduced into the acceleration factor estimator by any quantizer is approximately constant over the range of the measured variable. The resolution of the individual quantizers may be chosen so that the number of possible individual addresses calculated by address calculator  140  of FIG. 1 is as close as possible to the size of memory  150 , without exceeding it. 
     FIG. 3 is a flowchart  300  recounting the ordered functions of the acceleration factor estimator using tailored quantizers. Step  310  is the initialization step where all memory locations are set to zero. At step  320 , a decision is made in accordance with whether or not a sampling command is present from clock  160 . At step  330 , all of the sensors are sampled and, at step  340 , all of the samples from the sensors are quantized, each quantization being made according to the quantizer designed and tailored for its associated sensor over the monitoring range of that sensor. 
     At step  350 , the Kronecker address is computed. This address is a one-to-one mapping of the quantizer output signals to a memory address which is provided to the memory  150  (FIG.  1 ). The next step  360  involves unit incrementation of the content of the memory location specified by the Kronecker address. A preferred mode of generating the Kronecker address is to concatenate the output signals of the individual sensors to form a binary address. 
     As an example, consider the instant method and apparatus used in monitoring for reliability prediction of plastic-encapsulated-microcircuit (PEM) devices. The governing model of choice is the Department of Defense Reliability Analysis Center PEM model as described by Y-L. Mok and L-M. Ten in “A Review of Plastic-Encapsulated-Microcircuit Reliability-Prediction Models,” published in the proceedings of the Annual Reliability and Maintainability Symposium, 2000, on pages 200-209. This model uses Peck&#39;s empirical model that includes a temperature and relative humidity acceleration factor. This factor is a product of terms involving the cube of the effective relative humidity (RH), (cons tan t·RH) 3 , and an Arrhenius-like term containing e −costant t-activation energy  where the constant includes a function of the non-operating ambient temperature. 
     With two sensors, one monitoring the activation energy, which is assumed to be directly proportional to temperature, and the other sensor monitoring relative humidity, two bits are assumed allocated to the temperature quantizer and one bit to the relative humidity quantizer. Thus, for the example,  B     1     =2  and  B     2     =1 . For clarity of this example, the acceleration factor estimator,  {circumflex over (F)}     A   , is assumed to be described by the formula  {circumflex over (F)}     A     =(RH)     3     ·e     −T/100   , where  RH  is the relative humidity and the operational ranges are determined to be  0%≦RH≦90%  and  0° F.≦T≦200° F . Allowing two bits for the temperature quantization, they can be allocated as follows: 
     
       
         
               
               
               
             
           
               
                   
                   
               
               
                   
                  Temperature Range 
                 Temperature Quantizer 
               
               
                   
                 (degrees F.) 
                 Output Signal 
               
               
                   
                   
               
             
             
               
                   
                   0-29 
                 00 
               
               
                   
                 29-69 
                 01 
               
               
                   
                  69-139 
                 10 
               
               
                   
                 139-200 
                 11 
               
               
                   
                   
               
             
          
         
       
     
     One bit allowed for the relative humidity range can be allocated as follows: 
     
       
         
               
               
               
             
           
               
                   
                   
               
               
                   
                  Relative Humidity 
                 Rel. Humidity Quantizer 
               
               
                   
                 (%) 
                 Output Signal 
               
               
                   
                   
               
             
             
               
                   
                   0-71 
                 0 
               
               
                   
                 71-90 
                 1 
               
               
                   
                   
               
             
          
         
       
     
     The three-bit Kronecker address is formed by concatenating the relative humidity quantizer output signal to the temperature quantizer output signal. The memory required must thus have 2 3 =8 locations. From initialization to initialization (step  310  of FIG. 3) it is assumed that there is a maximum of a year&#39;s worth of sampling at a sampling rate of one sample per second. This is approximately 30 million samples and thus the memory words must be at least 25 bits long. 
     FIG. 4 depicts the functioning of the acceleration factor estimator using tailored quantizers for 4 samples according to the example. If the 8-locations of the example memory are assigned by the following correspondence to the Kronecker address bits: 
     memory location=4*first bit+2*second bit+third bit, 
     then the contents of the memory locations change as follows: 
     
       
         
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                  Content of Memory Location 
               
             
          
           
               
                  Sampling Time 
                  0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                  0 
                  0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 2 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
               
               
                 3 
                 1 
                 0 
                 0 
                 0 
                 2 
                 0 
                 0 
                 0 
               
               
                 4 
                 1 
                 0 
                 0 
                 0 
                 2 
                 0 
                 0 
                 1 
               
               
                   
               
             
          
         
       
     
     While only certain preferred features of the invention have been illustrated and described, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.
An apparatus for estimating the time to failure acceleration factor of a large industrial motor includes a sensor, a clock for controlling sensor sampling times, and a memory address calculator for mapping output signals of the sensor to a memory address. A unit is provided for incrementing the content of a specified memory address by unity.