Industrial production rose by a healthy 0.6 percent last month, but the growth was well below the 1.4 per cent recorded in April and 1.2 per cent in March that reflected a rebound from the cold weather and the loss of output due to the coal strike.

The Federal Reserve Board reported that, except for a decline in automobile production, "Moderate increases occurred in the output of most other products."

The May produciton figures tend to confirm the predictions of most private and govenment analysts that, after a big surge of production in the second quarter, exconomic growth will level off in the last half of the year.

The Commerce Department's deputy chief economist, William Cox, said the May report represents the "more normal and sustainable rate of growth we had been anticipating."

In a related development, the Commerce Department reported that business inventories rose by $3.8 billion in April although they fell to a 27-year low as a pecentage of total business sales.

The declining ratio may reflect continued caution on the part of businessmen who do not want to be stuck with a large supply of goods in the event the economy slows down. But at the same time, the low level of stocks to sales could augur some increased production if consumer and business sales do not dip sharply.

The Commerce Department said that the ration of goods in inventory to sales fell from $142 to $100 in March to $140 to $100 in April. The ratio usually is above $150 and, when it gets very high, business often precipitously move to cut their stocks (mostly by reducing new orders), a move that triggered the major recession of 1974 and 1975.

The Federal Reserve Board said that more than half the increase in output from the nation's factories, mines and utilities was due to a rise in materials production.

"Large increases occurred in production of durable goods materials, such as steel and equipment parts, and in energy materials," the nation's central bank said.

Steel makers, who were operating at less than 80 percent of capacity in the first quarter of the year, have been producing at well over 90 percent in recent months. They cite continued strong demand from automobile manufacturers - who are producing cars at a healthy 9.4 million annual rate despite the May decline - and a recent increase in demand for business equipment and construction.

The Federal Reserve said that output of business equipment such as machines rose 0.6 percent in May after 1.0 percent advances in February and April and a whopping 2.1 percent rise in March.

If the economy is to keep expanding and providing new jobs, business investment spending must take over from consumer spending as the driving force. Business investment also modernizes production facilities to make them more efficient and expands the capacity of business to manufacture goods.

Both can moderate inflation - which has become the Carter administration's chief economic worry - by lowering costs of production or by helping to assure that there are no bottle-necks in supply.

The Fed said that total consumer goods output was unchanged, mainly because of the decline in automobile output. The Fed recorded increases in production of home goods such as appliances and furniture and of nondurable consumer goods such as food and clothing.

In a related development, the respected Wharton Forecast of the University of Pennsylvania's Wharton School said the economy will grow at an annual rate of 9.1 percent in the second quarter but slow in the summer and autumn, leaving the overall growth rate for the year between 4 and 4.5 percent.

Wharton forecast that the economy will grow about 4.3 percent in 1979 and 3.3 percent in 1980. The Wharton model also predicts that inflation will remain at a 7 percent rate through 1980.